THERMAL SPECIFIC BIO-IMAGING AND THERAPY …bmoptics/docs/Iddo Final Version.pdf · The Iby and Aladar Fleischman Faculty of Engineering ... Iddo Michael Gescheit ... • A special

TEL AVIV UNIVERSITY The Iby and Aladar Fleischman Faculty of Engineering

The Zandman-Slaner School of Graduate Studies

THERMAL SPECIFIC BIO-IMAGING AND THERAPY

TECHNIQUE FOR DIAGNOSTIC AND TREATMENT OF

MALIGNANT TUMORS BY USING MAGNETIC

NANOPARTICLES

A thesis submitted toward the degree of

Master of Science in Biomedical Engineering

by

Iddo Michael Gescheit

October 2007

TEL AVIV UNIVERSITY The Iby and Aladar Fleischman Faculty of Engineering

The Zandman-Slaner School of Graduate Studies

THERMAL SPECIFIC BIO-IMAGING AND THERAPY

TECHNIQUE FOR DIAGNOSTIC AND TREATMENT OF

MALIGNANT TUMORS BY USING MAGNETIC

NANOPARTICLES

A thesis submitted toward the degree of

Master of Science in Biomedical Engineering

by

Iddo Michael Gescheit

This research was carried out in the Department of Biomedical Engineering under the supervision of Dr. Israel Gannot and Dr. Avraham Dayan

October 2007

i

To:

My parents Dorrit and Yehuda, who has always been there for me

My brothers Illai and Jonathan, who inspired me to complete this work

ii

Acknowledgments

I would like to take this opportunity to thank the people who helped me bring this work to

completion:

• My advisor Dr. Israel Gannot, who has been an advisor, a collaborator and a friend,

and has guided me through this work process while expanding my academic horizons

by exposing me to new areas in the bio-medical science.

• My advisor Dr. Avraham Dayan, who has guided me and supported me through all

thermal aspects of my work.

• A special thanks to Dr. Moshe Ben-David for spending countless hours talking to me

about this work and assisting in finalizing it.

• The staff at the Power Electronics Laboratory of the Electrical Engineering

Department Itai, Shelly, Bshara and especially Dr. Dror Medini for helping me with

the design and building of the electrical system.

• My dear friend Tomer Eruv, who has been there for me every day, supporting and

advising throughout this whole research process.

• Lastly, I would like to thank my family from the bottom of my heart, for their support

and caring: my mom Dorrit, my dad Yehuda, my dearest brothers Illai and Jonathan,

and Orti.

iii

Abstract

The objective of this research program is to develop a novel, non-invasive, low cost infrared

(8-12 μm spectral range) imaging technique that would improve upon current methods using

nanostructured core/shell magnetic/noble metal based imaging and therapies.

The biocompatible magnetic nanoparticles are able to produce heat under AC magnetic field.

This thermal radiation propagates along the tissue by thermal conduction reaching medium's

(tissue's) surface. The surface temperature distribution is acquired by a thermal camera and

could be analyzed to retrieve and reconstruct nanoparticles' temperature and location within

the tissue.

The aforementioned technique may function as a diagnostic tool thanks to the ability of

specific bio-conjugation of these nanoparticles to a tumor's outer surface.

Hence, by applying a magnetic field we could cause an elevation of temperature of the

selective targeted nanoparticles up to 5°C, which allows us the imaging of the tumor.

Furthermore, elevating the temperature over 65°C and up to 100°C stimulates a thermo-

ablating interaction which causes a localized irreversible damage to the cancerous site without

harming the surrounding tissue. While functioning as a diagnostic tool, this procedure may

serve as a targeted therapeutic tool under thermal feedback control as well.

iv

Contents

Acknowledgement………………………………………………………………….….i

Abstract…………………………………………………………………………….….ii

Contents……………………………………………………………………………….iii

List of Figures………………………………………………………………………....vi

List of Tables……………………………………………………………………….....ix

1 Introduction………………………………………………….…………………….….1

A. Cancer……………………………………………………………………….…1

B. Motivation………………………………………………………………..….…5

C. Cancer Imaging…………………………………………………………….…..7

1. Imaging for Cancer Diagnosis………………………………...………7

2. Current Imaging Methods…………………………………….....…….8

3. Trends in Cancer Imaging……………………………………………..9

4. The Role of Imaging…………………………………………………11

5. Thermal Imaging……………………………………………………..15

6. Treatment………………………………………………………...…..19

D. The Vision………………………………………………………………….…23

E. Bioconjugation……………………………………………………………..…26

F. References………………………………………………………………….…29

2 Heat Generation……………………………………………………………………..34

A. Introduction……………… …………………………………………………..34

B. Applications of Magnetic Nanoparticles…………………………………..….36

C. Objectives…………………………………………………………………..…38

D. Heating Mechanisms……………………………………………………….…38

v

E. Affecting Parameters……………………………………………………….…42

1. Field Parameters……………………………………………...………42

2. Material Properties……………………………………………….…..42

3. Size Dependence……………………………………………….…….45

4. Miscellaneous……………………………………………………..….48

F. References…………………………………………………………………….49

3 Thermal Analysis……………………………………………………………………52

A. Introduction…………………………………………………………………...52

B. Image Processing Approaches to IR Images………………………………….53

C. The Problem………………………………………………………………..…56

D. Method of Solution…………………………………………………………...58

1. Forward Problem and Analytical Solution…………………………...58

2. Pennes Equation…………………………………………………..….58

3. Heat Conduction Equation……………………………………...……60

E. Point Simulation……………………………………………………………....63

1. Forward Solution………………………...…………………………...63

2. Inverse Solution………………………………………………...……66

F. Spherical Simulation……………………………………………………….....74

G. References…………………………………………………………………….85

4 System Design………………………………………………………………………..88

A. Introduction………………………………………………………………...…88

B. Heat Generation……………………………………………………………....89

C. Antenna Configurations……………………………………………………....91

1. Solenoid…………………………………………………………...…91

2. C-Core………………………………………………………………..92

vi

3. Helmholtz Coil……………………………………………………….94

D. Current Generation…………………………………………………...……….96

E. Thermal Image Acquisition…………………………………………………..99

F. The Integrated System……………………………………………………..…99

G. References…………………………………………………………………...102

5 Conclusions and Future Work………………………………………………….....103

A. Conclusions……………………………………………….…………………103

B. Future Work………………………………………………………………....105

vii

List of Figures

Figure 1.1: Estimated number of new cancer cases for 2006, excluding basal and squamous

cell skin cancers and in situ carcinomas except urinary bladder. Note: State estimates are

offered as a rough guide and should be interpreted with caution. They are calculated

according to the distribution of estimated cancer deaths in 2006 by state. State estimates may

not add to US total due to rounding……………………………………………………..……..3

Figure 1.2.A: The electromagnetic spectrum and the IR region……………………......……17

Figure 1.2.B: Blackbody radiation curves showing peak wavelengths at various

temperatures…………………………………………………………………………..………17

Figure 1.3: Schematic description of the system employing a targeted imaging technique and

a closed-loop system for therapy under real-time

feedback…………………………………....25

Figure 1.4: Bioconjugation of magnetic nanopatricles by using the natural immune

system……………………………………………………………………………………..….26

Figure 1.5: Magnetic nanoparticles schematic siting along the tumor surface………………27

Figure 1.6: Histological staining: 5-day old tumor with CD-3 at magnitude ×200. A colume

layer where binding was detected can be seen on the left…………………………………....28

Figure 2.1: Relative sizes of cells and their components…………………………………….37

Figure 2.2: Relaxational losses leading to heating in an alternating magnetic field (H)…….38

Figure 2.3: Schematic illustration of the energy of a single-domain particle with uniaxial

anisotropy as a function of magnetization direction……………………………………….....40

viii

Figure 2.4: Crystal structure of Fe3O4 . Big balls denote oxygen atoms, small dark balls

denote A-site (tetrahedral) iron atoms, and small light balls denote B-site (octahedral) iron

atoms…………………………………………………………...……………………………..43

Figure 2.5.A: Fe Nanoparticles produced by Nanosonics Inc. Magnetic nanoparticles in

different particle size configured as powder………………………………………………….45

Figure 2.5.B: Fe Nanoparticles produced by Nanosonics Inc. Schematic illustration of a

single Fe-Au nanoparticles…………………………………………………………………....45

Figure 2.6: Dependence of magnetic loss power density on particle size for magnetite fine

particle (2MHz, 6. 5 kA/m)………………………………………………………………...…47

Figure 2.7: Grain size dependence of the loss power density due to Néel-relaxation for

small ellipsoidal particles of magnetite (6. 5 kA/m)………………………………………….48

Figure 3.1: The thermal problem description………………………………………..………57

Figure 3.2: Schematic description og the heat conduction problem………………………...61

Figure 3.3: Non-dimensional surface temperature over an embedded point heat source……64

Figure 3.4.A: MATLAB® simulation results: surface temperature T(0, r, Q) for various point

heat sources……………………………………………………………………………..…….65

Figure 3.4.B: Draper and Boag’s results: surface temperature T(0, r, Q) for various point heat

sources………………………………………………………………………………...………65

Figure 0.5: Surface temperature cross sectional distribution………………………….…….66

Figure 03.6: FWHM as a function of varying power (Q) for different depths

(a)…………………....68

Figure 3.7: FWHM as a function of depth for various tissues…………………………….....69

Figure 3.8: Computing source depth for a specific tissue…………………………………....70

Figure 3.9: Area below the surface temperature profile (A) as a function of the source power

(Q)……………………………………………………………………………………….……71

ix

Figure 3.10: Area (A) as a function of power (Q) for various source depths…………...……72

Figure 3.11: Exponential behavior of A(Q) slopes…………………………………………..72

Figure 3.12: Selected A(Q) curve based on the p-parameter……………………………..….73

Figure 3.13: Spherical model for thermal analysis of a tumor……………………..………..75

Figure 3.14: Spherical coordination system………………………………………………….76

Figure 3.15: Nanoparticles superficial distribution on the sphere……………………..…….76

Figure 3.16: Comparison of a point source and spherical source (R=0.01 cm). The curve of

spherical source is deliberately elevated by 1˚C in order to distinguish the two curves…..…78

Figure 3.17: Problem modeling in bispherical coordinate system………………………..….79

Figure 3.18: Validation of an auxiliary MATLAB® code simulating Small and Weihs

solution…………………………………………………………………………………….….81

Figure 3.19: Effective spherical model………………………………………………………83

Figure 3.20: Comparison of Small and Weihs solution with the spherical simulation……....83

Figure 4.1: Schematic description of the system………………………………………….....89

Figure 4.2: Schematic description of a C-core configuration………………………………..92

Figure 4.3: Schematic description of Helmholtz coils configuration………………..………95

Figure 4.4: Wave templates generated by the system…………………………………….….97

Figure 4.5: System's block scheme……………………………………………………..……98

Figure 4.6: The power generator's block scheme……………………………………….……98

Figure 4.7: Schematic description of the closed-loop system……………………………....100

Figure 4.8: Laboratory system………………………………………………………...……101

x

List of Tables

Table 1.1: Estimated new cancer cases and deaths by sex for all sites, US, 2006………….…4

Table 2.1: SAR values of samples in the applied magnetic field (80 kHz, 32.5 kA/m) and

coercivity Hc of samples………………………………………………………………...……46

Table 3.1: Point heat sources in various depths a and strength Q……………………………64

Table 3.2: Given parameters for illustrative problem………………………………………..67

Table 3.3: Comparison of real parameters and estimated parameters………………………..73

Chapter 1 Introduction

1–1

1. Introduction

1.A. Cancer

Cancer is a class of diseases or disorders characterized by uncontrolled division of cells and

the ability of these cells to spread, either by direct growth into adjacent tissue through

invasion, or by implantation into distant sites by metastasis. Transportation of cancerous cells

to distant sites is done through the bloodstream or lymphatic system. Cancer may affect

people at all ages, but risk tends to increase with age. It is one of the principal causes of death

in developed countries.

Cancer may attack any organ, e.g. liver, lung, breast etc. while the severity of disease depends

on various parameters such as the site and character of the malignancy and the

presence/absence of metastasis. Despite of the fact that modern medicine and medical

research and technology made significant progress on the last decades, still a definitive cancer

diagnosis usually requires the histologic examination of tissue by a pathologist. This tissue is

obtained by an invasive procedure as biopsy or surgery. Most cancer types can be treated and

some cured, depending on the specific type, location, and stage.

Once diagnosed, cancer treatment usually involves a combination of surgery, chemotherapy

and radiotherapy. In cases of late detection or no treatment, cancers may eventually cause

illness and death, though this is not always the case.


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The unregulated growth that characterizes cancer is caused by damage to DNA, resulting in

mutations to genes that encode for proteins controlling cell division. These mutations can be

caused by radiation, chemicals or physical agents that cause cancer, which are called

carcinogens, or by certain viruses that can insert their DNA into the human genome. As

known in the art, many forms of cancer are associated with exposure to environmental factors

such as tobacco smoke, radiation, alcohol, and certain viruses.

In order to understand the severity and prevalence of cancer, American Cancer Society

expected about 1, 399,790 new cancer cases to be diagnosed in 2006. This estimate does not

include carcinoma in situ (noninvasive cancer) or any site except urinary bladder, and does

not include basal and squamous cell skin cancer. More than 1 million cases of basal and

squamous cell skin cancers were expected to be diagnosed in 2006 (Figure 1.1).

In the same year, about 564,830 Americans were expected to die of cancer, more than 1,500

people a day. Cancer is the second most common cause of death in the US, exceeded only by

heart disease. In the US, cancer accounts for 1 of every 4 deaths. The National Institute of

Health (NIH) estimate overall costs for cancer in 2005 at $209.9 billion [1, 2]. A summary of

estimated new cancer cases and deaths for the US is shown in


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Figure 1.1 Estimated number of new cancer cases for 2006, excluding basal and squamous cell skin cancers

and in situ carcinomas except urinary bladder. Note: State estimates are offered as a rough guide

and should be interpreted with caution. They are calculated according to the distribution of

estimated cancer deaths in 2006 by state. State estimates may not add to US total due to rounding [3]


1–4

Table 1.1 Estimated new cancer cases and deaths by sex for all sites, US, 2006*

Estimated New Cases Estimated Deaths

Both

Sexes Male Female

Both

Sexes Male Female

All sites 1,399,790 720,280 679,510 564,830 291,270 273,560

Oral cavity & pharynx 30,990 20,280 10,810 7,430 5,050 2,380

Digestive system 263,060 137,630 125,430 136,180 75,210 60,970

Respiratory system 186,370 101,900 84,470 167,050 93,820 73,230

Bones & joints 2,760 1,500 1,260 1,260 730 530

Soft tissue (including heart) 9,530 5,720 3,810 3,500 1,830 1,670

Skin (excluding basal & squamous) 68,780 38,360 30,420 10,710 6,990 3,720

Breast 214,640 1,720 212,920 41,430 460 40,970

Genital system 321,490 244,240 77,250 56,060 28,000 28,060

Unary system 102,740 70,940 31,800 26,670 17,530 9,140

Eye & orbit 2,360 1,230 1,130 230 110 120

Brain & other nervous system 18,820 10,730 8,090 12,820 7,260 5,560

Endocrine system 32,260 8,690 23,570 2,290 1,020 1,270

Lymphoma 66,670 34,870 31,800 20,330 10,770 9,560

Multiple myeloma 16,570 9,250 7,320 11,310 5,680 5,630

Leukemia 35,070 20,000 15,070 22,280 12,470 9,810

Other & unspecified

primary sites† 27,680 13,320 14,360 45,280 24,340 20,940

*Rounded to the nearest 10; estimated new cases exclude basal and squamous cell skin and in situ carcinoma except urinary

bladder. About 61,980 carcinoma in situ of the breast and 49,710 melanoma in situ were expected to be diagnosed in 2006. †More

deaths than cases suggest lack of specificity in recording underlying causes of death on death certificates. Source: Estimates of new

cases are based on incidence rates from 1979 to 2002, National Cancer Institute's Surveillance, Epidemiology, and End Results

program, nine oldest registries. Estimates of deaths are based on data from US Mortality Public Use Data Types, 1969 to 2003,

National Center for Health Statistics, Centers for Disease Control and Prevention, 2006

©2006, American Cancer Society, Inc., Surveillance Research


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Cancer can also occur solely in young children and adolescents.

