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  • REVIEW OF SCIENTIFIC INSTRUMENTS 77, 041101 2006Photoacoustic imaging in biomedicineMinghua Xua and Lihong V. Wangb

    Optical Imaging Laboratory, Department of Biomedical Engineering, Texas A&M University, 3120 TAMU,College Station, Texas 77843-3120

    Received 15 January 2004; accepted 20 February 2006; published online 17 April 2006

    Photoacoustic imaging also called optoacoustic or thermoacoustic imaging has the potential toimage animal or human organs, such as the breast and the brain, with simultaneous high contrast andhigh spatial resolution. This article provides an overview of the rapidly expanding field ofphotoacoustic imaging for biomedical applications. Imaging techniques, including depth profiling inlayered media, scanning tomography with focused ultrasonic transducers, image forming with anacoustic lens, and computed tomography with unfocused transducers, are introduced. Specialemphasis is placed on computed tomography, including reconstruction algorithms, spatialresolution, and related recent experiments. Promising biomedical applications are discussedthroughout the text, including 1 tomographic imaging of the skin and other superficial organs bylaser-induced photoacoustic microscopy, which offers the critical advantages, over currenthigh-resolution optical imaging modalities, of deeper imaging depth and higher absorptioncontrasts, 2 breast cancer detection by near-infrared light or radio-frequencywave-inducedphotoacoustic imaging, which has important potential for early detection, and 3 small animalimaging by laser-induced photoacoustic imaging, which measures unique optical absorptioncontrasts related to important biochemical information and provides better resolution in deep tissues

    than optical imaging. 2006 American Institute of Physics. DOI: 10.1063/1.2195024I. INTRODUCTION

    The photoacoustic PA effect is the physical basis forPA imaging; it refers to the generation of acoustic waves bythe absorption of electromagnetic EM energy, such as op-tical or radio-frequency rf for simplicity, we will use rf torepresent either microwave or rf waves or both throughoutthe text waves. Alexander Graham Bell first reported theobservation of sound generated by light in 1880.1 Readersare referred to earlier reviews,26 books and conferenceproceedings,712 and original studies for the historical devel-opment of PA techniques in various branches of physics,chemistry, biology, engineering, and medicine.

    In the last decade, work on photoacoustic imaging inbiomedical applications has come a long way.1317 Nonion-izing waves, such as short laser or rf pulses, are often used toexcite megahertz ultrasound waves, referred to as photoa-coustic or thermoacoustic signals, in biological tissues. Themotivation for photoacoustic imaging is to combine ultra-sonic resolution with high contrast due to light, or rf, absorp-tion. Unlike ionizing x-ray radiation, nonionizing waves poseno health hazard. Unfortunately, however, in the pure opticalimaging methodologies, optical scattering in soft tissues de-grades spatial resolution significantly with depth. Since ul-

    aPresent address: Abramson Family Cancer Research Institute at the Uni-versity of Pennsylvania School of Medicine, Room 627 BRB II/III, 421Curie Boulevard, Philadelphia, PA 19104-6160.

    bAuthor to whom all correspondence should be addressed; also at the De-partment of Biomedical Engineering at Washington University in St.Louis, One Brookings Drive, Campus Box 1097, St. Louis, MO 63130-4899 as of June 2006; FAX: 979-845-4450; electronic mails:

    [email protected] and [email protected]; URL: http://oilab.tamu.edu

    0034-6748/2006/774/041101/22/$23.00 77, 04110

    Downloaded 30 Jul 2006 to 165.91.48.1. Redistribution subject to Atrasound scattering is two to three orders of magnitudeweaker than optical scattering in biological tissues,18 ultra-sound can provide a better resolution than optical imaging indepths greater than 1 mm. However, pure ultrasound im-aging is based on the detection of the mechanical propertiesin biological tissues, so its weak contrasts are not capable ofrevealing early stage tumors. Moreover, ultrasound cannotimage either oxygen saturation or the concentration of hemo-globin, to both of which optical absorption is very sensitive.These physiological parameters can provide functional imag-ing. Likewise, pure rf imaging cannot provide good spatialresolution because of its long wavelength.19 Utilizing oper-ating frequencies in the range of 500900 MHz, pure rf im-aging can only provide a spatial resolution of 1 cm.20 Thesignificance of PA imaging is that it overcomes the aboveproblems and yields images of high EM contrast at highultrasonic resolution in relatively large volumes of biologicaltissues.

    PA imaging can be considered either an ultrasound-mediated EM imaging modality or an ultrasound imagingmodality with EM-enhanced contrast. Upon absorption of ashort EM pulse, the spatial distribution of the acoustic tran-sient pressure inside the tissue that acts as the initial sourcefor the acoustic waves is simultaneously excited by ther-moelastic expansion. The acoustic waves from the initialacoustic source reach the surface of the tissue with varioustime delays. Ultrasound receivers are placed around the tis-sues to measure these outgoing acoustic waves, which arefurther used to determine the initial acoustic source distribu-tion that maps the EM energy deposition functions or absorp-

    tion properties. The spatial resolution of PA imaging, as well

    2006 American Institute of Physics1-1

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    http://dx.doi.org/10.1063/1.2195024http://dx.doi.org/10.1063/1.2195024

  • 041101-2 M. Xu and L. V. Wang Rev. Sci. Instrum. 77, 041101 2006as the maximum imaging depth, is scaleable with the de-tected ultrasonic bandwidth.21 For example, PA signals witha 1 MHz bandwidth can provide approximately 1 mm spatialresolution since the velocity of sound in soft tissues is1.5 mm/s.18 If the bandwidth is increased to 10 MHz,approximately 0.1 mm resolution can be achieved at the ex-pense of ultrasonic penetration.

    In a simple case where a wide beam of light pulse heatsa layered medium, the detected PA signal replicates the lightenergy deposition profile throughout the depth. Then, thedepth-dependent information of the sample, such as thedepth structure and properties e.g., the absorption coeffi-cient in a nonscattering medium can be determined directlyfrom the temporal PA signal. For convenience, this imagingconfiguration is termed PA depth profiling. However, to im-age more complicated structures, a more complex imagingmethod referred to as PA tomography PAT is preferred.PAT makes use of PA signals measured at various locationsaround the subject under study. PAT is also called optoacous-tic tomography OAT or thermoacoustic tomography TAT,with the term thermoacoustic emphasizing the thermal ex-pansion mechanism in the PA generation. OAT refers particu-larly to light-induced PAT, while TAT is used to refer torf-induced PAT. Depth profiling can be regarded as one-dimensional 1D PAT. There have been various reviews ofoptoacoustic imaging in the literature. Oraevsky and Karabu-tov discussed the generation and detection of optoacousticprofiles and applications of depth profiling for the measure-ment of tissue optical properties and 1D imaging;22 they alsopresented an analysis of optoacoustic tomography and itsapplications to the detection of cancer.23

    From a physical point of view, PAT represents an inversesource problem that belongs to the field of diffraction tomog-raphy, due to the diffractive nature of ultrasonic waves.Many imaging concepts and mathematical techniques forother imaging modalities, such as ultrasonic, x-ray, and op-tical tomographies, can be borrowed for use with PAT. Fo-cused ultrasonic transducers or acoustic lenses can be useddirectly to form images of the initial pressure distribution.Alternatively, computed tomography CT, with the measure-ments often acquired by unfocused ultrasonic transducers, isa more sophisticated method that requires computer-basedreconstruction.

    This article is intended to provide an overview of PAimaging, including both OAT and TAT. We will start by pro-viding a description of photoacoustics in soft tissues. Afterthat, we will discuss depth profiling, but only briefly, sincegood coverage is available in previous reviews.22,23 Next, wewill briefly discuss PA scanning tomography with focusedtransducers and image forming with acoustic lenses. Then,we will review PA computed tomography in detail. Emphasisthroughout will be placed on recent results. Representativeworks will be summarized with illustrative examples in-cluded.

    II. PHOTOACOUSTICS IN TISSUES

    A. EM absorption and penetration

    Electromagnetic energy in the optical from visible to

    near-IR and rf regions is often utilized for PA excitation in

    Downloaded 30 Jul 2006 to 165.91.48.1. Redistribution subject to Asoft tissues. This is not only because EM waves in theseregions are nonionizing and safe for human use but also be-cause they provide the high contrast and adequate penetra-tion depths18,2427 in biological tissues that are required forvarious applications. No other EM spectrum seems practicalfor PA generation in deep tissues. For example, terahertz raysthat lie between the above two EM spectra do not penetratebiological tissue well due to water-dominated absorption. Inthe short-wavelength spectrum below the visible region, suchas ultraviolet rays, radiation has high photon energy and,therefore, is harmful to human subjects.