The age of peak incidence of cancer in children occurs during the first year of life. Leukemia

(usually ALL) is the most common infant malignancy (30%), followed by the central nervous

system cancers and neuroblastoma. The remainder consists of Wilms' tumor, lymphomas,

rhabdomyosarcoma (arising from muscle), retinoblastoma, osteosarcoma and Ewing's

sarcoma [4]. Female and male infants have essentially the same overall cancer incidence rates,

but white infants have substantially higher cancer rates than black infants for most cancer

types.

1.B. Motivation

As known, cancer is a very prevalence disease with no satisfying cure and/or treatment. A

disease in which many resources are invested involving various research fields such as

biology, chemistry, engineering, medicine and behavioral science.

This research amongst others is motivated by several main statistics described as follows:

Diagnosis [5]

Small primary tumors go undetected. For many cancers, an internal, aggressive, noncalcified

tumor under containing fewer than 500,000 cells (i.e., under 2mm wide) is likely to pass

undetected through most body-region scans, including CT, MRI, ultrasound, radionuclide,

and metabolic PET. At this size, a tumor has effectively undergone 19 cell doublings about

halfway through doubling toward a predicted lethal load of 1010–1012 cells and is likely to be

sufficiently repleted with gene defects so that it will undergo continued and uninterrupted

growth if not treated.


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Staging

Metastatic disease underdiagnosed. For the reasons stated above, patients with negative scans

for metastases at initial presentation routinely go on to develop, and die from, metastatic

cancer. For example, about 20% of women with breast cancer clinically confined to the breast

and lymph nodes (low and intermediate risk), and the majority of men with local margin-

positivity after prostatectomy, will go on to have a recurrence of their disease, despite initially

negative bone and body imaging scans. Even though it did not appear in the image,

undetected residual and/or metastatic cancer must have been present at the time of the initial

scanning.

Margins

Residual disease common after surgery. After surgical resection, 30% or more of patients

with breast or prostate cancer have residual disease in the surgical field [6, 7], undetected by

even realtime surgical imaging, but yet which will be found on gross and histochemical

pathology in the days or weeks after the surgery has been completed, and the patient has been

closed and sent home. Cancer recurrence rates are 2.5× higher in multivariate analysis if the

margins are positive [8, 9] and these patients are significantly more likely to die of their

disease.

Therapy

Treatment response is poorly measured. ‘Measurable disease,’ a common yardstick for

monitoring response to treatment, is absent after surgical excision of many tumors. Therefore,

the standard of care is to blindly treat with chemotherapy selected by convention using prior

retrospective studies, and to consider this treatment a success or failure only in retrospect (i.e.,

success is when a patient survives 5 years, and failure is when a relapse occurs).


1–7

1.C. Cancer Imaging

1.C.1. Imaging for Cancer Diagnosis

Most cancers are initially recognized either because signs or symptoms appear or through

screening. Neither of these lead to a definitive diagnosis, which usually requires the opinion

of a pathologist. Roughly, cancer symptoms can be divided into three groups:

(i) Local symptoms: unusual lumps or swelling (tumor), hemorrhage (bleeding), pain and/or

ulceration. Compression of surrounding tissues may cause symptoms such as jaundice.

(ii) Symptoms of metastasis (spreading): enlarged lymph nodes, cough and hemoptysis,

hepatomegaly (enlarged liver), bone pain, fracture of affected bones and neurological

symptoms. Although advanced cancer may cause pain, it is often not the first symptom.

(iii) Systemic symptoms: weight loss, poor appetite and cachexia (wasting), excessive

sweating (night sweats), anemia and specific paraneoplastic phenomena, i.e. specific

conditions that are due to an active cancer, such as thrombosis or hormonal changes.

A cancer may be suspected for a variety of reasons, but the definitive diagnosis of most

malignancies must be confirmed by histological examination of the cancerous cells by a

pathologist. Tissue can be obtained from a biopsy or surgery. Many biopsies (such as those of

the skin, breast or liver) can be done in a doctor's office. Biopsies of other organs are

performed under anesthesia and require surgery in an operating room.

The tissue diagnosis indicates the type of cell that is proliferating, its histological grade and

other features of the tumor. Together, this information is useful to evaluate the prognosis of

this patient and choose the best treatment.


1–8

Cytogenetics and immunohistochemistry may provide information about future behavior of

the cancer (prognosis) and best treatment, however it should be appreciated that these aspects

of cancer and others such as cell biology, cancer origin, epidemiology etc are not on the scope

of this research [5].

1.C.2. Current Imaging Methods [5]

Although significant progress has been achieved in known and conventional radiologic

modalities since the first X-rays, still typical images relies on bulk characterization of the

tissue. The resulting anatomic signal is therefore epiphenomenal, being merely an expression

of the sum of nonspecific interactions of the imaging source with the tissues structure,

physiology and/or pathology. Thus, the the visualization and characterization of tumor by

conventional modalities such as CT, MRI, or ultrasound is merely dependent in distinction of

tumor from the surrounding tissue and inherent background noise, e.g. the ability of that

tumor to differentially scatter, absorb, or emit radiation in comparison to the surrounding

tissue. One of the main drawbaks of conventional modalities is the little specificity and

sensitivity for the detection of tumor, which stems in the ability to acquire data which is at

least in part, a function of cell density, microcalcifications, and the like - effects that are not a

significant signature of cancerous tissue.

Equally important, while the lethality of many solid tumors is due to the physical crowding or

bulk effects of the tumor, the majority of diagnosis, treatment selection, treatment

monitoring, and follow-up, involves decisions in which the physical, bulk characteristics of

the tumor are, not the driving question. Rather, the questions that require answers are those of

tumor presence vs. absence, of type and grade and distribution, and of gene expression, cell

function, and receptor positivity.


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As a result, oncology in particular has gone looking for methods that dovetail with the

emphasis in medicine: gene-specific or receptor-specific therapies, minimally invasive

treatments for early-diagnosed tumors, stage-specific treatment options.

1.C.3. Trends in Cancer Imaging [5]

Recent tumor imaging has been trying to neglect nonspecific imaging, and to adopt specific

imaging employing patient-specific, disease-specific, and cell-specific. Driving this change

are four trends.

Patient-specific medicine

The trend in oncology, as in medicine in general, is away from nonspecific diagnosis and

treatment, and toward patient-specific therapy. As cell receptor status and gene expression

become used with increasing frequency to manage the oncology patient, the diagnosis and

treatment for cancer becomes dependent on identifying the molecular and genetic makeup of

the tumor (for breast cancer, this is currently a palate of PR, ER, Her2-neu positivity, and

perhaps a mitotic rate assay such as Ki-66, or others, depending upon institution), rather than

upon the anatomic and pathologic grade of the tumor.

Specific markers

New markers are becoming available at a dizzying pace as a result of biochemical advances

and the genome project [10, 11]. Gene chips and other tools are allowing such markers to

begin to be correlated with clinical stage, tumor aggressiveness, outcome, and response to

treatment, while drug discovery seeks to use these identified markers as specific targets for

new pharmaceutical agents. From an imaging point of view, such markers are important as the


1–10

anatomic, or bulk effects, of tumors are absent at the early or minimal residual disease stages

of cancer, while genetic disturbances and receptor abnormalities remain present in small

tumor populations, and can be tumor-specific, stagespecific, and response-specific

(refer section 1.E).

Novel sensors

New sensors have allowed for new types of scanners, such as portable optical imagers for

visible and near-infrared photon detection. Examples of such new sensors include activatable

contrast agents and genetic expression elements which can be used to produce or amplify

local contrast in imaging studies. Advances in computing power, which has continued to

double the power every 18 months without increases in cost, make increasingly complex

calculation- and graphicsheavy imaging software routine, and possible in real-time or near-

real-time.

Less-invasive medicine

Last, the trend in medicine for the past 20 years has been toward reduced invasiveness. More

sensitive imaging allows diagnosis and therapy to be physically targeted to the tumor, as well

as allows less invasive monitoring of therapeutic response. Local, regionally limited surgical

procedures (such as lumpectomy, local ablation, endoscopic approaches) now permit con-

fined islands of disease, if located, to be treated quickly and effectively.


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1.C.4. The Role of Imaging [5]

Imaging will become less of a tool for initial gross staging. Instead, it will become more

frequent and integrate more effectively and seamlessly with patient management at all stages

of oncology diagnosis, treatment, and followup. Sensitive and specific imaging will allow for

a more proactive role for imaging in the following areas.

Diagnosis

At diagnosis, imaging will yield more sensitive detection of cancer, including optimally

imaging such features as receptor status, gene expression, and tumor grade now obtained only

through biopsy and analysis by pathology microscopy, immunohistochemistry, and PCR (i.e.

Polymerase Chain Reaction). The lower limit for tumor detection is improving. For example,

while the lower limit of tumor detection in human subjects is currently about 500,000 cells

(2–3mm diameter tumor), optical methods have moved the lower limit of tumor detection in

animal models down to fewer than 1,000 cells, noninvasively and specifically imaged [12].

The ability to image receptor status in vivo has been demonstrated using antigenically

targeted probes, such as those targeted to somatostatin [13]. More specific scans will also play

a role in avoiding invasive evaluations. The majority of all biopsies are negative, therefore a

reduction in invasive evaluations will be a benefit of more specific scans [14]. Despite such

improvements, there will always be some degree of a lag between the identification of new

markers via molecular biology and the ability to image those markers, and thus there will

likely continue to be a need for tissue samples to allow for testing of the latest markers for

optimal selection of therapy, as well as for banking of tissue, to allow for testing of future

markers when these become available.


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Staging

Staging will become more accurate, thus profoundly influencing patient segmentation and

treatment selection. Surgical staging procedures, such as nodal biopsy, may be able to be

reduced using imaging (or perhaps replaced entirely if tissue for pathology has already been

obtained), with imaging follow-up used to ensure accuracy of a negative scan. One step

toward this scenario – limiting the size of lymphatic staging by better imaging of the

sentinelnodes – has been achieved using radioemitter-based colloid imaging for melanoma

and breast, and this has led to a decrease in the physical extent of the surgical procedure, and

to reduced morbidity and a minimal loss of diagnostic accuracy (though with an unknown

effect of long-term outcome [15]). The next step is replacing the nonspecific radioemitter with

a specific and highly sensitive marker or reporter for tumor in the nodes. For breast cancer, if

this can be achieved, then only tumor-positive nodes would be therapeutically removed (and

sent to pathology), while the majority of women would be able to forego the therapeutic nodal

biopsy altogether.

Further, the detection of mediastinal (as opposed to axillary) nodes would be improved,

perhaps leading to elective removal of those mediastinal nodes using a minimally invasive

parasternal procedure.

Therapeutic monitoring and feedback

Early, course-correcting treatment feedback will become standard-of-care for many therapies,

especially when good alternative therapies exist. Rather than perform a bone scan months

down the road after treatment is initiated, tumor response will be evaluated with scans during

the first treatment doses. For example, MR spectroscopic imaging (MRSI) and/or PET

imaging before and after treatment to look for changes in cell metabolism consistent with a


1–13

response has already been studied as a potential method to identify responders from non-

responders months before current methods can do so [16-19].

Sequential scans may also be able to identify the emergence of resistance during ongoing

treatment, such that the treatment may be changed before the patient presents with clinical

signs of treatment failure.

Optical imaging has detected emergence of resistance in animal models of disease within days

to weeks [12], while MRI and PET have been used to image apoptosis in animals [20], and in

some instances in humans [21]. Another aspect of therapeutic monitoring is the

measurement of chemotherapy levels in the patient’s tissues, or in the tumor itself, using

noninvasive or minimally-invasive imaging techniques [22-26]. This would allow for patient-

specific dosing, based upon the actual tumor or tissue levels in a given patient, rather than

blindly based upon body surface area or weight. Using such approaches, gene therapies can be

immediately evaluated for efficacy of gene expression, and followed on an ongoing basis for

continued expression and/or tumor effect.

Similarly, cell trafficking may be followed, again as markers of anti-tumor activity or to help

assess clinical response. Such early and ongoing treatment response feedback likely to be

cost effective. While the cost effectiveness of oncologic screening tests has been hotly

debated, such as with routine mammography [27-29], a patient under treatment can

immediately balance the imaging costs against the cost of the therapy. Newer chemotherapy

agents are significantly more expensive than the older agents; therefore an early feedback

scan to measure treatment effect would prevent further use of an expensive agent that would

otherwise ultimately be without effect. Under this view, such treatment response imaging

scans may become a required part of care. Further, the patient can then rapidly be switched to


1–14

another, and hopefully more active chemotherapeutic agent, which is likely to have a positive

impact on overall response rates, survival time, and cost of care.

Image guidance

Image guided therapies will expand as the sensitivity of images to small regions of disease

increases. Benaron's group has been developing real-time tumor imaging systems sensitive to

the antigenic presence of residual tumor in the surgical field. Preliminary data [12] suggest

that such scans may lower the detectability limit of disease to 100µm islands. Such a tool,

deployed in the operating room, directly impacts the 30% of breast and prostate cancer

patients with residual disease in the surgical field after treatment, and could potentially allow

for reduction or even elimination of the presence of positive-margins, indicating residual

tumor, after surgical resection. Researchers have also been developing real-time sensors

embedded into the surgical tools themselves, to give feedback during the surgical process

[30]. Both of these approaches could lead to more effective treatment, and as well as enabling

more minimally invasive treatment procedures.

Follow-up

Many cancer patients are at high risk for relapse. While there are again economic issues that

have been used to argue for the limitation of access to follow-up imaging techniques, such

imaging is already standard for some cancers (such as lymphoma). Increases in the sensitivity

of follow-up scans will likely increase the benefit and applicability of such scans. For

example, six months after node-negative scans in the breast cancer patient who avoided a

nodal dissection due to negative initial, a repeat scan may be indicated to catch those patients

with early disease too small to be detected on the first pass.


1–15

Drug discovery

Imaging is playing an increasing role in the discovery and development of new agents, both

in humans and animals. The same imaging agents that can be used for imaging targets in

humans can be used during drug discovery and development for use in imaging animals.