    1. Optical propertiesThe optical properties of biological tissues in the visible

    400700 nm and near-IR 7001100 nm regions of theEM spectrum are related to the molecular constituents oftissues and their electronic and/or vibrational structures.They are intrinsically sensitive to tissue abnormalities andfunctions. Optical properties include scattering and absorp-tion. Optical scattering properties can reveal architecturalchanges in biological tissue at the cellular and subcellularlevels, whereas optical absorption properties can be used toquantify angiogenesis and hypermetabolism. Light scatteringis quite strong in biological tissues. The reduced or effectivescattering coefficient is described by s=s1g; where sand g are the scattering coefficient and the anisotropy factor,respectively. In the visible to near-IR region, typically s100 cm1 and g0.9, the absorption coefficients a varybetween 0.1 and 10 cm1 in biological tissues.24 Contrastagents, such as indocyanine green ICG, can be used toincrease optical absorption. There is an optical window, lyingtypically between 700 and 900 mm, that allows light to pen-etrate relatively deeply up to several centimeters into bio-logical tissues. In general, light propagation in tissues can bedescribed by the radiative transport equation or, with knowl-edge of the tissues optical properties, by a Monte Carlomodel. Multiple scattering leads to the spreading of lightbeams and a loss of directionality. Light propagation in deeptissues where multiple scattering prevails approximately fol-lows the diffusion law. Therefore, high-resolution optical im-aging modalities, based on ballistic or quasiballistic photons,can image only approximately one photon transport meanfree path 1 mm into tissue. Pure optical imaging methodswith diffusing light can only achieve a resolution of about1 cm.25 On the other hand, PA imaging actually detects theabsorbed photons and can, therefore, image deeper tissueswhere the diffusion photons are absorbed to generate ultra-sound in the 150 MHz range. Therefore, higher spatialresolution is possible because ultrasound scattering in tissueis two to three orders of magnitude weaker than optical scat-tering.

    Optical absorption in tissues is a function of the molecu-lar composition. For example, hemoglobin is a constituent inbiological tissue that exhibits several absorption bands.25 Theabsorption spectrum of hemoglobin changes when bindingoccurs. Oxygenated hemoglobin is a strong absorber up to600 nm at which point its absorption drops off very steeply,by almost two orders of magnitude, and remains low. The

    absorption of deoxygenated hemoglobin, however, does not

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  • 041101-3 Photoacoustic imaging in biomedicine Rev. Sci. Instrum. 77, 041101 2006drop dramatically; it stays relatively high, although it de-creases with increasing wavelengths. The isosbestic pointwhere the two extinction spectra intersect occurs at about800 nm. The oxygen saturation of hemoglobin is relatedclosely to the metabolic state of lesions and, hence, is animportant diagnostic parameter. Rapidly growing hyperme-tabolism cancer cells need additional blood and they gradu-ally develop a dense microvascular network angiogenesisaround themselves to perpetuate tumor growth.28,29 As a con-sequence, photoacoustic imaging that relies on optical prop-erties can be used to deduce certain physiological param-eters, such as the oxygen saturation of hemoglobin and theconcentration of hemoglobin, as well as, potentially, to quan-tify the hallmarks of cancer including angiogenesis and hy-permetabolism, thereby offering earlier cancer detection.More details about the optical properties of biological tissuescan be found in Ref. 25.

    2. rf propertiesThe rf properties of biological tissues are related to the

    physiological nature of their electrical properties. The elec-trical properties26 can be described by complex permittivity,*=0+ / j, or complex conductivity, *=+ j0,where is the conductivity S/m; is the relative permit-tivity dimensionless; 0=8.85 pF/m permittivity ofvacuum; and is the angular frequency. In terms of theseproperties, the wavelength of an EM wave in tissue is =c0 / f Re* /0 and the 1/e penetration depth of the fieldis =c0 / 2f Im* /0, where Re and Im represent the realand imaginary parts, respectively, and c0 is the velocity ofthe rf wave in vacuo.

    In the rf region, such as 0.33 GHz, EM waves can bereadily transmitted through, absorbed, or reflected by bio-logical tissue to varying degrees depending on the body size,tissue properties, and EM frequency; however, little scatter-ing occurs in tissues in this frequency range.27 The penetra-tion depth is equal to the reciprocal of the absorption coeffi-cient when scattering and diffraction are ignored. Forexample, the absorption coefficients of the electric field in fatlow water content and muscle high water content areabout 0.1 and 0.9 cm1, respectively, at 3 GHz and about0.03 and 0.25 cm1, respectively, at 300 MHz. The most in-vestigated and documented effect of rf power on biologicaltissues is the transformation of the energy entering the tis-sues into increased kinetic energy in the absorbing mol-ecules, which produces general heating in the medium.27 Thetwo properties that have the strongest effect on the degree ofrf absorption are ionic conductivity and the vibration of thedipolar molecules of water and proteins in the biologicaltissues.27 A small increase in ionic conductivity or water con-tent in tissue can produce a significant increase in rf absorp-tion.

    3. SafetyFor safety reasons, human exposure to EM radiation

    must be limited. One of the important technical parametersfor safety is the so-called maximum permissible exposureMPE, which is defined as the level of EM radiation to

    which a person may be exposed without hazardous effects or

    Downloaded 30 Jul 2006 to 165.91.48.1. Redistribution subject to Abiological changes. MPE levels are determined as a functionof EM wavelength or frequency, exposure time, and pulserepetition. The MPE is usually expressed in terms of eitherradiant exposure in J /cm2, or irradiance in W/cm2, for agiven wavelength and exposure duration. Exposure to EMenergy above the MPE can potentially result in tissue dam-age. Generally, the longer the wavelength, the higher theMPE; and the longer the exposure time, the lower the MPE.

    The IEEE Standard Std. C95.1, 1999 edition definesMPE levels, with respect to human exposure to rf fields,from 3 KHz to 300 GHz.30 For a rf radiation in the range of0.33 GHz in a controlled environment, MPE= f /300 mW/cm2, where f is the frequency in megahertz.The American National Standard Z136.1-2000 definesMPE levels for specific laser wavelengths 180 nm1 mmand exposure durations.31 For example, in the case of skinexposure to a laser beam in the visible and NIR range4001400 nm, MPE=20CA mJ/cm2 for a single shortpulse with a duration of 1100 ns, respectively, where CA=1.0 in 400700 nm, 1020.7 in 7001050 nm, and 5.0 in10501400 nm, respectively; is the wavelength in mi-crons. The above two standards also define formulas to de-termine the applicable MPE for exposure to repetitive illu-mination, which is dependent on the wavelength, the pulserepetition frequency, the duration of a single pulse, the dura-tion of any pulse groups, and the duration of the completeexposure.

    B. Photoacoustic generation

    Although other generation mechanisms exist, for medi-cal imaging, we are generally interested in using EM pulsesto excite transient ultrasonic waves through the thermoelasticmechanism with a low fluence of EM radiation. A sound orstress wave is produced because of the thermoelastic expan-sion that is induced by a slight temperature rise, typically inthe millikelvin range, as a result of the energy depositioninside the biological tissue through the absorption of the in-cident EM energy. The excited PA signal is locally deter-mined by the EM absorption and scattering properties, thethermal properties, including the thermal diffusivity and ther-mal expansion coefficient, and the elastic properties of thesample.

    The EM absorption property is of primary interest be-cause of the contrast it provides in biological tissues. Thethermoelastic mechanism has the following features thatmake PA techniques amenable for biomedical applications.First, it does not break or change the properties of the bio-logical tissue under study. Second, only nonionizing radia-tion is used, unlike in x-ray imaging or positron-emissiontomography. The nondestructive noninvasive and nonioniz-ing nature of PA techniques makes them ideal for in vivoapplications. Third, the relationships between PA signals andthe physical parameters of biological tissues are well defined.This advantage permits the quantification of various physi-ological parameters such as the oxygenation of hemoglobin.

    To generate PA signals efficiently, two conditions, re-ferred to as thermal and stress confinements, must be met.12

    The time scale for the heat dissipation of absorbed EM en-

    ergy by thermal conduction can be approximated by th

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  • 041101-4 M. Xu and L. V. Wang Rev. Sci. Instrum. 77, 041101 2006Lp2 /4DT, where Lp is the characteristic linear dimension of

    the tissue volume being heated i.e., the penetration depth ofthe EM wave or the size of the absorbing structure. Actually,heat diffusion depends on the geometry of the heated vol-ume, and the estimation of th may vary.

    32 Upon the absorp-tion of a pulse with a temporal duration of p, the thermaldiffusion length during the pulse period can be estimatedby5,32 T=2DTp, where DT is the thermal diffusivity of thesample, and a typical value for most soft tissues is DT1.4103 cm2/s.18 The pulse width p should be shorterthan th to generate PA waves efficiently, a condition that iscommonly referred to as thermal confinement where heatdiffusion is negligible during the excitation pulse. For ex-ample, for a rf pulse of p=0.5 s, T0.5 m, which ismuch less than the spatial resolution that most PA imagingsystems can achieve. Therefore, the thermal confinementcondition is typically met.

    Similarly, the time for the stress to transit the heatedregion can be estimated by s=Lp /c, where c is the speed ofsound. The pulse width p should be shorter than s, a con-dition that is commonly referred to as stress confinement.Under the stress confinement condition, high thermoelasticpressure in the sample can build up rapidly.12 For example,to achieve a spatial resolution at Lp=150 m, if c=1.5 mm/s and DT1.4103 cm2/s, then th40 msand s100 ns. Hence, p must be less than 100 ns to guar-antee the more stringent stress confinement. When both ther-mal and stress confinements are satisfied, thermal expansioncauses a pressure rise p0 that can be estimated by

    12,23

    p0 = c2/CpaF = A , 1

    where is the isobaric volume expansion coefficient in K1,Cp is the specific heat in J/K kg, a is the absorption coef-ficient in cm1, F is the local light or rf fluence in J /cm2, Ais the local energy deposition density in J /cm3: A=aF, and is referred to as the Grneisen coefficient expressed as =c2 /Cp.

    C. PA propagation and detection

    EM-pulse excited pressure acts as an acoustic source andinitiates further acoustic wave propagation in three-dimensional 3D space. For simplicity, the inhomogeneityof acoustic speed in soft tissues is usually neglected in cal-culating acoustic wave propagation. The speed of sound isrelatively constant at 1.5 mm/s with a small variation ofless than 10% in most soft tissues.18,33 If acoustic heteroge-neity becomes important, we should resort to a pure acoustictechnique, such as ultrasound tomography, to map out theacoustic inhomogeneity for a more accurate calculation ofthe PA wave propagation.

    In the low-megahertz frequency range, ultrasound in softtissues has the properties of low scattering and deeppenetration.18,33 The total attenuation results from the com-bined losses due to both absorption and scattering, while thescatter component accounts for about 10%15% of the totalattenuation. The attenuation of all tissues is temperature andfrequency dependent. The frequency dependency of ultra-sonic attenuation can be represented by the expression

    b=af , where is the ultrasonic attenuation coefficient, a and

    Downloaded 30 Jul 2006 to 165.91.48.1. Redistribution subject to Ab are constants, and f is the frequency of ultrasound.18 Amean value of ultrasound attenuation equals0.6 dB cm1 MHz1 for soft tissues.33 The attenuation in-creases with the frequency and the penetration decreaseswith the frequency. Typically, 3 MHz might be the maximumfrequency for a 15 cm penetration.33 In the high-megahertzfrequency range, both scattering and absorption increase tre-mendously, leading to a markedly decreased penetrationdepth.

    The outgoing ultrasound from the initial source reachesthe tissue surface and then can be picked up by an ultrasoundtransducer. Since it serves only as an acoustic receiver andthe emission efficiency is of no importance, the detector forPA measurement can be specially designed for sensitivity.The most often used ultrasound detectors in ultrasound-basedimaging are piezoelectric based;33 they have low thermalnoise and high sensitivity and can provide a wide band of upto 100 MHz.23,34 The employment of other kinds of sensors,such as those based on optical detection, is also feasible.3541

    Optical methods are often based on photoacoustic-pressured-induced surface displacement35,36,40 or refraction indexchanges,37 which means they have the potential for noncon-tact measurement and rapid monitoring of large areas.38 Thedisadvantages of optical detection relative to piezoelectricdetection are lower sensitivity and higher noise level in therange of acoustic frequencies greater than 1 MHz.23

    III. DEPTH PROFILING

    To begin our discussion of photoacoustic imaging, let ustake a simple case of depth profiling or one-dimensional im-aging in a layered medium. The temporal shape of a short-pulse excited PA signal in thermal and stress confinements islocally related to the absorption and scattering structure ofthe tissue sample, and this relationship can sometimes beexpressed by an analytic formula. In such a case, the tissueproperties e.g., the absorption coefficient in a nonscatteringmedium and structure can be characterized by analyzing thetemporal PA signal.4248 Other reviews22,23 have discussed1D or depth-resolved optoacoustic profiling. Here, we onlygive an example to illustrate the principle of depth profiling.

    As shown in Fig. 1, an optically absorbing semi-infinitemedium neglecting optical scattering in response to a wide-beam impulse t illumination generates an initial pressureor stress distribution p0z as

    p0z = aF0 exp 0z , 2

    where F0 is the incident laser fluence in J /m2. The pressure

    p0z serves as the source of an acoustic wave and further

    FIG. 1. Diagram of initial pressure distribution.prompts two plane waves of equal amplitude to propagate in

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  • 041101-5 Photoacoustic imaging in biomedicine Rev. Sci. Instrum. 77, 041101 2006opposite directions along z, respectively. Without consider-ing the reflected acoustic wave from the boundary or acous-tic attenuation, the PA wave, measured at z0 =ct0, is

    pz0,t =12aF0 exp act + z0 =

    12aF0 exp

    act t0, t t0. 3

    The absorption coefficient a can be determined from theamplitude aF0 /2, if the detection system is calibrated forabsolute measurement or from the exponential slope of thePA wave through fitting the curve with expact. Since itis easier to measure the relative profile than the absoluteamplitude, fitting the slope is more reliable. For a strongscattering medium, a more complex expression is available,where the exponential decay term in the diffusion regime isdetermined by the effective attenuation coefficient eff in-stead of a.

    Based on the above concept, depth profiling is able tocharacterize tissue optical properties. For example, Oraevskyet al.43 utilized the time-resolved detection of laser-inducedacoustic transients to determine the optical properties ab-sorption, scattering, and attenuation coefficients of variousmedia, including bovine liver, canine prostate, and humanfibrous atheroma; Kstli et al.46 used the PA method to mea-sure the effective attenuation coefficients of cartilage andchicken breast in the infrared light range.

    For a multilayered sample, each layer creates a portionof the temporal profile of the PA signal from which the valueof the absorption or attenuation coefficient of each layer canbe determined by piecewise exponential fitting.44,45 In thefitting process, the temporal profile of the laser pulse can betaken into account although the pulse width is typically quitesmall. In general, if the absorption or attenuation coefficientis a continuous function of depth in the sample, a reconstruc-tion algorithm is required to extract the absorption informa-tion from the detected PA temporal signals. Viator et al.47

    demonstrated this approach based on Beers law.However, except for phantom samples,44,45,47 the relative

    measurement error in these experiments43,46 is around 10%because of the property variations in tissue samples. Besides,the deduction of optical properties from PA signals in therange of the acoustic frequencies, where diffraction and at-tenuation are not negligible, can be complicated.43 If thelight penetration depth is small compared with the effectivepenetration depth of the acoustic wave, the acoustic attenua-tion decreases only the amplitude of the measured PA signaland does not alter its replication of the profile of the lightdistribution. Nevertheless, when the optical attenuation coef-ficient is similar to that of the acoustic attenuation, both theamplitude and exponential slope of the initial pressure orstress can change during acoustic-wave propagation in themedium. The diffraction of acoustic waves is prominentwhen the laser beam diameter is comparable to the light pen-etration depth.

    IV. SCANNING TOMOGRAPHY

    A. Principle

    Photoacoustic scanning tomography is often similar to

    B-mode ultrasonography. Figure 2a shows a diagram of

    Downloaded 30 Jul 2006 to 165.91.48.1. Redistribution subject to Ascanning tomography in the forward detection mode. A fo-cused ultrasound transducer scans along the tissue surface,and analogous to an ultrasonic A-line or A-scan, each de-tected time-resolved signal upon a pulsed-EM excitation canbe converted into a 1D image along the acoustic axis of thetransducer. Combining multiple A-scan images acquired se-quentially from various positions on the same plane formscross-sectional images. The axial resolution along the acous-tic axis is dependent on both the width of the radiation pulseand the width of the impulse response of the transducer. Thelateral resolution is determined by the focal diameter of theultrasonic transducer and the center frequency of the re-ceived PA signals. In this imaging configuration, the imagingzone is limited by the focal zone of the transducer.49 Outsidethe focal zone along the acoustic axis, the detection sensitiv-ity and image resolution decrease greatly. An alternative con-figuration of PA scanning tomography is analogous to theC-scan mode in ultrasonography, in which a cross-sectionalimage at a certain image depth is formed, and then slicesimaged at different depths can be stacked together to form a3D image.

    To achieve a better signal-to-noise ratio SNR, a high-energy pulse is preferred, since the amplitude of a PA signalis proportional to the absorbed EM energy. However, forsafety reasons, the pulse energy is limited. A focused trans-ducer can detect a PA signal with a high SNR because of its

    FIG. 2. a Diagram of thermoacoustic scanning tomography. b Thermoa-coustic image of a phantom sample: a piece of muscle buried in severallayers of fat.large numerical aperture. Therefore, a single EM pulse is

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  • 041101-6 M. Xu and L. V. Wang Rev. Sci. Instrum. 77, 041101 2006usually able to provide a scan line without the necessity ofaveraging data from multiple shots. However, the EM-pulserepetition frequency limits the scanning speed.

    B. rf-based scanning tomography

    A few researchers5052 have demonstrated rf-induced PAimaging by scanning a focused ultrasonic transducer. Thepulse duration of the rf source used is often in the range of0.11 s, which can excite ultrasound up to several mega-hertz since the bandwidth of the PA signal approximates thereciprocal of the EM pulse width. The megahertz signal canprovide axial spatial resolution in millimeters or submillime-ters through a multicentimeter thick tissue. Hence, it is suit-able for imaging large samples such as the human breast.Figure 2b shows a microwave-induced thermoacoustic im-age of a phantom sample,51 in which the boundaries of thetissues are clearly imaged. It indicates that rf can easily pen-etrate multiple centimeters through biological tissue to reachdeep tumors.

    C. Laser-based microscopic imaging

    PA imaging with pulsed-light excitation can operate in away that is similar to rf-based scanning tomography.53 How-ever, PA imaging with a laser can be scaled down for micro-scopic imaging. A laser system can easily generate laserpulses with a pulse energy of 100 mJ and a pulse duration of10 ns or shorter, which can sufficiently excite PA signals athigh frequencies up to 100 MHz in large-area soft tissueswith a good SNR. Therefore, laser-based PA scanning to-mography can perform microscopic imaging with an axialresolution of 30 m or less, which means it has potential forapplications in direct imaging of the skin and other superfi-cial organs or imaging endoscopically in the gastrointestinalGI tract.