Thus, better animal imaging permits for better and more rapid drug discovery, as well as for

better basic research [31]. Specific systems for imaging animals have been made available for

micro (small animal) CT [32, 33], PET [34, 35], MRI, and green fluorescent protein (GFP)

imaging. In addition to these imaging systems, designer animals, with desired combinations

of knockout target genes and add-in reporter genes, are playing an increasing role in the drug

discovery process. Animals with reporter genes tied to specific imaging modalities are already

being created.

1.C.5. Thermal imaging

The first documented application of Infrared (IR) imaging in medicine was in 1956 [36],

when breast cancer patients were examined for asymmetric hot spots and vascularity in IR

images of the breasts. Since then, numerous research findings have been published [37], [38],

[39] and the 1960s witnessed the first surge of medical application of the IR technology [40],

[41], with breast cancer detection as the primary practice. However, IR imaging has not been

widely recognized in medicine nowadays, largely due to the premature use of the technology,

the superficial understanding of IR images, and its poorly controlled introduction into breast

cancer detection in the 70s [42].


1–16

Recently, advances in a couple of related areas have pushed forward series of activities to

reappraise the role of IR imaging in medicine [42-48].

These advances, including the development of the new-generation infrared technology, smart

image processing algorithms, and the pathophysiological-based understanding of IR images,

will provide a cost-effective, non-invasive, non-destructive, and patient-friendly approach to

health monitoring and examination, as well as to assisting diagnosis [40], [49]

Thermal imaging relies on sensing the infrared radiation emitted by all objects above absolute

zero temperature. All objects emit photons as a result of transitions from a high-energy to

low-energy state. In solids, such transitions lead to a continuous distribution of energy

between different wavelengths according to the Planck equation (1901), shown as follows

[50]:

( )1

5

2

2( , )

exp 1b

Ce T

C Tλ

πλ

λ λ=

−

where λ is the wavelength, C1=hc2 and C2=hc/k; h is Planck's constant, k is Boltzmann's

constant and c is speed of light in a vacuum.

In general, IR radiation covers wavelengths that range from 0.75 µm to 1000 µm, among

which the human body emissions that are traditionally measured for diagnostic purposes only

occupy a narrow band at wavelengths of 8 µm to 12 µm (refer Figure 1.2.A) [51].

This radiation is not visible to the human eye but, in sufficient intensity, can be felt by the

human skin, one function of which is a low-sensitivity infrared array detector. The Planck

function is exponentially nonlinear in temperature.

This means that the lower- temperature objects emit order of magnitude less energy than do

higher-temperature objects (Figure 1.2.B). Therefore detection of infrared energy accurately is

a challenging task [52].


1–17

Figure 1.2.A The electromagnetic spectrum and the IR region.

Figure 1.3.B Blackbody radiation curves showing peak wavelengths at various temperatures.

Infrared imaging is a physiological test that measures the subtle physiological changes that

might be caused by many conditions, e.g. contusions, fractures, burns, carcinomas,

lymphomas, dermatological diseases, rheumatoid arthritis, diabetes mellitus, bacterial

infections, etc.


1–18

These conditions are commonly associated with regional vasodilation, hyperthermia,

hyperperfusion, hypermetabolism, and hypervascularization [51], [53-58] which generate

higher-temperature heat source.

Unlike imaging techniques such as X-ray radiology and CT that primarily provide

information on the anatomical structures, IR imaging provides functional information not

easily measured by other methods. Thus correct use of IR images requires in-depth

physiological knowledge for its effective interpretation [48].

However, there is still an existing nonspecificity in the process, which must be recognized and

addressed by improving the analytical tools and recognizing that, even with the most

improved tools, a fundamentally nonspecific diagnostic technique such as thermal imaging

can only be used as a powerful adjunct tool. Such recognition will avoid the controversy and

confusion often surrounding this issue. This aspect of IR imaging is discussed in chapter 2

and 3.

The use of nanoparticles in cancer imaging

The biological application of nanoparticles is a rapidly developing area of nanotechnology

that raises new possibilities in the diagnosis and treatment of human cancers.

Optical imaging techniques has strong potential for sensitive cancer diagnosis, particularly at

the early stage of cancer development involving fluorescent nanoparticle probes such as dye-

doped nanoparticles and quantum dots [59]. Nanoparticles such as supermagentic and gold

nanoshells have exciting possibilities as contrast agents for cancer detection (e.g. MRI, optical

techniques), and for monitoring the response to treatment [60], [61], [62], [63].

Magnetic nanoparticles also hold promise in the combination with thermal imaging improving

its nonspecifitiy and sensitivity as described in detail in chapters 2 and 3.


1–19

1.C.6. Treatment

Cancer can be treated by various modalities such as surgery, chemotherapy, radiation therapy,

immunotherapy, monoclonal antibody therapy or other methods. The choice of therapy

depends upon the location and grade of the tumor and the stage of the disease, as well as the

general state of the patient (performance status). The goal of treatment is a complete removal

of the cancer without causing any damage to the surrounding healthy body tissue. However,

each modality has its own limitations. Sometimes, complete tumor removal can be

accomplished by surgery, but the propensity of cancers to invade adjacent tissue or to spread

to distant sites by microscopic metastasis often limits its effectiveness. The effectiveness of

chemotherapy is often limited by toxicity to other tissues in the body. Radiation can also

cause damage to normal tissue. Therefore both the use of both methods is limited to a certain

amount of dosage, which can not be passed.

Surgery

In theory, cancers can be cured if entirely removed by surgery, but this is usually an

impractical wishful thinking. When cancerous tumor has already metastasized to distinct sites

in the body prior to surgery, complete surgical excision is usually impossible.

Examples of surgical procedures for cancer include mastectomy for breast cancer and

prostatectomy for prostate cancer. The goal of the surgery can be either the removal of only

the tumor, or the entire organ. A single cancer cell is invisible to the naked eye but can regrow

into a new tumor, a process called recurrence. For this reason, the pathologist will examine

the surgical specimen to determine if a margin of healthy tissue is present, thus decreasing the

chance that microscopic cancer cells are left in the patient.


1–20

In addition while removing a primary tumor, surgery has essential role in staging, e.g.

determining the extent of the disease and whether it has metastasized to regional lymph

nodes. Staging is a major determinant of prognosis and of the need for adjuvant therapy.

Occasionally, surgery is necessary to control symptoms, such as spinal cord compression or

bowel obstruction. This is referred to as palliative treatment [1], [64], [65], [66].

Chemotherapy

Chemotherapy is the phatrmaceutical treatment of cancer, i.e. therapy by using "anticancer

drugs" that are capable of destroying cancerous cells. It interferes with cell division in various

possible ways, e.g. with the duplication of DNA or the separation of newly formed

chromosomes. Most forms of chemotherapy target all rapidly dividing cells and are not

specific for cancer cells. Hence, chemotherapy has the potential to harm healthy tissue,

especially those tissues that have a high replacement rate (e.g. intestinal lining).

For instance, the treatment of some leukaemias and lymphomas requires the use of high-dose

chemotherapy, and total body irradiation (TBI). This treatment ablates the bone marrow, and

hence the body's ability to recover and repopulate the blood. For this reason, bone marrow, or

peripheral blood stem cell harvesting is carried out before the ablative part of the therapy, to

enable "rescue" after the treatment has been given. This is known as autologous

transplantation. Alternatively, bone marrow may be transplanted from a matched unrelated

donor (MUD) [67], [68], [69].


1–21

Immunotherapy

Immunotherapy is the use of immune mechanisms against tumors. These are used in various

forms of cancer, such as breast cancer (trastuzumab/Herceptin®) and leukemia (gemtuzumab

ozogamicin/Mylotarg®). The agents are monoclonal antibodies directed against proteins that

are characteristic to the cells of the cancer in question, or cytokines that modulate the immune

system's response.

Other, more contemporary methods for generating non-specific immune response against

tumours include intravesical BCG immunotherapy for superficial bladder cancer, and use of

interferon and interleukin. Vaccines to generate non-specific immune responses are the

subject of intensive research for a number of tumours, notably malignant melanoma and renal

cell carcinoma [70].

Radiation therapy

Radiation therapy (also called radiotherapy, X-ray therapy, or irradiation) is the use of

ionizing radiation to kill cancer cells and shrink tumors. Radiation therapy can be

administered externally via external beam radiotherapy (EBRT) or internally via

brachytherapy. The effects of radiation therapy are localised and confined to the region being

treated. Radiation therapy injures or destroys cells in the area being treated (the "target

tissue") by damaging their genetic material, making it impossible for these cells to continue to

grow and divide. Although radiation damages both cancer cells and normal cells, most normal

cells can recover from the effects of radiation and function properly. The goal of radiation

therapy is to damage as many cancer cells as possible, while limiting harm to nearby healthy

tissue. Hence, it is given in many fractions, allowing healthy tissue to recover between

fractions.


1–22

Radiation therapy may be used to treat almost every type of solid tumor, including cancers of

the brain, breast, cervix, larynx, lung, pancreas, prostate, skin, stomach, uterus, or soft tissue

sarcomas. Radiation is also used to treat leukemia and lymphoma. Radiation dose to each site

depends on a number of factors, including the radiosensitivity of each cancer type and

whether there are tissues and organs nearby that may be damaged by radiation. Thus, as with

every form of treatment, radiation therapy is not without its side effects [71], [72], [73].

Hormonal suppression

The growth of some cancers can be inhibited by providing or blocking certain hormones.

Common examples of hormone-sensitive tumors include certain types of breast and prostate

cancers. Removing or blocking estrogen or testosterone is often an important additional

treatment [74].

Hyprethermia

Hyperthermia is virtually causing damage to tissue by preferably eleveating the local

temperature. Several investigators have found that a major factor in cell killing at 42°C is the

irreversible damage to cancer cell respiration [75], [76]. While the exact mechanisms of heat

destruction remain poorly understood, coincident alterations appear to take place in nucleic

acid and protein synthesis that include a reduction of activity in many vital enzyme systems

[77],[78]. Hyperthermia may be carried out by various techniques such as low frequency

current fields, ferromagnetic coupling, microwaves, radiofrequency waves, magnetic

induction etc [79]. The use of hyperthermia in combination with nanoparticles is to be

discussed in detail hereinafter.


1–23

As depicted above, the majority of treatment modalities is not capable of distinguishing

between malignant cells and healthy tissue and does not provide the physician with adequate

precision and specificity while removing cancerous cells. Moreover, there is no real-time

control referring the physiological margins distinguishing the malignant and benign tissue.

The implicatinons of the latter are for example in surgery, if the surgeon does not remove all

the malignant cells, the progression or recurrence of the disease is almost without doubt. On

the other hand, if the surgeon removes more than necessary, the "extra" tissue being removed

is a healthy tissue and may be vital for the organ life cycle or patient's life.

1.D. The vision

The suggested system is schematically illustrated in

Figure 1.4 and is briefly described below:

The process begins in the insertion of the magnetic nanoparticles into the patient's body either

locally to a suspected tissue or systematically to the blood stream by IV injection. When the

nanoparticles arrive in short proximity to the tumor, the process of bioconjugation occurs (see

section 1.E). Eventually, the tumor's outer surface is bind with nanoparticles by virtue of a

strong chemical bonds configured as antigen-antibody complex. Since the biocompatible

magnetic nanoparticles are able to produce heat under AC magnetic field, the region of

interest (ROI) is placed under a suitable field. This emitted thermal radiation propagates along

the tissue by thermal conduction reaching medium's (tissue's) surface. The surface

temperature distribution is acquired by a thermal camera and could be analyzed to retrieve

and reconstruct nanoparticles' temperature and location within the tissue. In future minimal

invasive applications the IR radiation can be "guided" from internal compartments of the body


1–24

to the outside by waveguides and dedicated optical fibers, e.g. thermal imaging bundles

shown by Gannot and Ben-David [80-83].

The aforementioned technique may function as a diagnostic tool thanks to the ability of

specific bio-conjugation of these nanoparticles to a tumor's outer surface.

Hence, by applying a magnetic field we could cause an elevation of temperature of the

selective targeted nanoparticles up to 5°C, which allows us the imaging of the tumor.

Furthermore, elevating the temperature over 65°C and up to 100°C stimulates a thermo-

ablating interaction which causes a localized irreversible damage to the cancerous site almost

without harming the surrounding tissue. This procedure may serve as a targeted therapeutic

tool under thermal feedback control carried out by software such as LabView® software

which allows us on one hand, to maintain a sufficient heat generation, producing a readable

signal, and on the other hand the avoidance of an over-heating damage which endanger the

surrounding tissue. This is valid in both diagnostic and therapeutic purposes where the main

differences are in the targeted temperatures.

Thus, the treatment can be done immediately after imaging the tumor only by elevating the

temperature, with a continuous feedback imaging of the ROI, since those selective specific

targeted mediators are doing both tasks.


1–25

Figure 1.4 Schematic description of the system employing a targeted imaging technique and a closed-

loop system for therapy under real-time feedback.

Nanoparticles Injection

Bio-Conjugation

AC Magnetic Field

IR CameraTherapy

under IR Imaging

Analysis

Diagnosis

End of Process


Bio-Conjugation

AC Magnetic Field

IR CameraTherapy

under IR Imaging

Analysis

Diagnosis

End of Process


Bio-Conjugation

AC Magnetic Field

IR CameraTherapy

under IR Imaging

Analysis

Diagnosis

End of Process


1–26

1.E. Bioconjugation

An important issue lying on the basis of this work is the fact that the magnetic nanoparticles

are localized specifically and functions as madiators situated on the periphery of the tumor. In

order to target the tumor and deliver the nanoparticles reliably and specifically, the suggested

transportation leans on human's immune system. The malignant tumor tends to present

specific antigens on its outer surface. These antigens are able to communicate with

corresponding agents of the immune system (e.g. antibodies) to establish antigen-antibody

complexes which are characterized in strong chemical bonds. For instance, we can bind the

magnetic nanoparticles' surface to the antibodies via adhering polymers (e.g. PEG) so that

antibodies transport them towards the tumor being delivered by immune agents (T cell), and

conjugate them to the tumor retaining them along the tumor's outer surface

(Figure 1.5and Figure 1.6).

Figure 1.5 Bioconjugation of magnetic nanopatricles by using the natural immune system

Antibody Magnetic

Nanoparticles Labeled

Antibody

Specific

LocalizationLabeled

Antibody

T cell


1–27

Figure 1.6 Magnetic nanoparticles schematic siting along the tumor surface

This bioconjugation is analogous to that made with fluorophores in research conducted by

Fibich et al. [84] and Gannot et al [85]. That optical imaging technique is based on ‘‘Anti-

CD3’’ antibodies conjugated to a fluorescent marker (FITC or IRD38) [86], injected to the

tumor area, and specifically bind to receptors on T cells (‘‘sites’’). These T cells reach the

tumor area as part of the natural immune system reaction of the object to a cancerous tumor

[87]. They are shown in Figure 1.7 - histological staining of a 5-day-old tumor with CD-3 at

magnitude ×200. A volume layer where binding was detected can be seen on the left [84].

This specific, minimal invasive and almost natural technique of targeting the tumor, lays the

fundamentals for both novel diagnostic and therapeutic techniques targeted solely to the

malignant cells without harming the surrounding healthy tissue.

Labeled

Antibody

T cellSurface

Marker

Tumor


1–28

Figure 1.7 Histological staining: 5-day old tumor with CD-3 at magnitude

×200. A colume layer where binding was detected can be seen on the

left (reprinted from ref. [84]).