    Oraevsky and Karabutov23 demonstrated that optoacous-tic microscopy was capable of imaging and distinguishingearly stages of squamous-cell carcinoma in the oral mucousof golden hamsters in vivo. The imaging system they used,termed confocal optoacoustic microscopy imaging, is shownin Fig. 3a, where both the ultrasound detection and theexcitation light source are focused on the same spot.23,54 Thepulsed light is delivered via optical fiber and focused by acondenser gradient index GRIN lens onto the tissue sur-face through an optoacoustic OA lens. The induced ultra-sound propagates backward through the OA lens onto a ring-shaped piezoelectric film. This bright-field design suffersfrom the strong photoacoustic waves that are emitted fromoptical absorbers near the surface, the acoustic reverberationsfrom which can potentially overshadow the much weakerphotoacoustic signals from structures deep in the tissue.

    To prevent the occurrence of such overshadow problems,a reflection-mode microscopic photoacoustic imaging tech-nique that uses dark-field illumination, as in dark-field mi-croscopy, was recently reported by Maslov et al.,55 as shownin Fig. 3b. In this design, the light comes onto the tissuesurface in a doughnut or small ring shape, and then the dif-fusion photons transporting to the imaging axis are absorbed

    to generate ultrasound. As a consequence, this design par-

    Downloaded 30 Jul 2006 to 165.91.48.1. Redistribution subject to Atially averages out the shadows of superficial heterogeneityin the image and also reduces the potentially strong interfer-ence of the extraneous photoacoustic signals from the super-ficial paraxial areas. In their recent system, the lateral reso-lution was as high as 45 m in the tissue phantoms. Themaximum imaging depth was at least 3 mm. Further im-provement of the image resolution by increasing the ultra-sonic frequency is possible at the cost of imaging depth. Anin situ photoacoustic image similar to a C-scan image 100100, pixels; 0.1 mm step size is shown in Fig. 3c, inwhich the vascular distribution in rat skin was clearly im-aged.

    Because of the strong light scattering, PA imaging reso-lution beyond one optical transport mean free path in tissueis determined primarily by the ultrasonic detection param-eters. To provide high resolution, the acoustic detector musthave a wide bandwidth and a large numerical aperture NA.However, increasing the ultrasonic frequency too much canresult in an undesirably small penetration depth because theultrasonic attenuation in tissues, 0.73 dB cm1 MHz1 forhuman skin,56 for example, increases linearly with the fre-quency. Therefore, a large NA is essential for the desiredresolution.

    In summary, PA microscopy has critical advantages overother optical-contrast imaging methods, including currenthigh-resolution optical imaging techniques such as confocalmicroscopy and optical coherence tomography OCT. Theseoptical imaging techniques can image only approximately

    FIG. 3. a Diagram of a bright-field confocal photoacoustic microscope inthe backward detection mode. b Schematic of the photoacoustic sensor ofa dark-field reflection-mode photoacoustic microscope. c Photoacousticimage of vascular distribution in rat skin.one transport mean free path 1 mm into tissue because

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  • 041101-7 Photoacoustic imaging in biomedicine Rev. Sci. Instrum. 77, 041101 2006they depend on ballistic or quasiballistic photons. In addi-tion, they are sensitive to the backscattering that is related totissue morphology, but they are insensitive to the optical ab-sorption that is related to important biochemical information.PA microscopy imaging does not rely on ballistic or quasi-ballistic photons and can, therefore, penetrate deeper. Fur-ther, it provides high optical-absorption contrast while itmaintains high ultrasonic resolution due to the low scatteringof megahertz ultrasound. Consequently, structures with highoptical absorption coefficients, such as blood vessels, can beimaged clearly by PA microscopy.

    The emergence of PA microscopy in the early 2000s of-fers a novel opportunity for detecting and imaging skin can-cer e.g., melanoma in vivo. The precise imaging of lesionsize, location, and surrounding abnormal vascularity willdefinitely benefit tumor staging, surgery, and treatment.

    V. IMAGE FORMING WITH ACOUSTIC LENSES

    An acoustic lens can be used to diverge or convergeacoustic waves in a manner analogous to an optical lens re-fracting light. Also similar to an optical imaging system, anacoustic lens is able to image the initial PA pressure distri-bution in an optically turbid medium onto an image space inan optically transparent medium in which the initial pressuredistribution can be directly measured in real time without thenecessity of scanning detections or computational recon-structions. For example, a two-dimensional 2D ultrasonicdetector array with multiple small elements can be insertedinto an image space to get a slice of the focused image.Because of the slow speed of ultrasound relative to light,images should be taken after the EM-pulse illuminationwhen the ultrasound is focused on the image space, formingan approximate replica of the original PA pressure distribu-tion in the clear medium.

    Recently, Niederhauser et al.57 proposed an optical dark-field stereo imaging system using a 30 ns flash illuminationlight source to capture a snapshot of pressure-induced refrac-tion index changes in a water container at a predeterminedtime after the original laser pulse. In their system, the acous-tic lens system consisted of a biconcave aspheric alumi-num lens covered on both sides with distilled water, asshown in Fig. 4. The aluminum surfaces were coated with a40 m antireflex parylene coating to minimize acoustic re-flection at the boundary. The 4f lens configuration was cho-sen 46 mm water, 22 mm aluminum, and 46 mm water toprovide a unit magnification both laterally and axially when

    FIG. 4. Acoustic lens system with a focal length of f .the object is located at 2f and has a size much smaller than

    Downloaded 30 Jul 2006 to 165.91.48.1. Redistribution subject to A2f . Based on the lens-imaging formula 1/ 2f z+1/ 2f+z=1/ f , we have z=z / 1z / f and zz when

    z f . Therefore, any small displacement of the object planeby a distance z away from 2f results in a displacement ofthe corresponding focused image plane by the same value. Inthis case, the acoustic propagation time from each objectplane to the corresponding focused image plane remains thesame, independent of the exact individual object position.This results in a perfect 3D pressure image at a fixed timethat equals the acoustic propagation time from the objectplane to the corresponding imaging plane. The pressure im-age in this case is, therefore, identical to the initial pressuredistribution except for small alterations introduced by finiteaperture and lens aberrations.

    VI. COMPUTED TOMOGRAPHY

    A. Introduction

    A majority of recent works have focused onreconstruction-based PAT, which provides more flexibility indealing with measured PA signals than do the image formingmethods with focused transducers or focused lenses that havefixed imaging regions. Technically, each temporal PA signal,measured at various detection positions, provides one-dimensional radial information about the PA source relativeto the detector position; 2D surface scans offer other 2Dlateral information about the PA source. Combining the tem-poral and spatial measurements affords sufficient informationfor a complete reconstruction of a 3D PA source. Because thePA signal received by each ultrasound detector is the integralof the ultrasound waves over the sensing aperture of the de-tector, the reconstruction algorithms depend on the detectorapertures as well as the scanning geometries. Small-aperturedetectors are often used to approximate point detectors,which receive PA signals originating from spherical shells,centered at each point detector, with radii determined by theacoustic times of flight Fig. 5. Large-aperture detectorsneed different reconstruction algorithms. Recently, a recon-struction method based on measurements with large planardetectors was presented:58 this method is closely related tothe standard Radon transform of the energy deposition func-tion.

    In Sec. VI B, we will introduce the inverse source prob-lem. Then, we will review reconstruction based on point-detector measurements. Because of the 3D nature of acousticwaves, we will review 3D algorithms and methods with

    FIG. 5. Diagram of photoacoustic measurement at r0.point detectors in Sec. VI C, in which we will cite some of

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  • 041101-8 M. Xu and L. V. Wang Rev. Sci. Instrum. 77, 041101 2006the related literature about 2D reconstructions. In Sec. VI D,we will discuss spatial resolution. Finally, we will introducea reconstruction method using large planar receivers in Sec.VI E.

    B. Inverse source problem

    In response to a heat source, Hr , t, the pressure, pr , t,at position r and time t in an acoustically homogeneous liq-uidlike medium obeys the following wave equation ignoringthermal diffusion and kinematic viscosity:5,6,12,59

    2pr,t 1

    c22

    t2pr,t =

    Cp

    tHr,t , 4

    where Hr , t is a heating function defined as the thermalenergy deposited by the EM radiation per time per volumeCp and are defined after Eq. 1. The validity of theabove equation requires LpDTp i.e., thermal confine-ment: pth; LpDT /c i.e., sth and c2pDT i.e.,stress propagation lengthheat diffusion length: cpDTp; and c2p /0 where /0 is the kinematic vis-cosity of the liquid.6 Under the above conditions, the initiallyexcited acoustic stress or pressure is determined by the localEM absorption.

    The forward solution, based on the free-space Greensfunction, can be found in the physics or mathematicsliterature.6062 In general, the solution to Eq. 4 in the timedomain can be expressed by

    pr,t =

    4Cp

    d3rr r Hr,tt t=trr/c.5

    The heating function can be written as the product of a spa-tial absorption function and a temporal illumination functionunder the condition of thermal confinement,

    Hr,t = ArIet . 6

    Then, Eq. 5 can be rewritten as a convolution between thetemporal profile Iet and the acoustic wave form pr , t thatis excited by an infinitely short pulse t,

    per,t =

    +

    Iet pr,d , 7

    where

    pr,t =

    t 14 rr=ct p0rd , 8where d is the solid-angle element of vector r with re-spect to the point at r; and p0r is the initial pressure excitedby a t EM source, computed by p0r=rAr, whichacts as the source of the propagating acoustic wave.

    For simplicity, a t EM source is assumed and the PAsignal is detected at position r0 by a point detector Fig. 5,

    pdr0,t =

    t t4 r0r=ct p0rd , 9where d is the solid-angle element of vector r with respect

    to the point at r0. Then, the key to the inverse algorithm in

    Downloaded 30 Jul 2006 to 165.91.48.1. Redistribution subject to APAT is to reconstruct the initial source p0r from the mea-sured data pdr0 , t.

    C. Algorithms and methods

    1. Overview

    a. Radon transform. The projections on the detectors arerepresented by the integrals over the spherical shells asshown in Eq. 9, in contrast to line integrals in straight-raytomography such as x-ray CT. The development of an exactalgorithm based on the solution of Eq. 9 has serious math-ematical difficulties. Therefore, some researchers have ap-plied approximations of the well-known standard Radontransform to PAT reconstruction. For convenience, Eq. 9 isrewritten as

    Fr0,t =4

    t

    0

    t

    pdr0,tdt =

    r0r=ct

    p0rd . 10

    If the object is enclosed in the center region by a sphericalmeasurement surface and its size is much smaller than theenclosed volume, the spherical shells over which the surfaceintegral in Eq. 10 is computed approximate the planes, andEq. 10 approximates the Radon transform used in x-ray CT.

    Based on the above concept, Kruger and co-workers6365

    suggested a filtered back-projection algorithm under thespherical measurement geometry, i.e., the inverse of Eq. 10approximating

    p0r 1

    2

    S0

    dS0r0

    2 tpdr0,tt + 2pdr0,tt=rr0/c,11

    where dS0 is the detector element at r0. Liu66 derived an

    expression identical to Eq. 11 based on what he called a ptransform. Other researchers such as Andreev et al. did nu-merical simulations based on 2D Ref. 67 or 3D Ref. 68Radon transform approximations, and Xu et al.69 tested a 2DRadon transform approximation with a Hilbert transform.

    In general, the Radon transform approximation providesa satisfactory reconstruction for an object located near thecenter of the spherical or circular detection geometry. How-ever, the fact that this approximation does not hold when thesource deviates from the center of the spherical geometrylimits its application. Significant reconstruction artifacts oc-cur when the integration spherical shells are far differentfrom the planar surfaces.

    Finally, it must be pointed out that PAT mathematicallybelongs to the generalized spherical Radon transform. Math-ematicians have obtained an inverse formula for the sphericalgeometry, which will be discussed in Sec. VI C 3.

    b. Back projection. Algorithms for ultrasound imaging,such as back projection delay and sum and synthetic aper-ture, have also been borrowed for PAT reconstruction. Forexample, Hoelen and de Mul and co-workers70,71 constructeda time-domain delay-and-sum focused beam-forming algo-rithm to locate the PA sources in a sample in a planar scanconfiguration; Kstli et al.72 reported an image reconstruc-tion of detected 2D pressure distributions using back projec-

    73tion. Feng et al. applied a synthetic-aperture method to

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  • 041101-9 Photoacoustic imaging in biomedicine Rev. Sci. Instrum. 77, 041101 2006linear-scanning microwave-induced thermoacoustic tomog-raphy in biological tissues. Liao et al.74 reported on a studyof optoacoustic imaging with synthetic aperture focusing andcoherence weighting. Yin et al.75 used a phase-controlled fo-cus algorithm in their fast photoacoustic imaging systemwith a multielement linear transducer array.

    For the spherical and cylindrical geometries, Xu etal.76,77 approximated the rigorous Fourier-domain recon-struction formulas detailed later to the so-called modifiedback-projection formula as

    p0r 1

    2

    S0

    dS0r r02 n0s n0tpdr0,t

    t

    t=rr0/c, 12

    where n0s is the normal of surface S0 pointing to the source

    and n0=r0 /r0. The formula for the planar geometry replaces2 by in Eq. 12. In the approximation, it is assumed thatthe distances between the PA sources and the detectors aremuch greater than the wavelengths of the PA signals that areuseful for imaging. The modified back-projection formulaindicates that in 3D reconstruction, the back-projection quan-tity is related to the first derivative of the acoustic pressure,rather than simply to the acoustic pressure itself. A weightingfactor t compensates for the 1/ t attenuation of a sphericalpressure wave as it propagates through a homogeneous me-dium. The contribution to a reconstruction point P from anelement of receiving area dS0 is proportional to the sub-tended solid angle of this element dS0 when viewed from thepoint P. The solid angle is inversely proportional to thesquare of the distance between the receiving element dS0 andthe point P. Hence, the modified back-projection formula ofEq. 12 is more general than the Radon transform approxi-mation formula of Eq. 11.

    Recently, exact back-projection formulas for the spheri-cal, planar and cylindrical geometries have been reported,which will be detailed in Sec. VI C 3.

    c. Fourier- and time-domain algorithms. Recently, ana-lytical algorithms have been derived both in Fourier-domainand time-domain for reconstruction of both TAT and PAT.These algorithms are exact for the full-view data and canserve as a basis for reconstruction of TAT and PAT. We deferdiscussion of these methods in Secs. VI C 2 and VI C 3, re-spectively, where we discuss them in detail.

    d. Other methods. In principle, Eqs. 9 or 10 can berewritten in its discrete form as

    M P0 = D , 13

    where matrix P0 represents the unknown initial pressure, ma-trix D represents the measured PA signals, and the sensitivitymatrix M consists of the known coefficients linking P0 to D.Then, the standard techniques for solving a linear equationsystem can be used to compute P0. For example, Paltauf etal.78 studied an iterative reconstruction algorithm to mini-mize the error between the measured signals and the theoret-ical signals calculated from the reconstructed image; Xu andWang79 also studied an iterative algorithm based on the trun-

    cated conjugate gradient TCG method. Compared with the

    Downloaded 30 Jul 2006 to 165.91.48.1. Redistribution subject to Aapproximation methods discussed in Secs. VI C 1 a andVI C 1 b, the iterative method may give a more accurate re-sult. However, the iterative methods multiple steps takemore computation time since each step takes an amount oftime comparable to all of the steps in the other methods. Inaddition, large objects require more computer memory forstorage of the discrete matrix.

    In addition, Zhulina80 developed another interesting al-gorithm based on an optimal statistical approach. The es-sence of this algorithm includes 1 the summing of all sig-nals in the image plane with the transform from the timecoordinates of the signals to the spatial coordinates of theimage and 2 the optimal spatial filtration of this sum. Anas-tasio et al.81 reported on half-time reconstruction approaches;they revealed that half-time reconstructions permit the ex-plicit control of statistically complementary information thatcan result in the optimal reduction of image variances. Theyalso demonstrated that half-time reconstructions can mitigateimage artifacts due to the heterogeneous acoustic propertiesof an object. Zhang et al.82 presented weighted expectationmaximization reconstruction algorithms, in which they dem-onstrated that suitable choices of weighted algorithms caneffectively mitigate image artifacts that are attributable to thetemporal truncation of the measured data.

    2. Fourier-domain algorithmsa. Spherical geometry. Based on the assumption of a

    constant sound speed, Xu and Wang referred to mathematicaltechniques for ultrasonic reflectivity imaging83 and reportedan exact Fourier-domain reconstruction for the sphericalgeometry.76

    Taking the following Fourier transform with respect tovariable t=ct,

    pdr0,k =

    +

    pdr0, texpiktdt , 14

    where k= /c=2f /c with frequency f . Equation 9 can berewritten in the frequency domain as

    pdr0,k = ik d3rp0rGkr0,r , 15where the Greens function Gkr0 ,r=expikr0r / 4r0r represents a monochromatic spherical acoustic waveemanating from a point source.

    We denote the spherical measurement surface r0= r0 ,0 ,0 in the spherical polar coordinates r= r , ,Fig. 6a, where is the polar angle from the z axis and is the azimuth angle in the xy plane from the x axis. Thesample under study lies inside the sphere, i.e., p0r= p0r , , where rr0 and p0r=0 when rr0. The exactreconstruction formula for p0r can be written as

    76

    p0r =1

    22

    0

    d00

    dkpdr0,k

    i=0

    2l + 1jlkr

    hl1kr0

    Pln0 n , 16where d0=sin 0d0d0; n=r /r and n0=r0 /r0 are unit vec-

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  • 041101-10 M. Xu and L. V. Wang Rev. Sci. Instrum. 77, 041101 2006tors; jl, hl1, and Pl are a spherical Bessel function of

    the first kind, a spherical Hankel function of the first kind,and a Legendre polynomial function, respectively. If thesource p0r and the measurement pdr0 ,k are expanded inspherical harmonics as

    p0r,, =1

    22l=0+

    m=l

    +l

    ilYlm*,

    0

    +

    k2dkjlkrp0lmk , 17

    and

    pd0,0,k = l=0

    +

    m=l

    +l

    qlmkYl

    m*0,0 , 18

    where the symbol * denotes the complex conjugate, then therelationship between the source distribution and the mea-sured data can be expressed by

    p0lmk =

    + il4qlmk

    k2hl1kr0

    . 19

    The imaging reconstruction follows in three steps: 1take the spherical harmonics expansion of pd0 ,0 ,k in-verse of Eq. 18 to find the decomposition ql

    mk of m andm m

    FIG. 6. Diagram of measurement configurations: a spherical geometry, bplanar geometry, and c cylindrical geometry.l as a function of k, 2 compute p0lk from ql k based on

    Downloaded 30 Jul 2006 to 165.91.48.1. Redistribution subject to AEq. 19, and 3 take the Hankel transform over k of p0lmk

    and then the summation, i.e., Eq. 17, to find the initialpressure p0r , ,.