1–29

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Gleysteen JJ: Radiation-Therapy as Definitive Treatment for Selected Invasive

Rectal-Cancer. Surgery 1993, 114:850-857. 72. Pollack JM: Radiation Therapy Options in the Treatment of Prostate Cancer.

Cancer Investigation 2000, 18:66-77. 73. Phan TP, Puthawala A, Sharma A, Syed AN: Treatment of Localized Prostate

Cancer with External Beam Radiation Therapy and High Dose Rate Interstitial

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Estrogen Suppression with Aminoglutethimide and Hydrocortisone as Treatment


1–33

of Human-Breast Cancer - Correlation of Hormonal Data with Clinical-

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Biochemical Mechanism of Selective Heat Sensitivity of Cancer Cells. I. Studies

on Cellular Respiration. Eur J Cancer 1969, 5:129-136. 77. Mondovi B, Finazzi Agro A, Rotilio G, Strom R, Moricca G, Rossi Fanelli A: The

Biochemical Mechanism of Selective Heat Sensitivity of Cancer Cells. II. Studies

on Nucleic Acids and Protein Synthesis. Eur J Cancer 1969, 5:137-146. 78. Strom R, Santoro AS, Crifo C, Bozzi A, Mondovi B, Fanelli AR: The Biochemical

Mechanism of Selective Heat Sensitivity of Cancer Cells. IV. Inhibition of RNA

Synthesis. Eur J Cancer 1973, 9:103-112. 79. Storm FK, Morton DL: Localized Hyperthermia in the Treatment of Cancer. CA

Cancer J Clin 1983, 33:44-56. 80. Ben-David M, Inberg A, Gannot I, Croitoru N: The Effect of Scattering on the

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Dysplasia and Carcinoma. British Journal of Cancer 2002, 86:1444-1448.

Chapter 2 Heat Generation

2–34

2. Heat Generation

2.A. Introduction

Nanobiotechnology, defined as biomedical applications of nano-sized systems, is a rapidly

developing area within nanotechnology. Nanomaterials, which measure 1–1000 nm, allow

unique interaction with biological systems at the molecular level. They can also facilitate

important advances in detection, diagnosis, and treatment of human cancers and have led to a

new discipline of nano-oncology [1, 2]. Nanoparticles are being actively developed for tumor

imaging in vivo, biomolecular profiling of cancer biomarkers, and targeted drug delivery.

These nanotechnology-based techniques can be applied widely in the management of different

malignant diseases [3]. Nanoparticles coupled with cancer specific targeting ligands can be

used to image tumors and detect peripheral metastases [4].There are various nano-mediators

being investigated in the cancer imaging and therapy fields. Semiconductor fluorescent

nanocrystals, such as quantum dots, have been conjugated to antibodies, allowing for

simultaneous labeling and accurate quantification of target proteins in a tumor [4-6]. The use

of gold-containing nanoparticles (i.e., Raman probes) [7] may allow the simultaneous

detection and quantification of several proteins on small tumor samples, which will ultimately

allow the tailoring of specific anticancer treatment to an individual patient’s specific tumor

protein profile [8]. Nanotechnological approaches (e.g. nanocantilevers and nanoprobes) are

being actively investigated in cancer imaging [9]. Metal nanoshells are a novel type of

composite spherical nanoparticle consisting of a dielectric core covered by a thin metallic

shell which is typically gold. Nanoshells possess highly favorable optical and chemical and

physical properties for biomedical imaging and therapeutic applications.


2–35

By varying the relative dimensions of the core and the shell, the optical resonance of these

nanoparticles can be precisely and systematically varied over a broad region ranging from the

near-UV to the mid-infrared. These nanoshells may be used as contrast agents for optical

coherence tomography (OCT), and the use of absorbing nanoshells in NIR thermal therapy of

tumors [10, 11]. Additional example is the Au/Ag nanocages which have been developed and

investigated for the purpose of optical coherence tomography (OCT) contrast agents

maintaining an optical resonance peak in the near-IR range (800 – 1200 nm) [12]. Alternative

optical imaging applications are based on the combination of contrast agents and polarization

[13].

Since the light-tissue interactions field is usually characterized by low signal and high energy

losses (low Signal to Noise ratio) due to the fact that human tissue is a turbid media (i.e. high

absorption and scattering), one should consider other exciting methods such as example

magnetic, micro-, radio- or ultrasonic waves.

Magnetic nanoparticles that have a metal core show promising results for simultaneous

imaging and targeting of cancer implemented with MRI [14, 15] or alternating magnetic fields

as depicted below.


2–36

2.B. Applications of magnetic nanoparticles

Magnetic nanoparticles offer some attractive possibilities in biomedicine. First, they could be

manufactured in different sizes ranging from a few nanometers up to tens of nanometers,

which places them at dimensions that are smaller than or comparable to those of a cell (10-

100 µm), a virus (20-450 nm), a protein (5-50 nm) or a gene (2 nm wide and 10-100 nm long)

(Figure 2.1). This means that they can 'get close' to a biological entity of interest. Indeed, they

can be coated with biological molecules to make them interact with or bind to a biological

entity, thereby providing a controllable means of 'tagging' or addressing it.

Second, the nanoparticles are magnetic, which means that they obey Bio-Savart's law, and can

be manipulated by an external magnetic field gradient. This 'action at a distance', combined

with the intrinsic penetrability of magnetic fields in human tissue, opens up many applications

involving the transport and/or immobilization of magnetic nanoparticles, or of magnetically

tagged biological entities. In this way they can be made to deliver a package, such as an

anticancer drug, or a cohort of radionuclide atoms, to a targeted region of the body, such as a

tumor.

Third, the magnetic nanoparticles can be made to resonantly respond to a time-varying

magnetic field, with advantageous results related to the transfer of energy from the exciting

field to the nanoparticle. For example, the particle can be made to heat up, which leads to

their use as hyperthermia agents, delivering toxic amounts of thermal energy to targeted

bodies such as tumors; or as chemotherapy and radiotherapy enhancement agents, where a

moderate degree of tissue warming results in more effective malignant cell destruction. These

and many other potential applications are made available in biomedicine as a result of the

special physical properties of magnetic nanoparticles [16].


2–37

Among the leading applications of magnetic nanoparticles are magnetic separation, drug

delivery, hyperthermia treatments and MRI contrast agents [16-18], however since the scope

of this research work focuses on the generation of heat via these particles, other applications

will not be discussed in detail.

Figure 2.1 Relative sizes of cells and their components

As disclosed in chapter 1, one of the functions we seek to accomplish in this research is

thermal therapy by generating heat using nanoparticles. The use of iron oxides in tumor

heating was first proposed by Gilchrist et al [19] and there are currently two different

approaches. The first is called magnetic hyperthermia and involves the generation of

temperatures up to 45-47 ˚C by the particles. This treatment is currently adopted in

conjunction with chemotherapy or radiotherapy, as it also renders the cells more sensitive

[20]. The second technique is called magnetic thermoablation, and uses temperature of 43-

55˚C that have strong cytotoxic effects on both tumor and normal cells [21, 22]. The reason

for using higher temperatures is due to the fact that about 50% of tumors regress temporarily

after hyperthermic treatment with temperatures of up to 44˚C, therefore researchers prefer to

use temperatures up to 55˚C [22]. The problem of deleterious effects on normal cells is

reduced by intratumoral injection of the particles [23].


2–38

2.C. Objectives

As previously mentioned, the objectives of this research is to cause local elevation in

temperature on the surface of a tumor where the magnetic nanoparticles are located, without

causing any damage to the healthy surrounding tissue. Generation of heat in a non-invasive

and human-friendly technique in the form of magnetic fields is most desired.

2.D. Heating mechanisms

There exist at least three different mechanisms by which magnetic materials can generate heat

in an alternating field [18]:

(i) Generation of eddy currents in bulk magnetic materials,

(ii) Hysteresis losses in bulk and multi-domain magnetic materials,

(iii) Relaxation losses in ‘superparamagnetic’ single-domain magnetic materials.

We wish to focus on single-domain particles in which mechanism (i) and (ii) contribute very

little to the heating of these particles (if at all) [24], while the significant mechanism in

contribution with heating is the relaxation mechanism (iii) [25, 26].

Relaxation losses in single-domain magnetic nanoparticles fall into two modes: (a) rotational

(Brownian) mode and (b) Néel mode [25, 27]. The principle of heat generation due to each

individual mode is shown in Figure 2.2.

Figure 2.2 Relaxational losses leading to heating in an alternating magnetic field (H).


2–39

In the Néel mode (Figure 2.2.A), the magnetic moment (dotted arrow) originally locked along

the crystal easy axis (solid arrow) rotates away from the crystal axis towards the external field

(H). The Néel mechanism is analogous to the hysteresis loss in multi-domain magnetic

particles whereby there is an ‘internal friction’ due to the movement of the magnetic moment

in an external field that results in heat generation.

In the Brownian mode (Figure 2.2.B), the whole particle oscillates towards the field with the

moment locked along the crystal axis under the effect of a thermal force against a viscous

drag in a suspending medium. This mechanism essentially represents the mechanical friction

component in a given suspending medium [23].

Each of the relaxation modes that lead to heat generation is characterized by a time constant.

Nτ is the Néel time constant given by

0 exp BN

B

E

k Tτ τ

=

(Equation 2.1)

where B u

E K V= is analogous to an activation energy that has to be overcome by the thermal

energy B

k T to overcome the inherent magnetic anisotropy energy.

The energy barrier EB is represented by the constant Ku, which is a material property and is

the anisotropy constant, multiplied by V, which is the volume of the magnetic nanoparticle.

The thermal energy is represented by the constant B

k named by Stephan Boltzmann

multiplied by the absolute temperature T. The constant 0τ is of the order of 10−9 seconds [25].


2–40

For the spherical particles with an uniaxial anisotropy the energy is:

2sin

uE K V θ= (Equation 2.2)

where Ku is the anisotropy constant and θ the angle between the easy axis and the

magnetization. The energy barrier (EB = Emax-Emin=KuV) separates the two minima at θ=0 and

θ=π corresponding to a magnetization parallel and antiparallel to the easy axis (Figure 2.3).

For small particles at 300 K the energy barrier becomes comparable to the thermal energy.

Thus the magnetization will fluctuate between the two energy minima. This results in a

superparamentic relaxation. This fluctuation of magnetization due to the thermal activation

between two easy-axis orientations is called superparamagnetism.

Figure 2.3 Schematic illustration of the energy of a single-domain particle with uniaxial

anisotropy as a function of magnetization direction.

Since the Néel-type superparamagnetic relaxation time is temperature dependent we should

denote a special temperature TB - the blocking temperature. Below TB the free movement of

the spins is blocked by anisotropy, while above TB the thermal energy will disrupt the bonding

of the total amount of the particles and the system turns superparamagnetic. The types of

magnetic nanoparticles in the scope of this research are characterized by blocking temperature

estimated by dozens of Kelvin. Hence, we may confidently assume superparamagnetism

throughout this paper.


2–41

The Brownian time constant is represented by Bτ is given by

3

HB

B

V

k T

ητ = (Equation 2.3)

where VH is the hydrodynamic volume of the magnetic nanoparticle which is the effective

volume (including that of the nanoparticle and coating or surfactant attached to the

nanoparticle), η is the viscosity of the liquid carrier and B

k T is the thermal energy.

The resultant power generation is a strong function of the effective time constant (and the

field parameters and is given by

( )2

0 0 0 2

2

1 2SPM

fP H f

f

π τπµ χ

π τ=

+ (Equation 2.4)

where H0 and f are the amplitude and frequency of the applied alternating magnetic field

respectively, 0χ is the magnetic susceptibility, 0µ is the permeability of free space and τ is

the effective time constant given by1 1

N B

ττ τ

= + [18, 25].


2–42

2.E. Affecting parameters

There are numerous parameters affecting the heat generation, which is produced by magnetic

nanoparticles excited by a magnetic field. Given below a few examples for some crucial

parameters one should take into consideration when heating with magnetic nanoparticles.

2.E.1. Field parameters

According to Equation 2.4, it is obvious that field strength and frequency are controllable

parameters that directly affect the power produced by the nanoparticles when alternative

magnetic field is applied. It should be appreciated that the proportional of field parameter is

not straightforward to the generated power but more complex, and depends on additional

parameters such as the nanoparticles' material properties [28].

2.E.2. Material Properties

Iron oxides

An interesting class of magnetic materials are iron oxides such as Fe3O4, γ-Fe2O3 and

MO·Fe2O3 (where M is Mn, Co, Ni, Cu) [29], because they display ferrimagnetism.

Magnetite (Fe3O4), meghemite (γ-Fe2O3) and hematite (α-Fe2O3) are the most common iron

oxides and they are discussed below.


2–43

Magnetite (Fe O · Fe2O3) is the oldest known magnetic material [29]. At room temperature,

bulk magnetite crystallizes in the inverse spinel structure as is shown in Figure 2.4. it should

be noticed that in a spinel structure the Fe3+ ions are located on the B sites, while the divalent

ions M2+ on the A sites. The oxygen atoms form the close-packed face-centered-cubic (fcc)

lattice with the iron atoms occupying interstitial sites [30]. Each cubic spinel contains eight

oxygen (fcc) cells. The so-called A sites are characterized by tetrahedral oxygen coordination

around the Fe ions and B sites which have octahedral oxygen coordination. The A sites are

occupied by Fe3+ and the B sites are occupied by equal numbers of Fe2+ and Fe3+. Below 851

K magnetite is ferromagnetic with A-site moments aligned antiparallel to the B-sites.

Magnetite undergoes a first-order phase transition at 120 K (Verwey transition), with a

change of crystal structure, latent heat and decrease of the dc conductivity. The distribution of

Fe3+ and Fe2+ in B sites changes from a dynamic disorder to a long range order with an

orthorhombic symmetry below 120 K. At room temperature, Fe3O4 very easily undergoes a

transformation to meghemite [31].

Figure 2.4 Crystal structure of Fe3O4 . Big balls denote oxygen atoms, small dark balls denote

A-site (tetrahedral) iron atoms, and small light balls denote B-site (octahedral) iron

atoms. (reprint ref. [30] )


2–44

Two additional used Iron Oxides in this field of research are the Meghemite

(γ-Fe2O3) [32] and Hematite (α-Fe2O3), which are not currently investigated in this research.

Meghemite has a good chemical stability and can be prepared involving low prices and cheap

technology. It was found that small γ-Fe2O3 nanoparticles exhibit a strong exchange

interaction and a magnetic training effect. Recently, a low temperature spin-glass transition

was found at T = 42 K [33]. In the dry state, γ-Fe2O3 transforms to α-Fe2O3 (hematite) at

temperatures ranging from 370 – 600 ˚C [31]. Hematite is the most stable iron oxide [31].

Iron-Gold nanoshells

The magnetic nanoshells were designed and characterized by Nanosonic Inc. to generate heat

in response to external magnetic field (Figure 2.5.A). The nanoshells are comprised of an iron

core with diameter of 8 nm coated with a layer of gold. The gold coatings are made in order to

prevent oxidation, hence demagnetization; ultrathin noble metal coatings of Au (~2 nm) were

prepared to provide long-term stability and biocompatibility for the Fe core.