    In addition, the 2D reconstruction formula over a circu-lar scan can be referred to as the solution of ultrasonic re-flectivity imaging for a 2D reflecting medium.84

    b. Planar geometry. Based on the mathematical tech-niques for ultrasonic reflectivity imaging,83 Xu et al.85 de-rived an exact Fourier-domain reconstruction formula forplanar geometry. Kstli et al.86,87 presented a similar for-mula.

    We assume that the measurement surface lies in the z=0 plane, i.e., r0= x0 ,y0 ,0 in a Cartesian coordinate systemr= x ,y ,z Fig. 6b. The sample with a finite size liesabove the plane, i.e., p0r= p0x ,y ,z where z0, andp0r=0, otherwise. The exact reconstruction formula forp0r can be written as

    77,85

    p0r =1

    43

    +

    dx0dy0

    +

    dkpdr0,k

    =0

    =k

    dudv exp

    iz sgnkk2 2expiux0 x + ivy0 y ,20

    where =u2+v2, sgnk=1 when k0, and sgnk=1when k0. If the source p0r and the measurement pdr0 ,kare expanded in the Fourier domain as

    p0x,y,z =1

    23 p0u,v,wexp iux ivy iwzdudvdw , 21

    and

    pdx0,y0,k =1

    22 +

    qu,v,kexp iux0

    ivy0dudv , 22

    then the relationship between the source distribution and themeasured data can be expressed by

    p0u,v,w =2w sgnw

    u2 + v2 + w2qu,v,sgnwu2 + v2 + w2 .

    23

    Implementing the fast Fourier transform FFT acceler-ates the reconstruction computation. The reconstruction fol-lows in three steps: 1 take the 2D FFT of pdx0 ,y0 ,k in-verse of Eq. 22 to find the Fourier decomposition qu ,v ,kof u and v as a function of k, 2 compute p0u ,v ,w fromqu ,v ,k based on Eq. 23, and 3 take the inverse FFT ofp0u ,v ,w, i.e., Eq. 21, to find the initial pressurep0x ,y ,z.

    In addition, the 2D reconstruction formula can be re-ferred to as the diffraction tomography theory as described ina book by Kak and Slaney88 or as the solution for ultrasonicreflectivity imaging in the case of an omnidirectional source

    89receiver translated in a straight line.

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  • 041101-11 Photoacoustic imaging in biomedicine Rev. Sci. Instrum. 77, 041101 2006c. Cylindrical geometry. Xu et al.90 derived an exactreconstruction formula for the cylindrical geometry. This for-mula is much simpler and more stable than the reconstruc-tion method reported for ultrasonic reflectivity imaging witha cylindrical scanning surface.83

    As shown in Fig. 6c, we assume that the measurementsurface is a circular cylindrical surface r0= 0 ,0 ,z0 in acircular cylindrical coordinate system r= , ,z. Thesample with a finite size lies within the cylinder, i.e., p0r= p0 , ,z where 0, and p0r=0, otherwise. The exactreconstruction formula for p0r can be written as

    77

    p0r =1

    23

    0

    2

    d0

    +

    dz00

    +

    dkpdr0,k

    k

    +k

    d expiz0 z n=

    +

    expin0

    Jnk2 2

    Hn10k2 2

    , 24

    where Jn and Hn1 are the Bessel function of the first

    kind and the Hankel function of the first kind, respectively. Ifthe source p0r and the measurement pr0 ,k are expandedin circular harmonics as

    p0,,z =1

    2

    +

    d exp iz1

    2 n=+

    exp in

    in

    2

    0

    +

    dJnp0n, , 25

    and

    pd0,z0,k =1

    2

    +

    d exp iz01

    2 n=+

    exp

    in0qn,k , 26

    then the relationship between the source distribution and themeasured data can be expressed by

    p0n, =4+ inqn,2 + 22 + 2Hn10

    . 27

    The reconstruction process follows in three steps: 1take the 2D FFT of pd0 ,z0 ,k inverse of Eq. 26 to findthe Fourier decomposition qn ,k of n and as a functionof k, 2 compute p0n , from qn ,k based on Eq. 27,and 3 take the Hankel transform over of p0n , andthen inverse 2D FFT, i.e., Eq. 25, to find the initial pressurep0 , ,z.

    In addition, Norton and Vo-Dinh91 presented a 2.5-dimensional 2.5D i.e., homogeneous along the z axis re-construction algorithm, which actually can be obtained di-rectly by simplifying the 3D solution of Eq. 24.

    3. Time-domain algorithmsIn Sec. VI C 1, we introduced approximate time-domain

    algorithms, such as the Radon transform approximation for-mula Eq. 11 and the modified back-projection formula Eq.

    9212. Following these algorithms, Finch et al. reported on a

    Downloaded 30 Jul 2006 to 165.91.48.1. Redistribution subject to Atime-domain reconstruction formula for the spherical geom-etry based on the inverse of the spherical Radon transform.Based on Eq. 9, the formula takes the following form as

    p0r = 1

    2r02

    S0

    dS0r0, t = r r0

    r r0

    , 28

    where r0 , t= t0t pdr0 , tdt and is the gradient over vari-

    able r. The reconstruction first back-projects the data r0 , tto the image space and then takes the space filtering by 2.Both Eqs. 16 and 28 are exact inverse solutions. In addi-tion, if we introduce velocity potential r , t defined byr , t=0

    t pr , tdt /c , the density,59 we can rewriteEq. 28 as

    0r = 1

    2r02

    S0

    dS0dr0, t = r r0 , 29

    where 0r=p0r /c and dr0 , t=0t pdr0 , tdt /c.

    r , t are smooth functions that can significantly depressnoise.

    In a study of exact Fourier-domain reconstructions, Xuand Wang93 derived a universal back-projection formula forall three types of imaging geometries: planar, spherical, andcylindrical surfaces as follows:

    p0r = 2

    0

    S0

    n0sdS0 pdr0, t

    t

    t=rr0

    , 30

    where 0 is the solid angle of the whole measurement sur-face S0 with respect to the reconstruction point insideS0 :0=2 for the planar geometry and 0=4 for thespherical and cylindrical geometries. The inversion formulaEq. 28 for the spherical geometry given by Finch et al.92

    can be simplified to Eq. 30 See Ref. 93 for details.Further, Eq. 30 can be rewritten in a back-projection

    form as

    p0r = 0

    br0, t = r r0d0/0, 31

    with the back-projection term related to the measurement atposition r0,

    br0, t = 2pdr0, t 2tpdr0, t/t , 32

    where d0=dS0 / rr02 n0s rr0 / rr0, and the unit

    vector n0s is the normal of the measurement surface pointing

    to the source. The element d0 is the solid angle of the smallelement dS0 with respect to the point P of the reconstruction.Actually, the ratio d0 /d0 is the solid-angle weightingfactor, which stands for the contribution from the detectionelement dS0 to the reconstruction at point P. The factorn0

    s rr0 / rr0 is the angle between the normal of dS0and rr0 the vector pointing from the point of detection tothe point of the reconstructed source. The factor t= rr0

    compensates for the acoustic wave diffraction attenuationthat is inversely proportional to the traversing distance fromthe acoustic source to the detection element. Obviously, themodified back-projection Eq. 12 is an approximation of Eq.31 under the following conditions: 1 2pdr0 , t / t is negli-

    s sgible as k

    rr01, and 2 n0 rr0 / r0rn0

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  • 041101-12 M. Xu and L. V. Wang Rev. Sci. Instrum. 77, 041101 2006 n0 as r r0, i.e., the source is located near the centerregion. In reality, the measured PA signals may have someamplitude or phase distortions caused by the temporal re-sponse of the detection system, including the illuminationpulse or the pulse response of the detector. If the systemresponse can be known, a deconvolution method can be usedto minimize these distortions and recover pdr0 , t orpdr0 , t /t. A discussion about how to implement the back-projection algorithm can be found in Ref. 93.

    In addition, Xu and Wang94 applied the time reversalmethod to PAT and TAT with a diffracting source using onlythe field, rather than both the field and its gradient, measuredon an arbitrary closed surface that enclosed the initial source.They presented a formal back-projection solution with theexpression of Greens function subject to the homogeneousDirichlet boundary condition. However, it is usually difficultto find an analytic expression for an arbitrary boundary.Therefore, under the ray approach a geometrical optics ap-proximation that ignores the multiple reflections from theDirichlet boundary, they derived an approximation formulathat is identical to Eq. 31 in the full view case. This resultactually indicates that, in the spherical geometry, the multiplereflections from the Dirichlet boundary cancel out in the end.See Ref. 93 for detailed proof.

    4. Aperture enclosing and limited viewIn exact algorithms, the PA sources should be detectable

    in a full view by a closed spherical surface, a planar surfaceof an infinite extent, or a cylindrical surface of an infinitelength. In other words, as shown in Figs. 7a and 7b, eachpoint of the object can be detected by the detectors trajec-tory with 4 steradians in the 3D enclosing case sphere andcylinder and with 2 radians in the 2D enclosing casecircle; 2 steradians are required in the planar surface and radians for a line measurement.

    Actually, we can regard the planar geometry as a specialenclosing case if we assume that at r0 there is another mea-surement surface S0 that is parallel to S0 and that these canbe combined to provide a 4 steradian enclosure, as shownin Fig. 7b. However, since S0 is far away from the finite-size object, the measurement pdr0 , t over S0 alone is suffi-cient to provide an exact reconstruction in the limits of theRadon transform r0, as discussed above in Sec.

    FIG. 7. Measurement surface enclosing: a and b. Diagram of detectionregion: c and d.VI C 1. Therefore, it is reasonable that the measurement

    Downloaded 30 Jul 2006 to 165.91.48.1. Redistribution subject to Apdr0 , t over S0 alone offers an exact reconstruction. Like-wise, the line measurement in the 2D case with a radianenclosure is sufficient for an exact reconstruction.

    However, in practical applications, the measurement sur-faces are generally finite and partially closed, and the PAsignals cannot be collected from all directions. For example,the solid angle of detection is at most 2 steardians for abreast in a hemispherical form. Therefore, what we face inmany actual cases is an incomplete data problem. Algorithmsfor full-view data can be extended to the limited-view casesimply by assuming that the unmeasured data are zero or byestimating them from measured data through other methods,such as interpolation. In practical implementations, limited-view problems usually result in the loss of some part of thehigh-frequency information and, hence, the blurring of somesharp details.69,95

    Both Xu et al.69 and Pan et al.95 have conducted numeri-cal simulations in 2D circular measurement cases. Their re-sults indicate that for many objects possessing boundaries,the images reconstructed from reduced-scan data, such as the-scheme data, can have a numerical accuracy that is similarto that of full-scan images. Similar results hold in the 3Dcase.

    Patch96 presented a study of the partial scan problem inTAT using ultrasound transducers located on the bottom of aspherical bowl, where z0. The inversion formulas for thecomplete data case, where the transducers measured allover the bowl, weight the data from the lower hemispheremore heavily as reconstruction points in z0. The unmea-sured data, corresponding to transducer locations on the topof the bowl, could be estimated from the measured databased on the consistency conditions of the data; however,this process is clearly unstable, but somewhat tempered bythe reconstructions 1 /r weighting.

    A detection region, within which all points have suffi-cient detection views, can be defined by the following rule:69

    All lines connecting nondetection points along the scanningcircle in 2D imaging or a sphere in 3D imaging cover theinvisible domain and its complement is covered by all ofthe lines connecting the detection points from the detectionregion. In the invisible domain, some boundaries can be re-covered stably while others blur away. Namely, the parts ofthe boundaries that allow normal lines to pass through adetector position, and only those, can be stably recovered.The above conclusions are illustrated in Figs. 7c and 7d,where the invisible parts of the object boundaries, i.e., theones that will be blurred during the reconstructions, areshown with dotted lines and the detection region is shaded.

    Particularly, the scanning view is quite limited in themeasurement of only a part of a line or a plane; conse-quently, artifacts and interface blurring appear in the recon-structed images. In fact, one can never have an object im-mersed entirely into the detection region in the planar andlinear detection geometries because the normal lines to anyinterfaces that are orthogonal to the detector plane linenever pass through a detector. Consequently, those parts of

    the interfaces will be blurred in any kind of reconstruction.

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  • 041101-13 Photoacoustic imaging in biomedicine Rev. Sci. Instrum. 77, 041101 2006To reduce the artifacts, we can combine multiplanar mea-surements by including, for example, an open-box-shapedmeasurement surface.

    In the reconstruction, view-angle weighting can help tominimize a particular distortion as described below. For ex-ample, when imaging a human breast with a hemisphericalmeasurement surface, the solid angle for all detectors on thehemispherical surface with respect to a location inside thebreast is less than 4 and varies at different locations. Thus,for sources at different locations but with the same ampli-tudes, the amplitudes in the reconstruction image will vary atdifferent locations as well, which causes distortion in recon-struction. A straightforward way to compensate for this kindof reconstruction distortion, which results from a limitedview, is to normalize the reconstruction at each location by atotal solid angle weight d0, as shown in Eq. 31.

    Half-closed 2 steradians for 3D and radians for 2Dmeasurement can provide a reasonable reconstruction. Themeasured data become more Radon-like as the integrationshells arcs approximate planes lines when the detectorsmove away from the objects; therefore, more accurate im-ages can be reconstructed from a half-enclosing scan.

    D. Spatial resolution

    Spatial resolution, one of the most important parametersin imaging, is limited in PAT by many factors. The aforemen-tioned reconstruction model is based on the following as-sumptions: 1 homogeneous sound speed, 2 full-angleview, 3 impulse excitation, 4 wideband detection, 5point detector measurement, and 6 continuous sampling.Sometimes, these assumptions may not be realistic. For ex-ample, acoustic inhomogeneity blurs a reconstructed imagebecause the resulting sound speed variations may cause asignificant change in the time of flight for sound to travelfrom the source to detectors. In practice, we may slightlyadjust the time of flight in the reconstruction to obtain a goodfocused image of the region of interest. As discussed pre-viously, a limited-angle view also affects spatial resolutiondue to gaps in the raw data. In the investigation of an objectof a size larger than the micron scale in soft tissue, the ther-mal diffusion effect on the PA signal excited by a pulse witha duration of less than the micron scale is negligible, i.e., thethermal confinement condition is met. However, the stresspropagation in the pulse duration can significantly blur thePA signal as expressed by a convolution in Eq. 7, i.e., thestress confinement condition is not met. This blurring effectactually is due to the bandwidth of the PA signal that isdetermined by the finite width of the excitation pulse.

    In reality, any ultrasound detector has a finite sensingaperture, rather than a point, which results in a finite spatial-frequency bandwidth, and any detection system includingan ultrasound detector has a finite response time, which re-sults in a finite temporal-frequency bandwidth. If the detec-tion system is linear and time invariant, the real signal de-tected at position r0 can be expressed by the convolution ofthe surface integral over the aperture of the detector over the

    impulse response Idt of the detection system,

    Downloaded 30 Jul 2006 to 165.91.48.1. Redistribution subject to Apdr0,t =

    +

    dIdt r

    d2rWrper0 + r, ,

    33

    where r points to an element on the surface of the detectorwith respect to the position of the detector r0, Wr is aweighting factor that represents the contribution from thevarious surface elements of the detector to the total signalreceived by the detector, and per0 , t is expressed in Eq. 7.The measured data pdr0 , t are used to reconstruct the initialpressure p0r. We combine the excitation pulse with the PAdetection system and denote the temporal impulse responseof the detection system as Ht that equals

    Ht =

    +

    dIdt Iet . 34

    Then, one can rewrite Eq. 33 in the Fourier domain as

    pdr0,k = Hk r

    d2rWrpr0 + r,k , 35

    with Hk being the Fourier transform of Ht and

    pdr0,k = ik d3rp0rGkr,r0 . 36The pressure pdr0 ,k is the idealized measurement with apoint detector Wr=r and a Dirac-delta impulse ex-citation and detection Ht=t. As mentioned before,p0r can be perfectly recovered from the idealized measure-ment pdr0 ,k.

    A point-spread function PSF can be used to describespatial resolution. PSFs in the full-angle view, as a functionof the bandwidth of the measurement system and the finitesize of the detector aperture, have been investigated for thespherical, planar, and cylindrical detection surfaces.97,98 Be-low, we summarize the results as well as discuss the discretespatial sampling effect on reconstruction.

    1. BandwidthAs shown in Eq. 35, the temporal-frequency bandwidth

    of a detection system determines the temporal-frequencybandwidth of the detected PA waves. The resolution of a PAimage is actually limited by the bandwidth of the detectedPA waves. If we set the zero time point at the center of theimpulse response of the detection system Ht, then Ht isassumed to be split into even and odd portions as Et andOt, respectively; and, further, the corresponding PSF isfound to be97

    PSFR = 12R

    dERdR

    , 37where R is the distance between the point of observation andthe acoustic source. The odd part is canceled out in the re-construction.

    We take the rectangle-shaped bandwidth, which is cutoff at the frequency fc, as an example. In this case, the im-pulse response function Ht is the sinc function,sincKtK /, where sincx=sinx /x and K=2 /c c, the

    cutoff wavelength=2c / fc. We find that the dependence of

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  • 041101-14 M. Xu and L. V. Wang Rev. Sci. Instrum. 77, 041101 2006the PSFs on the bandwidth of all of the measurement geom-etries shares the same space-invariant expression as97

    PSFR = K322

    j1KRKR

    , 38where j1 is a first-order spherical Bessel function of thefirst kind. If the full width at half maximum FWHM of thePSF is used to represent the spatial resolution, then, in thiscase, RH0.80c. In an analogy to the Rayleigh criterion, analternative definition of spatial resolution is the distance be-tween two points in the object space when the maximumpositive of the first PSF overlaps with the first minimumnegative of the second. By this definition, the spatial reso-lution becomes RR0.92c, which is slightly wider than theFWHM definition. The Rayleigh criterion is more appropri-ate, as negative-value artifacts are introduced into the recon-struction due to the band limit. Note that this temporal-frequency bandwidth-limited resolution is isotropic aroundthe point of observation.

    2. Sensing apertureAs shown in Eq. 35, the finite sensing aperture of the

    transducer, or element, in an array acts as a spatial filteralong the measurement surface; this actually determines thespatial-frequency bandwidth of the detected PA waves.Hence, the finite sensing aperture blurs the resolution of thePAT image, but the dependence of the PSF on the aperturesize differs among the various measurement configurations.97

    Rigorous expressions can be given when the detector sur-faces are assumed to have the same curvature properties asthe measurement geometries and the temporal bandwidth isunlimited. Of course, the detector aperture is much smallerthan the measurement surface. The axial extension of thePSF due to the detector aperture is negligible compared tothe lateral extension.