The Fe core was over-coated with a series of block copolymer stabilizers that are compatible

with analgesics to prevent flocculation in the arterial system in vivo (see Figure 2.5.B).

In addition, the block copolymers assist in preventing agglomeration.

Other materials are also being investigated including Platinium compounds, Vanadium

Oxides, Cobalt, Nikel, Lanthanum and Manganase [34], [35].


2–45

Figure 2.5 Fe Nanoparticles produced by Nanosonics Inc. (A) Magnetic nanoparticles in different

particle size configured as powder. (B) Schematic illustration of a single Fe-Au nanoparticle

2.E.3. Size dependence

The size of the nanoparticles is a fundamental characteristic in this field. Ma et al. [36]

investigated the specific absorption rate (SAR) values of aqueous suspensions of magnetite

particles with different diameters varying from 7.5 to 416 nm by measuring the time-

independent temperature curves in an external altering magnetic field

(80 kHz, 32.5 kA/m). Results indicate that the SAR values of magnetite particles are strongly

size dependent. For magnetite larger than 46 nm, the SAR values increase as the particle size

decreases where hysteresis loss is the main contribution mechanism. For magnetite particles

of 7.5 and 13 nm which are superparamagnetic, hysteresis loss decreases to zero and, instead,

relaxation loss (Néel loss and Brownian rotation loss) dominate.

A B


2–46

The dividing line between the two cases depicted above is given by the ferromagnetic

exchange length ex

d A K≅ using the material parameters of magnetite

( 4 3 111.35 10 , 10K J m A J m−= × = ), the exchange length is estimated as 27ex

d nm≅ .

Therefore, when the particle size is larger than ex

d , the hysteresis loss increases as the

particle size decreases. However, once the particle size is less than ex

d , hysteresis loss will

vanish and the main contribution will be of relaxation losses. This is shown in Table 2.1 by

Ma et. al [36]:

Table 2.1 SAR values of samples in the applied magnetic field (80 kHz, 32.5 kA/m) and

coercivity Hc of samples, Ma et al., 2004.

Samples

Particle Diameter

(nm)

SAR Values

(W/[g of Fe])

Coercivity

Hc (Oe)

A 7.5 15.6 6.4

B 13 39.4 20.9

C 46 75.6 101.9

D 81 63.7 88.9

E 282 32.5 62.4

F 416 28.9 53.9


2–47

This phenomena was also investigated by Hergt et al. [24]. Based on their research it is shown

in Figure 2.6 that in the critical particles size region where hysteresis losses vanish (dotted

line), Néel losses (full line) grow as a new loss mechanism which, roughly speaking, extends

the loss region toward even smaller particle sizes [24].

SAR optimization is currently under investigation and, concerning its dependence on

magnetic core size, calculation should allow the optimization of particle diameter with respect

to frequency [17], as shown by Hergt et al [24] in Figure 2.7. This figure shows the particle

size dependence of the loss power density due to Néel relaxation calculated for three values

of frequencies while all parameters were chosen according to the goal of their application for

hyperthermia [24].

Figure 2.6 Dependence of magnetic loss power density on particle size for magnetite fine

particle (2MHz, 6. 5 kA/m) (Reprinted from ref. [24]).


2–48

Figure 2.7 Grain size dependence of the loss power density due to Néel-relaxation for

small ellipsoidal particles of magnetite (6. 5 kA/m) (Reprinted from ref. [24]).

2.E.4. Miscellaneous

The aforementioned parameters discussed in section 2.E. are merely few examples for a larger

collection of affecting parameters. Some of them have been investigated and some are

probably yet unknown. Amongst them is the concentration of the nanoparticle inserted into

the body [18]. The concentration should be large enough to effectively produce heat, but yet

in amount that won't be toxic for the human body. The coating of nanoparticles (e.g.

derivatives of dextran, polyethylene glycol (PEG), polyethylene oxide (PEO) and poloxamers

and polyoxamines) and suspending medium also affect the heat generation [18], [23], [37].

The period of time of excitation filed application and profile (e.g. continuous, pulsatile)

deeply affect the SAR which is proportional to the power dissipated [38].

Another affecting parameter under investigation is the presence of nanoparticles'

agglomeration in comparison with the heat generated in single or dispersed nanoparticles

[39].


2–49

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Electromagnetically Excited Nanoparticles. Journal of Applied Physics 2006, 100:054305.

Chapter 3 Thermal Analysis

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3. Thermal Analysis

3.A. Introduction

Following the heating of the bioconjugated nanoparticles as described previously in chapter 2,

we now may consider our challenge as a heat transfer problem. The heat source, namely the

tumor, and in particular the tumor's surface, is actively heated by external and controlled

magnetic fields. Based on the 2-dimensional thermal image acquired from the tissue surface,

we seek to derive two fundamental characteristics: the depth of the tumor and the temperature

of the tumor and its surroundings. Knowing the temperature in real-time is crucial in order to

avoid any damage to all tissues in the diagnostic mode on one hand, and on the other hand,

operating in therapeutic mode, we expect to damage only the malignant tissue leaving the

healthy surrounding tissue with minimal damage.


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3.B. Image processing approaches to IR images [1]

The application of computerized image processing methods in diagnosis, i.e. computer-aided

diagnosis (CAD) has been playing an important role in the analysis of IR images, since the

analysis task often requires high concentration and accuracy, memory and tremendous

analytic ability, factors that are influenced by human "limitations" such as fatigue, being

careless, limited human visual system etc. On top of all these factors, a shortage of qualified

radiologists also put an urgent demand on the development of CAD technologies.

Currently, research on smart image processing algorithms for IR images tends to improve the

detection accuracy from three perspectives: smart image enhancement and restoration

algorithms, asymmetry analysis of the thermogram including automatic segmentation

approaches, and feature extraction and classification. Following is a brief review of these

three perspectives of IR image algorithms.

Smart Image Enhancement and Restoration Algorithms

One of the solutions for low resolution of thermograms was proposed by Synder et al. [2] who

developed an algorithm to increase the effective resolution by 2:1 ratio while at the same time

removing the noise and preserving edges in the image. This algorithm is based on a

minimization strategy known as mean field annealing, which takes into account processes of

blur, noise, and image correlations, to make an optimal estimate of the missing pixels.

The Minimally Invasive Optical Biopsy System developed at MIT [3] uses infrared light in

conjunction with an intravenously injected dye and special computer software to create a

clear, high contrast image.


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Kaczmarek and Nowakowski [4] proposed the use of active dynamic thermography (ADT),

commonly adopted in nondestructive testing of materials, to further enhance the image

quality.

Asymmetry Analysis

Comparing between contra-lateral images is a procedure carried out routinely by radiologists.

One of the popular methods especially for breast cancer detection is to make comparisons

between contralateral images. When the images are relatively symmetrical, small asymmetries

may indicate a suspicious region. In thermal infrared imaging, asymmetry analysis normally

needs human intervention because of the difficulties in automatic segmentation.

In order to provide a more objective diagnostic result, there is a need to design an automatic

approach to asymmetry analysis in thermograms. It includes automatic segmentation and

supervised pattern classification [5].

When images are relatively symmetrical, small asymmetries may indicate a suspicious region.

Generally, these small asymmetries are not easily detectable and require an automatic

approach to eliminate human factors. There have been a few papers addressing techniques for

asymmetry analysis of mammograms [6], [7], [8].

Head et al. [9], [10] recently analyzed the asymmetric abnormalities in IR images. Qi et al.

[11] developed an automatic approach to asymmetry analysis in IR images. It includes

automatic segmentation and pattern classification. Mabuchi et al. [12] designed a

computerized thermographic system, which would produce images of the distribution of

temperature differences between the affected side and the contra-lateral healthy side.


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Feature Extraction and Classification

Upon segmentation, different features can be extracted from the segments. Asymmetric

abnormalities can then be identified based on mature pattern classification techniques. In this

process, feature extraction is crucial to the success of computer-aided diagnosis. For example,

Kuruganti et al. [13] shows that the high-order statistics (e.g. variance, skewness, and

kurtosis) and joint entropy are the most effective features to measure the asymmetry, while

low- order statistics (e.g. mean) and entropy do not assist asymmetry detection. Additional

research works were conducted by Jakubowska et al. [14] also addressed the importance of

using statistical parameters (1st and 2nd order) in extracting thermal signatures for asymmetry

analysis


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3.C. The problem

This problem, in virtue, may be classified as an inverse problem whose its solution is non-

trivial since being referred as an ill-posed problem involving complicated and complex methods of

solution. Hadamard coined the term ill-posed in the sense that the conditions of existence and

uniqueness of solution are not necessarily satisfied and the solution may be unstable to perturbations

in input data [15]. Inverse problems have practical implications in thermal transport systems which

involve conduction, convection and radiation. Inverse problems of heat-conduction, or IHCPs, can be

subdivided into three categories: boundary problems, retrospective problems, and identification

problems [16]. The most popular of all inverse problems is the boundary heat-flux reconstruction in a

conducting solid given temperature measurements at various points within the solid. Its popularity

stems in the fact that its applications extend in many areas of engineering, including thermal

processing of materials, thermal monitoring in nuclear engineering, and crystal growth and

solidification processes [16, 17]. Various methodologies have been proposed and successfully been

implemented for the solution of the IHCP mentioned above [16-18]. Several of these techniques

involve restatement of the ill-posed inverse problem as a conditionally well-posed functional

optimization problem, addressed by using appropriate techniques including Tikhonov regularization

[19]. In this dissertation, we will not provide any review of deterministic inverse methods

for the IHCP since such methods are very well-documented elsewhere in the literature

[16-18, 20-22]. An alternative approach is the use of stochastic inverse modeling and uncertainty

analysis techniques for continuum systems which have been developed considerably in the last two

decades. Powerful techniques like the extended perturbation method [23, 24], the improved Neumann

expansion method [25], and generalized polynomial chaos techniques [26-30] have been proposed and

successfully used to analyze uncertainty propagation in various continuum systems, or for example,

two new methods for addressing the IHCP in a fully stochastic setting introduced by Zabaras [31].

The solution techniques are not suitable to our problem since in our case, temperature is acquired non-

invasively and therefore we cannot rely on temperature value inside the solid medium (i.e. tissue) but


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solely on its surface. Moreover, since we are using a thermal camera, we are acquiring only IR

radiation emitted from tissue's surface.

To clarify and determine the model of the problem, please refer to Figure 3.1.

SURROUNDINGS

Yq

Xq

IR Camera

2D Thermal Image

IR Camera

2D Thermal Image

TISSUEQ

Tq

Figure 3.1 The thermal problem description

The tumor and nanoparticles, being a general heat source, are embedded in a medium, namely a tissue.

The heat source's location is noted by the coordinates (Xq, Yq) and Q is the power being generated.

Assuming that by smart positioning of the IR camera, the number of unknown parameter may be

reduced to (i) the depth of the heat source and (ii) the generated power.

The given parameters are tissue characteristics, ambient characteristics and the IR data embodied in

the thermal image.


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3.D. Method of solution

3.D.1. Forward Problem and Analytical Solution

Since dealing with the solution of the inverse problem may be mathematically complicated

and cumbersome, a time consumer and flaws in reliability, it seems advisable to address this

problem analytically. The solution of the forward heat transfer problem is well-posed and

shows good results. Based on these straightforward solutions I believe it is possible to

implement the aforementioned to the opposite direction of solution (i.e. solving the inverse

problem) by taking advantage of computerized simulations and experimental set-ups.

3.D.2. Pennes Equation

The first comprehensive bio-heat equation was developed by Pennes in 1948 [32]. The

equation is controversial and over the years it has come under criticism, from, e.g. [33], [34]

and has been defended by others. Despite the controversy and the criticism most of the

mathematical analysis carried out in bio-heat transfer has and is being done using this

equation [35].

Following the revision made by E. H Wissler [36], Pennes' principal theoretical contribution

was that the rate of heat transfer between blood and tissue is proportional to the product of the

volumetric perfusion rate and the difference between the arterial blood temperature and the

local tissue temperature.


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The relation is expressed as follows:

( ) ( )1b b b ah V C T Tρ κ= − − (Equation 3.1)

where hb is the rate of heat transfer per unit volume of tissue, V is the perfusion rate per unit

volume of tissue, ρb is the density of blood, Cb is the specific heat of blood, κ is a factor that

accounts for incomplete thermal equilibrium between blood and tissue, Ta is the temperature

of arterial blood, and T is the local tissue temperature. Pennes assumed that 0 1κ≤ ≤ , although

he set 0κ = when he computed his theoretical curves, as have most subsequent investigators.

Following Pennes’ suggestion, the thermal energy balance for perfused tissue is expressed in

the following form

2m b

TC k T h ht

ρ ∂= ∇ + +

∂ (Equation 3.2)

where ρ and C refer to tissue, k is the thermal conductivity of tissue, and hm is the rate of

metabolic heat production per unit volume of tissue.


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3.D.3. Heat Conduction Equation

Assumptions

Since the solution of Pennes equation Eq. 3.2 is not trivial, the problem can be degenerated

for simplicity, relying on the following assumptions:

Let us assume a homogeneous and isotropic medium (i.e. tissue) with constant characteristics

(i.e. k, ρ and C are constant). Metabolism (i.e. hm=0) and perfusion (i.e. hb=0) are neglected.

These assumptions are valid especially when dealing with an adipose or muscle tissues.

The approach of dealing with the problem is to pursue an analytical solution while assuming

symmetry in a cylindrical coordination system.

An additional assumption is that there are no temporal changes in temperature (i.e. steady

state, 0Tt

∂=

∂).

As a fundamental problem, let us assume a point heat source, modeling a very small tumor.

Trying to best model the boundary conditions of the real problem, Newtonian boundary

conditions are adopted as shown in Eq. 3.3 hereinafter, where E is a constant, called the

"surface conductance", which is made up of radiative, convective and evaporative

components: rad conv evapE E E E= + + .

Thus the problem is set (described in Figure 3.2) in cylindrical coordination system:

2

2

1 0T Try r r r∂ ∂ ∂⎡ ⎤+ =⎢ ⎥∂ ∂ ∂⎣ ⎦

(Equation 3.3)


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with the boundary conditions:

0 :

0 : 0 : y

Ty K ETy

T rT

∂∀ = =

∂∀ → →∞∀ → →∞

Point Source

Following Draper and Boag [37], the analytical steady-state solution of the three-dimensional

thermal conductivity equation due to an embedded continuous point source as depicted above,

is given by:

r

y

aQ

Ta

Tsy=0

K

E

Figure 3.2 Schematic description og the heat conduction problem.


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[ ]

( ) ( )

( ) ( )

1 12 22 22 2

0

0

( , ) (0, ) (0, )

1 1 4

exp

2

aET y r T T T yK

QK y a r y a r

y a J rQ dE K

π

λ λ λλ

π λ

∞

= ∞ + ∞ −

⎡ ⎤⎢ ⎥

+ −⎢ ⎥⎡ ⎤ ⎡ ⎤⎢ ⎥− + + +⎣ ⎦ ⎣ ⎦⎣ ⎦

− +⎡ ⎤⎣ ⎦++∫

(Equation 3.4)

This exact solution was developed for a point source relying on the exact solution for a buried

line source developed by Awbery [38] in 1929.

The first term of the solution establishes the absolute value of the temperature in relation to a

point at great distance from the origin of the coordinate system. The second term stems from

the fact that the ambient temperature (Ta) is less than the undisturbed skin temperature

T (0, ∞) and that the thermal gradient in the body at points far from the source is linear, which

should be a good approximation for a region limited to a couple of centimeters (even if the

skin surface is slightly curved as in the case of the female breast). Q is the energy radiating

(Watts) from the point source situated at a distance a below the surface and J0 is the zero

order Bessel function. E and K are the resulting ‘surface conductance’ and the mean thermal

conductivity, respectively.

In thermal imaging studies (IR imaging) the temperature distribution on the skin surface is

measured, which simplifies the solution of Eq. 3.4 by the substitution of y = 0. The resulting

expression reads

( ) ( )0

0

exp(0, ) (0, )

2y a J rQT r T dE K

λ λ λλ

π λ

∞ − +⎡ ⎤⎣ ⎦= ∞ ++∫ (Equation 3.5)


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When applying this equation, the interest is normally focused on a description of the surface

temperature distribution not very far from the origin of the coordinate system or immediately

above the embedded tumor.

3.E. Point Simulation

3.E.1. Forward Solution

The problem depicted above has been simulated by a MATLAB® code.

The simulation describes a semi-infinite medium which represents the previously described

tissue.

The tissue is assumed to be homogeneous and symmetrical. Its thermal properties are time

and space independent. A point heat source representing the tumor, is embedded within the

medium, in a distance a beneath the medium's surface (y=0) generating power of Q Watts.

The simulation gets the following input parameters: y, assigned as zero for surface level, a as

the heat source depth, E the 'surface conductance' constant, K the medium's conductivity

constant, Q the power generated by the heat source, Ts the undisturbed surface temperature, Ta

the ambiance temperature and the radial axis dimensions including resolution.

Figure 3.3 shows a non-dimensional surface temperature. The non-dimensional variables

( )* *, ,Bi rφ were computed by utilizing Buckingham's-PI- theorem where the non-dimensional

surface temperature is presented by( )* sK T T a

Qφ

−= and the radial axis by * rr

a= .

The characteristic curve depends on the Biot modulus EBi aK

= ⋅ .


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Figure 3.3 Non-dimensional surface temperature over an embedded point heat source

Validation

Validation of the simulation is carried out by comparing simulation results to the one

published by Draper and Boag [37]. Figure 3.4.A shows the surface temperature T(0, r, Q)

for point sources at various depths a and of strength Q produced by the simulation as detailed

in Table 3.1:

Table 3.1 Point heat sources in various depths a and strength Q

A [cm] Q [mW]

0.2 6.15

0.5 17.6

1 41.5

2 104

4 285

6 534


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These parameters were chosen to produce maximum temperature of 1˚C. The compared

results of Draper and Boag [37] are shown in Figure 3..B:

Figure 3.4.A MATLAB® simulation results: surface temperature T(0, r, Q) for various point heat sources

Figure 3.4.B Draper and Boag's results: surface temperature T(0, r, Q) for various point heat sources


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3.E.2. Inverse Solution

Based on the simulation that solves the relevant thermal forward problem (given the tissue

and ambient parameters: resulting ‘surface conductance’ E, mean thermal conductivity K and

ambient temperatures) a simple and fast method of computing the ill-posed inverse problem

yielding with the depth and power of the tumor is suggested. The method models a point heat

source in a simple semi analytical algorithm. The algorithm is based on the cross-sectional

temperature profile derived from the surface temperature, i.e. the thermal image acquired by

an IR camera.

Figure 3.5 Surface temperature cross sectional distribution

w


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To better understand the algorithm let us look at the following example in which the surface

temperature of a point heat source is produced, given the following parameters:

Table 3.2 Given parameters for illustrative problem

Parameter Value

Depth (a) 1.2 [cm]

Power (Q) 0.1 [Watt]

Thermal conductivity (K) 34 10 WKcm C

− ⎡ ⎤= × ⎢ ⎥⋅⎣ ⎦o

Surface conductance (E) 212.5 WEm C⎡ ⎤= ⎢ ⎥⋅⎣ ⎦o

Ambient temperature (Ta) 25 [˚C]

Surface temperature (Ts) 32 [˚C]

The surface temperature cross-sectional distribution shown in Figure 3. may be fitted to a

Lorentzian function in 2-dimensional Cartesian coordination system as follows:

( ) ( )0 2 2

0

24

A wy yx x wπ

= + ⋅− +

(Equation 3.6)

where y0 and x0 are the vertical and horizontal offsets, respectively, w is the width at half

height, i.e. full width half maximum (FWHM), and A is the area lying under the curve.

This non-linear curve fitting based on the Levenberg-Marquardt algorithm provides two

essential parameters which can be extracted out of the Lorentzian temperature profile:

(i) Full Width Half Maximum (FWHM)


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(ii) Area lying under the curve (A).

In this example the derived values are 3.005 [cm] and 8.896 [cm2] respectively (R2=0.9998).

The advantage of using the FWHM parameter is based on two behaviors discovered by Feasey

et. al. [39]. Following their research, the FWHM was found to be constant for a given source

depth, i.e. the temperature distribution across the area of the hot spot is a function only of the

depth, and is independent of surface cooling and heat output of the source.

More particularly, in correspondence with Draper and Boag's paper [40], Davison confirms

experimentally (in vitro) that a linear relation exists between FWHM and depth [41]. This

behavior has been validated too by our simulation as shown in Figure 3.6 and Figure 3.7.

Fig. 3.6 shows constant behavior of the FWHM parameter as a function of varying power (Q)

for different depths (a). Fig. 3.7 shows linear behavior of FWHM as a function of depth for

various tissues.

Figure 3.6 FWHM as a function of varying power (Q) for different depths (a)


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Figure 3.7 FWHM as a function of depth for various tissues

Each tissue represented by the quotient E/K has its own corresponding unique linear curve.

Thus, given the FWHM which is derived from the surface temperature profile allows the

direct computation of the point source depth (Figure 3.7).


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Figure 3.8 Computing source depth for a specific tissue

In this example, given the tissue represented by E and K in Table 3.2 it is possible to select

the relevant linear curve (Figure 3.8) and to extract the heat source depth:

$0.42896 1.25 [ ]

2.0534FWHMa cm−

= = (Equation 3.7)

After computing the source depth, the source power may be computed. The computation is

based on the linear relation between the curve area (A) and source power (Q). The simulation

results show that for a specific E/K quotient, each depth has its own unique linear curve A(Q).

Figure 3.9 shows this behavior for the example.


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The slopes of these A(Q) curves (see Figure 3.10) can be well fitted as a sum of two decaying

exponents as source depth deepens. This exponential behavior is shown in Figure 3.11.

Estimating the source power (Q), should be carried out by substituting the already computed

source depth a in the exponential expression fitted in Figure 3.11 in order to derive the right

slope (p):

$ $ $1.691 0.17571.25 [ ] 87.25 95.58 87.272a aa cm p e e− ⋅ − ⋅= ⇒ = + = (Equation 3.8)

This slope parameter facilitates the selection of the appropriate linear curve of A(Q)

(see Figure 3.12), calculating the power Q straightforwardly, since the approximated value of

the area (A) is already known from the primary Lorentzian curve fitting:

[ ]2 8.8968.896 Q 0.187.272

AA cm Wattp

⎡ ⎤= ⇒ = = =⎣ ⎦ (Equation 3.9)

Figure 3.9 Area below the surface temperature profile (A) as a function of the source power (Q)


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Figure 3.10 Area (A) as a function of power (Q) for various source depths

Figure 3.11 Exponential behavior of A(Q) slopes

p=125.01

p=96.172

p=80.491

p=70.189

p=62.749

p=57.053

p=125.01

p=96.172

p=80.491

p=70.189

p=62.749

p=57.053


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Figure 3.12 Selected A(Q) curve based on the p-parameter

In conclusion, the estimation of the depth and power of heat source in comparison with the

real parameters is shown in Table 3.3:

Table 3.3 Comparison of real parameters and estimated parameters

Parameter Real Value Estimated Value Variation

Depth (a) 1.2 [cm] 1.25 [cm] 4.167 %

Power (Q) 0.1 [Watt] 0.1 [Watt] 0 %

The variation between real values and estimated values shown in Table 3.3 may occur

primarily in the forward solution calculations. Due to the fact that the computation is carried

out discretely, the spatial resolution in the radial direction is an influencing factor. To improve

and eliminate this factor, the resolution may be reduced or suitable interpolation and/or

smoothing may be applied.


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Moreover, since the calculation of the infinite integral( ) ( )0

0

exp y a J rd

E Kλ λ λ

λλ

∞ − +⎡ ⎤⎣ ⎦+∫ , which

comprises the most of Eq. 3.5, is impossible to be carried out analytically, the method and

accuracy of its computation are significant in the final results.

Additional and influential factors may occur during the inverse procedure that mostly consists

of curve fitting operations. Various methods and functions for curve fittings can present

variations in the final results.

3.F. Spherical Simulation

Following the solution assuming a point heat source as shown in section 3.D., the problem

may be broadened and a spherical heat source can be assumed. This model is based

analogously on a study conducted by Gannot et. al. [42] that deals with the detection and

localization of tumors in tissue by virtue of fluorophore conjugated specific antibodies as

tumor surface markers. In particular, their study focuses on the understanding and

quantification of the pharmacokinetics of fluorophore conjugated antibodies in the vicinity of

a tumor.

Hence, in our model we have located the binding sites of nanoparticles in a volume layer

around the tumor surface as shown in Figure 3.13. The application of external AC magnetic

field induces the heating of nanoparticles' outer layer creating roughly two spherical

temperature regions: the tumor region (marked in yellow) and a higher temperature region

comprised of the magnetic nanoparticles (marked as red).


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For simplicity, we assume an average uniform temperature representing each region: Ttumor

and Tnp, respectively. Since the outer region (red) shows significantly higher temperature

(assumed ~ΔT ≥ Tnp - Ttumor ≥ 5˚C), we may refer to the nanoparticles layer only, while

neglecting the tumor's temperature, i.e. a spherical shell with a constant and uniform

temperature field of Tnp. We still assume an infitisimal width of nanoparticles' layer.

Figure 3.13 Spherical model for thermal analysis of a tumor

The simulation modeling a spherical shell heat source is based on the use of fundamental

solution for a point heat source shown in section 3.D. A spherical shell characterized by a

radius R and an effective power Q is embedded while its center is located in depth a beneath

the surface. The shell's surface is represented by the superposition of discrete point sources

scattered in a predetermined spatial resolution. The point sources' spreading is determined

according to a spherical coordination system ( ), ,z θ φ (see Figure 3.14). Since each point

source is representing a different fraction of the spherical surface, it owns a corresponding

effective power source (Figure 3.15). This is taken into account by multiplying the

fundamental surface field temperature Tz with its corresponding weight (Wi) as shown

hereinafter.

Tnp

Tumor

Bound magnetic nanoparticles

Tumor

Ttumor


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The Tz vector is the temperature field at the surface (y=0) produced by a single point source

located in depth z. It is designated as a fundamental parameter since it is being calculated for a

unit of power source, i.e. 1 Watt.

Figure 3.14 Spherical coordination system

Figure 3.15 Nanoparticles superficial distribution on the sphere


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The weights are calculated using the following expression shown below:

spherei i

sphere

QW S

S= ⋅ (Equation 3.10)

where

iW is the corresponding weight,

sphereQ is the total power generated by the entire sphere,

sphereS is the total surface of the sphere,

iS is the fractional surface represented by a certain point source,

Hence, each point source surface field temperature (Tpoint) is calculated by the expression

point i zT W T= ⋅ (Equation 3.11)

In our model the nanoparticles' shell is characterized by an infitisimal width dimension.

Computing a shell with a different width dimension, may be simply carried out by the

superposition of various shells with different radiuses.

Validation

The validation of the simulation modeling a spherical shell source is much more complex than

a point heat source; hence, we chose to execute it in two different approaches.

The first approach is trivial. We compare a spherical shell with a radius R 0 and a point

source. Results are shown in Figure 3.16 and present an expected behavior of the two curves.


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However this validating approach hasn't convinced us completely. Therefore, we seek to

compare our simulation results to a close-enough analytical solution. The comparable solution

proposed by Small and Weihs [43] introduces an exact solution in series form for the steady

temperature distribution in a semi-infinite solid medium bounded internally by a spherical

inclusion of uniform temperature. Heat transfer at the interface is via convection. Their

analysis is performed in an orthogonal coordinate system tailored to the specific problem, i.e.

bispherical coordinate system ( ), ,η θ ψ allowing simpler boundary conditions and the

achievement of an exact solution (Figure 3.17).

Figure 3.16 Comparison of a point source and spherical source (R=0.01 cm). The curve of

spherical source is deliberately elevated by 1˚C in order to distinguish the two curves


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Figure 3.17 Problem modeling in bispherical coordinate system

(Small and Weihs, reprinted of ref. [43] )

Following mathematical transformation, the problem, including boundary conditions, is

described as follows:

( )

2 0: 1: 0 1

0 : cosh 0

aa

qhk

φη φ

η φφη η ξ φη

∇ =∀ = − =∀− ≤ ≤ ≤

∂∀ = − + =

∂

(Equation 3.12)

φ is the nondimensional temperature excess, a defines the spherical surface and cosξ θ= .

The physical parameters of the problem are the heat transfer coefficient (h), thermal

conductivity of the medium (k) and the distance between limiting points

( 2 22 2q D R= − , D – distance from sphere center to interface, R – sphere radius).


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The solution suggested by Small and Weihs [43] for the nondimensional temperature

distribution in the solid medium is depicted as:

( ) ( ) ( )( )

12

0

sinh tanh cosh, cosh cosh2

cosh

n

n man

B m ma mP me

ma

η ηφ η ξ η ξ ξ η

∞

−=

+ ⋅⎡ ⎤⎢ ⎥= − ⎢ ⎥+⎢ ⎥⎣ ⎦

∑ (Equation 3.13)

where Pn is the Legendre polynomial of order n and m is constant depend of n.

Bn may be found by several techniques described in detail in their work. In spite of being

exact and complete, the analytical derivation of Bn is extremely cumbersome to apply due to

the lengthy algebraic expressions. Therefore, we chose an approximated numerical method in

computing the Bn coefficients.

The surface temperature field which is in interest for our needs is achieved by substituting

0η = in Eq. 3.13. Naturally, the implementation of the solution depicted in detail above

requires strong computational means.

So before exploiting it as a validation tool, we are committed to ensure the validity of this

solution itself. Figure 3.18 shows the validation of this solution versus Small and Weihs

results demonstrating the surface distribution for various D/R and Bi = 1 (Biot Modulus).


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Figure 3.18.A Simulating Small and Weihs solution

Figure 3.18.B Solution suggested by Small and Weihs (1977), (Reprinted ref. [43])

Figure 3.18 Validation of an auxiliary MATLAB® code simulating Small and Weihs solution


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Now that we were convinced with the credibility of our validating simulation, we are able to

validate our spherical model (via 2nd approach). Nevertheless, we face one main hurdle when

using this comparison. While Small and Weihs's model deals with constant temperature at the

sphere surface, our case involves a spherical shell with variable temperature as a function of

depth.

Dealing with this hurdle, we compared the two models under the constrains D>>R and h>>k.

Then, we found an effective spherical shell for our model presenting constant temperature,

with new effective parameters D* and R* as shown schematically in Figure 3.19.

Now we are allowed to compare it with the solution suggested by Small and Weihs.

An example is shown in Figure 3.20 where 3230 ; 4.2 10W WE K

m C cm C−⎡ ⎤ ⎡ ⎤= = ×⎢ ⎥ ⎢ ⎥⋅ ⋅⎣ ⎦ ⎣ ⎦o o

.

The red curve represents an "analytical" solution computed based on Small and Weihs's

solution. It is being compared to the blue curve representing the spherical simulation results.

Based on the results mentioned above we validated our spherical simulation which is capable

of simulating the surface temperature generated by an embedded spherical shelled heat

source.


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Figure 3.19 Effective spherical model

Figure 3.20 Comparison of Small and Weihs solution with the spherical simulation

The results shown above validate of the simulation of an embedded spherical shelled heat

source, by solving the forward problem.

r

y

R

r

y

R

Ta

Ta

D, R D*, R*

a>>R

E>>K

D


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These results may lay the basis for a future inverse model of a spherical source based on the

forward problem's solution, analogously presented with regard to a point heat source.

Since a problem which includes a spherical source obtains an additional parameter (i.e. radius

of the sphere), its solution is much more complex and compels the discovery of supplemental

mathematical relations.


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3.G. References

1. Qi H, Diakides NA: Thermography (Invited). In Encyclopedia of Medical Devices and Instrumentation. 2nd Ed. edition. Edited by Webster JG: John Wiley & Sons; 2006

2. Snyder WE, Qi H, Elliott RL, Head JF, Wang CX: Increasing the Effective Resolution of Thermal Infrared Images. Engineering in Medicine and Biology Magazine, IEEE 2000, 19:63.

3. Braunstein M, Chan RW, Levine RY: Simulation of Dye-Enhanced Near-IR Transillumination Imaging of Tumors. In.; 1997: 735.

4. Kaczmarek M, Nowakowski A: Analysis of Transient Thermal Processes for Improved Visualization of Breast Cancer Using IR Imaging. In.; 2003: 1113.

5. Qi H, Kuruganti PT, Snyder WE: Detecting Breast Cancer from Thermal Infrared Images by Asymmetry Analysis (chapter 27). In Medical devices and systems. Taylor & Fracis Group; 2006

6. Walter FG, Bin Z, Yuan-Hsiang C, Xiao Hui W, Glenn SM: Generalized Procrustean Image Deformation for Subtraction of Mammograms. In. Edited by Kenneth MH. SPIE; 1999: 1562-1573.

7. Fang-Fang Y, Maryellen LG, Kunio D, Carl JV, Robert AS: Computerized Detection of Masses in Digital Mammograms: Automated Alignment of Breast Images and its Effect on Bilateral-Subtraction Technique. Medical Physics 1994, 21:445-452.

8. Zheng B, Chang YH, Gur D: Computerized Detection of Masses from Digitized Mammograms: Comparison of Single-Image Segmentation and Bilateral-Image Subtraction. Acad Radiol 1995, 2:1056-1061.

9. Jonathan FH, Charles AL, Robert LE: Computerized Image Analysis of Digitized Infrared Images of Breasts from a Scanning Infrared Imaging System. In. Edited by Bjorn FA, Marija S. SPIE; 1998: 290-294.

10. Lipari CA, Head JF: Advanced Infrared Image Processing for Breast Cancer Risk Assessment. In.; 1997: 673.

11. Hairong Q, Head JF: Asymmetry Analysis Using Automatic Segmentation and Classification for Breast Cancer Detection in Thermograms. In.; 2001: 2866.

12. Mabuchi K, Chinzei T, Fujimasa I, Haeno S, Motomura K, Abe Y, Yonezawa T: Evaluating Asymmetrical Thermal Distributions Through Image Processing. Engineering in Medicine and Biology Magazine, IEEE 1998, 17:47.

13. Kuruganti PT, Hairong Q: Asymmetry Analysis in Breast Cancer Detection Using Thermal Infrared Images. In.; 2002: 1155.

14. Jakubowska T, Wiecek B, Wysocki M, Drews-Peszynski C: Thermal Signatures for Breast Cancer Screening Comparative Study. In.; 2003: 1117.

15. Hadamard J: Lectures on Cauchy's Problem in Linear Differential Equations. New Haven, CT: Yale University Press; 1923.

16. Alifanov OM: Inverse Heat Transfer Problems. Berlin: Springer-Verlag; 1994. 17. Beck JV, Blackwell B, Clair CS: Inverse Heat Conduction: Ill-Posed Problems. New

York: Wiley; 1985. 18. Murio DA: The Mollification Method and the Numerical Solution of Ill-Posed

Problem. New York: Wiley; 1993. 19. Tikhonov AN: Solution of Ill-Posed Problems. Washington, DC: Hlasted; 1977. 20. Beck JV, Bleckwell B: Inverse problems. In Handbook of Numerical Heat Transfer.

Edited by Minkowycz WJ, Sparrow EM, Schneider GE, Pletcher RH. New York: Wiley; 1988


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21. (Editor) KAW: Inverse Engineering Handbook. Boca Raton, FL: CRC Press; 2002. 22. Ozisik MN, Orlande HRB: Inverse Heat Transfer: Fundamentals and Applications.

New York: Taylor & Francis; 2000. 23. Hisada T, Nakagiri S: Stochastic Finite Element Method Developed for Structure,

Safety and Reliability. In 3rd International Conference on Structure, Safety and Reliability; New York. Wiley; 1989: 395-408.

24. Hisada T, Nakagiri S: Role of Stochastic Finite Element Methods in Structural Safety and Reliability. In 4th International Conference on Structure, Safety and Reliability. 1985: 385-394.

25. Shinozuka M, Deodatis G: Response Variability of Stochastic Finite Element Systems. Journal of Engineering Mechanics 1988, 114:499-519.

26. Xiu D, Lucor D, Su C-H, Karniadakis GE: Stochastic Modeling of Flow-Structure Interactions Using Generalized Polynomial Chaos. Journal of Fluids Engineering 2002, 124:51-59.

27. Jardak M, Su C-H, Karniadakis GE: Spectral Polynomial Chaos Solutions of the Stochastic Advection Equation. Journal of Scientific Computation 2002, 17:319-338.

28. Xiu D, Karniadakis GE: Modeling Uncertainty in Flow Simulations via Generalized Polynomial Chaos. Journal of Computational Physics 2003, 187:137-167.

29. Narayanan VAB, Zabaras N: Stochastic Inverse Heat Conduction Using a Spectral Approach. International Journal for Numerical Methods in Engineering 2004, 60:1569-1593.

30. Narayanan VAB, Zabaras N: Variational Multiscale Stabilized FEM Formulations for Transport Equation: Stochastic Advection-Diffusion and Incompressible Stochastic Navier-Stokes Equations. Journal of Computational Physics 2005, 202:94-133.

31. Zabaras N: Inverse Problems in Heat Transfer, Chapter 17. In Handbook of Numerical Heat Transfer. 2nd Ed. edition. Edited by Minkowycz WJ, Sparrow EM, Murthy JY: John Wiley & Sons; 2004

32. Pennes HH: Analysis of Tissue and Arterial Blood Temperatures in the Resting Human Forearm. J Appl Physiol 1998, 85:5-34.

33. Wulff W: Energy Conservation Equation for Living Tissue. IEEE Transactions On Biomedical Engineering 1974, BM21:494-495.

34. Weinbaum S, Jiji LM: A New Simplified Bioheat Equation for the Effect Of Blood-Flow on Local Average Tissue Temperature. Journal of Biomechanical Engineering-Transactions of the ASME 1985, 107:131-139.

35. Rubinsky B: Numerical Bio-Heat Transfer. In Handbook of Numerical Heat Transfer. 2nd Ed. Edited by Minkowycz WJ, Sparrow EM, Murthy JY: Whily & Sons; 2006

36. Wissler EH: Pennes' 1948 Paper Revisited. J Appl Physiol 1998, 85:35-41. 37. Draper JW, Boag JW: Calculation of Skin Temperature Distributions in

Thermography. Physics In Medicine And Biology 1971, 16:201-&. 38. Awbery JH: Heat Flow when the Boundary Condition is Newtonians's Law.

Philosophical Magazine 1929, S. 7:1143-1153. 39. Feasey CM, Davison M, James WB: Effects of Natural and Forced Cooling on

Thermographic Patterns of Tumors. Physics in Medicine and Biology 1971, 16:213-&.

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41. Davison M: Skin Temperature Distributions over veins and tumors. Physics in Medicine and Biology 1972, 17:309-310.

42. Fibich G, Hammer A, Gannot G, Gandjbakhche A, Gannot I: Modeling and Simulations of the Pharmacokinetics of Fluorophore Conjugated Antibodies in Tumor Vicinity for the Optimization of Fluorescence-Based Optical Imaging. Lasers in Surgery and Medicine 2005, 37:155-160.

43. Small RD, Weihs D: Thermal Traces of a Buried Heat Source. Journal of Heat Transfer-Transactions of the ASME 1977, 99:47-52.

Chapter 4 The System

4–88

4. The System

4.A. Introduction

The design of a system implementing an early detection of malignant cell, i.e. cancerous

tumor and essential treatment, is expected to fulfill several fundamental requirements to be

applicable. This novel method should be non-invasive or at least minimally invasive since the

nanoparticles should be inserted into the human body (e.g. injected into the blood circulation).

The system should be cost-effective, accurate, reliable and capable of being implemented as a

bed-side device, unlike other modalities such as MRI and CT. The application of a closed-

loop system allows the detection and treatment procedures to be performed in a single device

and enabling a real-time treatment based on an imaging feedback. The lack of a feedback is a

drawback of many modalities known in the art. A description of the suggested system is

depicted hereinafter.

Figure 4.1 illustrates the main building blocks of the suggested system comprised of means

for:

(i) Heat generation

(ii) Thermal image acquisition

(iii) Thermal image Analysis (see Chapter 3)


4–89

Figure 4.1 Schematic description of the system

4.B. Heat Generation

Heat generation is conceptually comprised of two parts:

(i) Magnetic nanoparticles (for “heat emission”)

(ii) Magnetic field (for nanoparticles’ excitation)

Heat generation is established by the application of an alternative magnetic field on the

magnetic nanoparticles which are already located within the tissue, bioconjugated to the

tumor's surface. The magnetic nanoparticles (heating mechanism and affecting parameters)

were discussed broadly in chapter 2. This section focuses on the generation of appropriate

magnetic fields, which is not a trivial task considering the requirements we introduce in this

work.


4–90

The magnetic field is generated by a magnetic system usually comprised of:

(i) Antenna (e.g. coils)

(ii) AC current generator

The design of the magnetic system is implemented bottom-to-up, i.e. after choosing the

desirable field parameters (e.g. field strength, frequency), we are capable of designing the

system itself (e.g. coils, circuitry). Determination of the desirable parameters is not trivial

since the system is characterized by a large number of degrees-of-freedom.

Previous research works investigated various fields: Kalambur et al (2005) used a 1kW

generator and 4 turn RF coil to produce field strength of 0 14 kAH m⎡ ⎤= ⎣ ⎦ and frequency

[ ] 175f kHz= ; Giri et al (2005) examined the fields [ ]( )10 45 ,300kA kHzm⎡ ⎤− ⎣ ⎦ ;

Ma et al used a 15kW RF generator to produce the field [ ]( )32.5 ,80kA kHzm⎡ ⎤⎣ ⎦ ; Hergt et al

(2004) shows losses under the AC field [ ]( )11 ,410kA kHzm⎡ ⎤⎣ ⎦ ; Pankhurst et al (2003)

investigated nanoparticles under the extensive field region of [ ]( )0 15 ,0.05-1.2kA MHzm⎡ ⎤− ⎣ ⎦

and Kim et al examined the influence of fields of [ ]( )110 ,0.1-15A MHzm⎡ ⎤⎣ ⎦ .

The two principle parameters of the externally applied magnetic field, i.e. the frequency and

strength, are limited by deleterious physiological responses to high frequency magnetic fields

[1, 2]: stimulation of peripheral and skeletal muscles, possible cardiac stimulation and

arrhythmia, and non-specific inductive heating of tissue. Generally, the useable range of

frequencies and amplitudes is considered to be f = 0.05 – 1.2 MHz and H = 0 – 15 kA/m.


4–91

Experimental data on exposure to much higher frequency fields comes from groups such as

Oleson et al [3] who developed a hyperthermia system based on inductive of tissue, and

Atkinson et al [4] who developed a treatment system based on eddy current heating of

implantable metal thermoseeds. Atkinson et al. concluded that exposure to fields where the

product H · f does not exceed 4.85 × 108 kA/(m·s)-1 is safe and tolerable [5].

Hence, following the physiological constraints shown above and based on previous research

results such as those mentioned above, the desirable averaged working point was chosen to

be [ ]0 10 ; 100kAH f kHzm⎡ ⎤≈ ≈⎣ ⎦ .

4.C. Antenna Configurations

4.C.1. Solenoid

Trying to meet with the fundamental objectives of the suggested system, particularly cost-

effectiveness and bed side capability, we seek an alternative technology for the commonly-

used giant and expensive RF generators of several kilo-Watts and up, since they cost about

10k-100k of dollars and are not comfortable to locate near the patient’s bed or at the clinic.

Most of research works in this field are using a single RF coil with a few turns, e.g. 3-4 turns,

as shown in section 4.B.

A major drawback of the coil configuration is that there is no accessibility for any imaging

element, such as an IR camera. If we had desired to use that kind of solenoid coil, it would

have been had to be characterized with a very large diameter, and the camera would have

been exposed to the AC field. Hence, this configuration is not applicable and does not apply

to our needs.


4–92

4.C.2. C-Core

Another suggested alternative which have been considered is the C-core configuration.

The use of a C-shaped ferrite core wounded with a conducting wire is common in the field of

transformers. While air gaps in the field of transformers and power electronics are of the

order of a few millimeters or less, we seek to obtain an air gap of about 5 centimeters

enabling us to place there the tissue sample and to allow imaging device accessibility.

Figure 4.2 Schematic description of a C-core configuration

Figure 4.2 shows schematically the C-core configuration. In our theoretical calculations we

assumed that the core is made of some sort of an iron (e.g. silicon-iron for losses reduction).


4–93

From Maxwell's equation we can write:

∫∫ ⋅=⋅sc

dsJdlH (Equation 4.1)

Assuming a coil with N turns and current i, we get a discrete form of Eq. 4.1:

which in our case can be written as:

(Equation 4.2)

where:

Hc, lc are the core magnetic field strength and length respectively.

Hg, lg are the air gap magnetic field strength and length respectively.

Substitution of the relation BHμ

= in Eq. 4.2 yields in:

0

gcc g

BB l l Niμ μ

+ = (Equation 4.3)

Since we may assume that , B= c g c gB B BAφ φ φ φ= = ⇒ = = ,

we can write: 0 0

g gc c

c g

l ll lNi NiA A A

φφ φμ μ μ μ

⎛ ⎞⎛ ⎞ ⎡ ⎤+ = ⇒ + =⎜ ⎟⎜ ⎟ ⎢ ⎥⎜ ⎟⎝ ⎠ ⎣ ⎦⎝ ⎠

(Equation 4.4)

where φ is the magnetic flux.

For simplicity, we may assume that the core permeability (µr) is much larger than air

permeability (µ0), i.e. µr >> µ0


4–94

hence: [ ]0 weberg

NiAlμφ = (Equation 4.5)

Following Eq. 4.5, it is noticeable that we should try to have as much as large area A (trying

to avoid fringe effects), and as much as small lg, trying to achieve a larger magnetic flux.

The core material should be picked according to its saturation value of flux density (since we

wish it wouldn't be saturated, we plan working on the linear region, satLiBNA

= where µr and

Bsat are properties of the material).

Unfortunately, the C-core alternative is an impractical solution. Since we would like it to be a

bed-side device with a sufficiently large lg (e.g. 5 cm) which enables the positioning of an

organ for example therebetween, it is necessary to provide a large power source, which cannot

be portable. The C-core configuration also limits us to a predetermined length lg, which

cannot be adjusted upon user’s discretion. An example for an attempt to implement a system

for the purpose of treatment solely is depicted in the work of Jordan et al [6].

4.C.3. Helmholtz Coil

An alternative preferred method relies on a Helmholtz coil configuration. A Helmholtz coil is

a parallel pair of identical coils (e.g. circular coils) which are spaced one radius apart and

wound so that the electrical current flows through both coils in the same direction, as shown

in Figure 4.3. The fundamental premise of this configuration is that it produces a uniform

(homogeneous) magnetic field between the coils with the primary field component parallel to

the axes of the two coils and its amplitude which behaves according to the approximated

formulation given below [7] (This formula relates to an ideal set of Helmholtz coils):


4–95

( )

20

3 3 32 22 2 2 2 2

2 2 2 2

1 1

2 22 1 1x

NibBx ax x axb ab a b a

μ

⎡ ⎤⎢ ⎥⎢ ⎥

= × +⎢ ⎥⎛ ⎞ ⎛ ⎞+ −+ ⎢ ⎥+ +⎜ ⎟ ⎜ ⎟⎢ ⎥+ +⎝ ⎠ ⎝ ⎠⎣ ⎦

(Equation 4.6)

where:

Bx – the magnetic field, in [Teslas], at any point on the axis of the Helmholtz coil. The

direction of the field is perpendicular to the plane of the loops.

i - the current in the wire, in [Amperes].

N – number of turns per coil.

b – the radius of the current loops, in [meters].

a – the distance, on axis, from the center of the Helmholtz coil, in [meters].

Figure 4.3 Schematic description of Helmholtz coils configuration


4–96

Additional advantages of the Helmholtz configuration are that (1) it enables an open

workspace for sample (tissue) handling and imaging device accessibility, i.e. an easy and safe

path for placing the IR camera, and (2) it enables the change of the distance between the two

coils, i.e. adjustable workspace (unlike the C-core configuration, for example).

For simplicity, the design is based on the magnetic flux density applied on the center between

the two coils where x=0, then Eq. 4.6 is reduced the expression:

0

32

0|

45x

LNIBR

μ=

⎛ ⎞= ⋅⎜ ⎟⎝ ⎠

(Equation 4.7)

4.D. Current Generation

We would like to induce a simple alternative current (AC) in the pair of Helmholtz coils, e.g.

triangular wave, for simplicity. Since the derivative of the current over the coils is

proportional to the voltage, we should generate a square-shaped wave (see Figure 4.4).

Fortunately, designing a generator which produces a symmetrical squared wave over the coils

may be relatively cost-effective and energy conservative. This design also allows the

maximization of components' efficiency.

The voltage over coils should be high enough to facilitate current elevation from minimum to

maximum during a single half-cycle:

maxmax

2 42

LL S

IdIV L L I L fTdt⋅

= ⋅ = ⋅ = ⋅ ⋅ ⋅ (Equation 4.8)


4–97

The chosen wires comprising the coils are made of common insulated copper wires (Ø1[mm])

and the coils themselves are characterized by a radius of R=0.05[m] while each coil has 85

turns (N=85). The magnetic induction of each coil was measured and found to be L=2.4[mH].

Figure 4.4 Wave templates generated by the system

t

B(t)

Bmax

-Bmax T

t

IL(t)

IL ,max

- IL ,max T

t

VL(t)

VL

- VL ,max T


4–98

In order to produce a desired high voltage over the coils, the system design includes power

transformer for voltage elevation, as shown on the system's block scheme in Figure 4.5.

Figure 4.5 System's block scheme

The power transformer has turns ratio of 1:n, and therefore:

; bL b L

IV n V I n= ⋅ = (Equation 4.9)

The power supply of the system is composed of an oscillator (PMW controller) with a tunable

frequency, boost transformer and a push-pull full bridge inverter (H-bridge), as shown in

Figure 4.6. The full bridge is mainly composed of four FETs to allow the alternate current.

Figure 4.6 The power generator's block scheme

Power Supply

Vb

Power

Transformer

1: n

Helmholtz

Coils

N, L, R

Ib IL

Vb ± VL ±

PWM Controller

VPWM

Boost

Transformer

Full Bridge

Ib IFB

Vb ± VFB ±


4–99

4.E. Thermal Image Acquisition

The thermal imaging is carried out by an IR camera (FLIR A40), which detect the infrared

emission which is emitted from the examined object’s surface (e.g. phantom).

The IR camera is positioned perpendicularly above the object, which is situated within the

magnetic field induced between the two coils. When the magnetic field is applied the

nanoparticles generate heat which can be detected by the IR camera.

4.F. The Integrated System

Integrating the main building blocks of the required system mentioned above comprises the

system as shown in Figure 4.7. The system should preferably include a closed-loop

feedback to allow the adjustment of the field parameters (generated by the coils) according to

the temperature readings (acquired via the IR camera).


4–100

Figure 4.7 Schematic description of the closed-loop system

Obviously, interruption by the user (e.g. physicist) is possible, such as for example the tuning

of magnetic field when changing its mode of operation (e.g. achieving therapy requires a

substantial increase of the temperature within the treated tissue).

Yet, the current laboratory system that has been designed and built as shown in Figure 4.8 is

not capable of generating the required magnetic field due to technological issues. Still, it

requires more than 300 Volts to theoretically generate 5 mT only. This may also require

dedicated cooled coils and the incorporation of safety means. Moreover, a closed loop

feedback has not been implemented yet.


4–101

Thermal Camera FLIR

Coils

Power Transformer

Power Supply

Full-Bridge

Thermal Camera FLIR

Coils

Power Transformer

Power Supply

Full-Bridge

Figure 4.8 Laboratory system


4–102

4.G. References

1. Oleson J R, Cetas T C, Corry P M: Hyperthermia by Magnetic Induction: Experimental and Theoretical Results for Coaxial Coil Pairs. Radiat. Res.1983, 95:175-186.

2. Reilly J P: Principle of Nerve and Heart Excitation by Time-Varying Magnetic

Fields. Ann. New York Acad. Sci. 1992, 649:96-117. 3. Oleson J R, Heusinkveld R S, Manning M R: Hyperthermia by Magnetic Induction:

II. Clinical Experience with Concentric Electrodes. Int. J. Radiat. Oncol. Biol. Phys. 1983, 9:549-556.

4. Atkinson W J, Oleson J R, Heusinkveld R S, Manning M R: Hyperthermia by

Magnetic Induction: II. Clinical Experience with Concentric Electrodes. Int. J. Radiat. Oncol. Biol. Phys. 1983, 9:549-556.

5. Pankhurst Q A, Connolly J, Jones S K, Dobson J: Applications of Magnetic

Nanoparticles in Biomedicine. J. Phys. D: Appl. Phys. 2003, 36:167-181. 6. Jordan A, Scholz R, Maier-Hauff K, Johannsen M, Wust P, Nadobny J, Schirra H,

Schmidt H, Deger S, Loening S, Lanksch W, Felix R: Presentation of a New Magnetic Field Therapy System for the Treatment of Human Solid Tumors with Magnetic Fluid Hyperthermia. Journal of Magnetism and Magnetic Materials 2001, 225:118-126.

7. Lerner L S: Physics for Scientists and Engineers. Jones and Bartlett, 1997.

Chapter 5 Conclusions and Future Work

5–103

5. Conclusions and Future Work

5.A. Conclusions

This research deals with a system for the detection of malignant tumors and for the treatment

of those tumors. The physical principle is the generation of heat for both diagnosis and

therapy. The heat generation and its amplification above the body’s normal temperature level

are achieved by biocompatible magnetic nanoparticles that are bioconjugated to the tumor and

their stimulation by a suitable external magnetic field.

This procedure is specifically targeted to the tumor since it relies on the capability of the

immune system and its detectability, i.e. the body knows best to locate the malignant cells.

Hence, the bioconjugation of the nanoparticles to the antigen-antibody complex is probably

the most accurate method to reach the real malignancies.

The thermal model that was developed as a part of this research enables the derivation of two

crucial parameters: the depth of a heat source and its local temperature. This algorithm is

based on a single 2D thermal image of the medium surface solely. Thus, there is no need for

multiple angles, images and/or invasive measurements of temperature. The algorithm which

relies on solving the forward thermal problem is simple, does not require extensive resources

and does not require special involvement from the side of the patient and/or physicist.

On top of the in-silico validation that has been conducted, still there is a need for an in-vitro

validation and ex-vivo and/or in vivo examination of this model.

Moreover, the whole concept for enabling the unique system is presented. A preferable

configuration for the generation of the AC magnetic field is proposed and its characteristics

should be still evaluated.


5–104

In conclusion, this research work may serve as a novel fundamental concept for having both

diagnosis and therapy in a single device, where the transfer between both modes is merely a

simple change of field parameters. The minimally-invasive method is selective and has the

potential of being very accurate, reliable and friendly both to the operator (e.g. physician) and

to the patient. It incorporates various field of research and I believe and hope that it can be

developed into a bedside, cost effective and applicable device that may assist in a better and

improved detection and treatment of one of the prevalence diseases that the medical industry

currently has to deal with.


5–105

5.B. Future Work

This research shows a fundamental design of the system which is meant to pursue thermal

diagnosis and therapy in one single device which is still not bulky and can operate near the

patient’s bed, be accurate, reliable and cost effective. The concept and modularly design that

were described in this research work is the basis for such a system. The system comprises

several main modules: heat generation (including nanoparticles and the external field

generation), thermal imaging, analysis and feedback. This multi-disciplinary system

incorporates various scientific and technological fields. Furthermore, each module may be

investigated and improved independently with no direct relation to the other modules.

Producing the required external magnetic field should be designed to generate a higher

magnetic field, preferably with adjusted parameters, e.g. magnitude, frequency, distance

between the coils. One of the goals in my view is to increase the efficiency of this module

and to enable the use of standard voltage and current of a domestic electrical infrastructure.

The analysis module is based on the acquired raw thermal image and includes the processing

for improving the data quality and derivation of desired parameters. This module may be

approached by various methods implementing different mathematical models, computational

algorithms etc. It is desirable to try and derive additional parameters (other than tumor’s

depth and tumor’s temperature) such as for example 3D geometrical boundaries of the tumor.

The current model is a basic model that relies on ideal assumptions (e.g. homogeneous tissue,

steady state). Furthermore, the inverse model assumes a point source which is merely an

ideal approximation for much more complicated scenarios that involve undefined tumor

boundaries, noise signals, physiological, anatomical abnormalities etc.


5–106

The closed-loop feedback that allows control on the external magnetic field’s parameters (e.g.

magnitude and frequency) can be automatically adjusted based on the thermal imaging to

maintain appropriate contrast and to achieve control on the heat expansion within the tissue in

real-time in order not to harm surrounding healthy tissue. This can be carried out by a for

example LabView® dedicated program.

The first stage to be investigated is naturally in-vitro, i.e. examining the behavior of the

nanoparticles within a tissue-mimicking material. It is not trivial to choose this phantom

material since it has to fulfill two qualities: to imitate the thermal characteristics of a tissue

and on the same time to imitate the magnetic characteristics of a tissue, preferably on a

specific frequencies range. This may be important for testing the tissue behavior under the

alternative external magnetic field. For instance, the tissue will probably heat up only from

the magnetic field effect, a factor which should be taken into consideration and be eliminated

during thermal analysis. Such materials may compose derivatives of agar, carrageenan or

special plastics such as A150.

Obviously, examining this method in-vivo requires also progress in the biological field of

bioconjugation and the discovery of new and more specific signals for detection of malignant

cells such as for example novel cancer specific-antigens.

תקציר

תקציר

, אשר תהה חדשנית )IR( אדומה- ארמטרת מחקר זה הינה לפתח טכניקת דימות תרמית המבוססת על קרינה אינפ

- ננויתרונותיהם של ותשפר את השיטות הקיימות והמוכרות לנו כיום תוך ניצול , לא פולשנית ובעלת עלות נמוכה

הינם בעלי יכולת ייצור של ) קומפטביליים- ביו(ל שאינם מזיקים לגוף האדם "החלקיקים הנ. חלקיקים מגנטיים

מגיע לפני השטח של הריקמה ונפלט , מתקדם בריקמההנוצר החום . חום תחת השפעתו של שדה מגנטי משתנה

ניתוח טמפרטורת פני השטח של הריקמה מאפשר גזירה של .י עדשה של מצלמה תרמית"ע תהנרכש IRכקרינת

.בסביבתםהמתהווה ה המקומית הרל הטמפרטומיקום החלקיקים בעומק הריקמה וש

.ספציפי של החלקיקים לפני השטח של הגידולביולוגי טכניקה זו יכולה לשמש ככלי אבחוני הודות לצימוד

מעלות ( 5°C בלמשללהעלות את הטמפרטורה של החלקיקים המצומדים יתןנ, תחת שדה מגנטי מתאים, כך

העלאת הטמפרטורה באיזור הגידול . של הגידול ללא גרימת נזק לריקמהתרמי דבר המאפשר דימות , )צלזיוס

גורמת להרס מקומי ובלתי הפיך לאתר הממאיר ללא פגיעה , 100°Cועד 65°Cבין למשל ,באופן משמעותי

ככלי טיפולי ממוקד בגידולים אף תהליך זה יכול להוות עבורנו , בנוסף לדימות התרמי .רקמות השפירות השכנותב

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סליינר -ש זנדמן "בית הספר לתארים מתקדמים ע

תרמיים ממוקדים לאבחון וטיפול בגידולים וריפוישיטה לדימות

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רפואית-בהנדסה ביו" המוסמך אוניברסיט"חיבור זה הוגש כעבודת גמר לקראת התואר

ידי-לע

עידו מיכאל גשייט

רפואית-העבודה נעשתה במחלקה להנדסה ביו

ר אברהם דיין"ר ישראל גנות וד"בהנחיית ד

ח"מרחשוון התשס

אביב -אוניברסיטת תל ש איבי ואלדר פליישמן"הפקולטה להנדסה ע

סליינר -ש זנדמן "בית הספר לתארים מתקדמים ע

תרמיים ממוקדים לאבחון וטיפול בגידולים וריפוישיטה לדימות

חלקיקים מגנטיים- י שימוש בננו"ממאירים ע

רפואית-בהנדסה ביו" מוסמך אוניברסיטה"חיבור זה הוגש כעבודת גמר לקראת התואר

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ח"מרחשוון התשס

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