    If the detection scan is along a straight line, such as aplanar scan or a z scan in the cylindrical scan, the lateralextension of the PSF approximates RLh,

    97 where h isthe distance of the point source to the scan line and is thediameter of the detector. Hence, the lateral resolution in thiscase is blurred by the detector aperture no matter where thepoint source is.

    If the detection scan is along a circle, such as a sphericalor cylindrical scan, the lateral extension of the PSF can beestimated by RCrr /r0,

    97,98 where r is the distance be-tween the point source and the center of the scan circle, r0 isthe radius of the scan circle, and is the diameter of thedetector. The farther the point source is away from the center,the wider the PSF is and vice versa. Therefore, the lateralresolution improves when the point source approaches thecenter of the scan. This is because the scan along a circleactually measures the angular information with a resolutionof /r0.

    3. Discrete samplingDiscrete sampling in the measurement will also affect

    the resolution of a PAT image. The PA signals are sampledaround the source at a series of discrete spatial detection

    positions with a spatial sampling period the inverse of the

    Downloaded 30 Jul 2006 to 165.91.48.1. Redistribution subject to Afrequency, and at each detection position the signals aresampled at a series of discrete temporal points with a tem-poral sampling period. According to the sampling Nyquisttheorem, to reconstruct a signal from its periodically sampledversion, the sampling frequency must be at least twice themaximum frequency of the signal, which is applicable toboth spatial and temporal samplings. Otherwise, aliasing ar-tifacts occur and cause confusion and serious measurementerrors, in which frequency information that is higher thanhalf the sampling frequency will disguise itself as low-frequency information. From a users point of view, aliasinglimits the useful frequency range such that the highest fre-quency component is no more than half the sampling fre-quency, which, consequently, limits the spatial resolution ofthe reconstruction.

    If the spatial sampling period is less than half the diam-eter of the sensing aperture of the detector, the reconstructioncan avoid, or significantly reduce, aliasing due to the spa-tially discrete sampling. However, a further decrease in thespatial sampling period does not improve the spatial resolu-tion of the images nor provide other significant advantages.It does, however, cause an increase in the amount of rawdata. In practice, it is reasonable to set the discrete spatialsampling period to be two to five times smaller than thesensing aperture of the detector in a scanning system. Then,the sensing aperture size of the detector limits the lateralresolution while the temporal-frequency bandwidth affectsboth the axial and lateral resolutions.

    E. Large planar detector

    For simplicity, assuming that Wr=1 and a t EMsource is used, we can simplify Eq. 32 to

    psr0,t = r

    d2rpdr0 + r,t , 39

    where the subscript s denotes the measurement is a surfaceintegral. Substituting Eq. 9 into Eq. 39,

    psr0,t = r

    d2r

    t t4 r0+rr=ct p0rd .40

    Now, the problem is to reconstruct p0r from psr0 , t basedon Eq. 40. It will be mathematically difficult if the detectorhas a random-shaped aperture. However, in special cases,such as with a planar-surface detector, Eq. 40 can be furthersimplified. Taking the Fourier transform of Eq. 40, we have

    psr0,k = ik d3rp0r r

    d2rGkr,r0 + r .

    41

    As shown in Fig. 8, we assume the planar detector has alarge surface, ideally infinite in size. The vector r0 is alongthe normal of the planar surface, and r in this case is per-pendicular to r0. We use the local coordinate system alignedwith r0, in which r0 0,0 ,0, r xl ,yl ,zl, r xl ,yl ,0, and rd

    2r=sdxldyl. Then, considering the

    expansion of Greens function in the Cartesian coordinates

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  • 041101-15 Photoacoustic imaging in biomedicine Rev. Sci. Instrum. 77, 041101 2006function see, e.g., Ref. 97, we can simplify Eq. 41 to

    ps0,k =1

    2 p0xl,yl,zlexpikzldxldyldzl.

    42

    Further, taking the inverse Fourier transform of Eq. 42, weget in the local coordinate

    2ps0, t = p0xl,yl,zl = tdxldyl. 43The above equation indicates that the PA signal detected by aplanar surface at a given time actually measures the integralof the initial PA source, or energy density function, over aplanar surface parallel to the detector surface at a delayeddistance characterized by the acoustic time of flight betweenthese two planar surfaces. Therefore, the standard Radontransform can be directly applied to the measured data thatare detected through rotating the planar detector tangentiallyto a spherical surface of the object under study. Thus, if weassume that the detector scans over a spherical surface with aradius of r0, the reconstruction formula can be written as

    p0r = 1

    42

    0

    2

    t2psr0, t = r0 r0 rr0 d0, 44

    where 0 denotes the detection spherical surface and covers4 steradians and r0 is along the radius of the detectionspherical surface and perpendicular to the detectors surface.In addition, replacing 4 by 2 in Eq. 44 gives the reconstruc-tion formula with the measured data only on half of thedetection spherical surface since a 2-steradian measure-ment is sufficient in the Radon transform. A mathematicalproof can be found in Ref. 58. Similarly, if the sample isfrom a homogenous distribution along the z axis, a circularscan around the cylinder enclosing the sample is sufficientfor the reconstruction based on the 2D Radon transform.

    Spatial resolution using a planar receiver is determinedby the temporal frequency bandwidth, since the finite size ofthe receiver is explicitly included in the measurement andreconstruction. Spatial resolution is space invariant and high-resolution imaging should be possible with a high-bandwidth

    FIG. 8. Diagram of photoacoustic measurement at r0 with a large planardetector.receiver. However, it is not practical to make a transducer

    Downloaded 30 Jul 2006 to 165.91.48.1. Redistribution subject to Aarray using multiple large planar receivers and, therefore, wehave to rotate a large receiver to cover the entire measure-ment surface. By contrast, as discussed in the previous sec-tions, small receivers, used for simulating point measurementdata, introduce some blurring effects in the reconstructionwith analytical inversion formulas. However, a transducerarray with multiple small elements can speed the data acqui-sition.

    VII. EXPERIMENTS

    A. Breast imaging and cancer detection

    Breast cancer remains a leading cause of death amongwomen in many parts of the world. However, better diagno-sis and treatment have noticeably improved the outcomes forwomen contracting this disease. Even though we now knowthat the earlier treatment begins, the greater the chances forsurvival, the current technologies for breast cancer detectionare not particularly well suited for identifying small and/ordeep tumors in the human breast. Film-screen x-ray mam-mography is still the gold standard of breast imaging tech-nology, although it may miss up to 20% of existing lesionswhile at the same time identifying many false positives. Ac-cording to the U.S. Institute of Medicine,99 the variety andsophistication of alternative imaging technologies under de-velopment have increased greatly. These methods can be di-vided into three general categories: 1 those that are cur-rently in use, such as x-ray mammography and ultrasound,and are being further refined; 2 those that are commonlyused for medical imaging, such as magnetic resonance imag-ing MRI, but that are still experimental with regard tobreast cancer detection; and 3 novel imaging modalitiesthat may be used in the future.

    PAT, or TAT, belongs to the third imaging category forbreast cancer detection. The following advantages make PATstand out among the numerous new imaging modalities: 1PAT uses nonionizing radiation and, therefore, is harmless tohumans unlike x-ray mammography; 2 PAT relies on rf orlight absorption that is sensitive to tissue abnormality, andhence it has the potential for early cancer detection; 3 PATcan provide submillimeter spatial resolution with the detec-tion of megahertz ultrasound exited by short rf or laserpulses; 4 PAT does not require breast compression and,therefore, is less painful than x-ray mammography; 5 PATcan potentially be applied in vivo for real-time imaging withthe implementation of an ultrasound detection array, and thesame array can also produce conventional ultrasound imagesfor comparison and codisplay of two types of contrast; 6 aPAT system is relatively inexpensive comparable to the ul-trasound system plus a rf or laser source; 7 a PAT systemcan also easily incorporate other rf or optical detection sys-tems to produce pure rf or optical images so that differenttypes of contrast in the same imaging region can be codis-played to provide more information for diagnostics; and 8PAT is particularly well adapted for use with the physicalproperties of the human breast. Human breast consists of softtissues with a speed variation in the range of 10%,18 in whichultrasound propagation distortion is tolerable.79 Breast tissue

    is also easily accessible to both EM energy delivery and

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  • 041101-16 M. Xu and L. V. Wang Rev. Sci. Instrum. 77, 041101 2006ultrasound detection. Based on EM excitation sources, twotypes of PAT technologies for breast imaging are currentlyunder development: rf-based TAT and laser-based PAT.

    1. rf-based imagingCancer tissue is more rf absorbant than the surrounding

    normal tissue due to its increased water or ionicconcentration.100 Figure 9 shows a comparison of the EMpenetration depth in different types of tissues, which wascomputed based on the data reported in Ref. 100. In thatdata, the rf contrast between malignant breast tissue and nor-mal breast is about two times. It is possible that contrastagents may further improve rf absorption in a tumor region.However, so far, no research on rf absorption contrast agentsin soft tissues has been reported.

    Two groups have made significant contributions in thearea of rf-induced ultrasound imaging for breast cancer de-tection. One group, under the leadership of Dr. RobertKruger, has developed thermoacoustic computed tomogra-phy TCT scanners with 434 MHz radio waves to image thebreast. They have designed several different versions of TCTsystems.101104 At the beginning, they situated multiple singletransducers on a spherical bowl to provide array detection.However, the calibration of a large number of transducerswas difficult, so later they used an ultrasonic array with mul-tiple elements. After tests with phantom samples, such as alamb kidney65 or a porcine kidney,102 they moved to clinicaltesting.103,104 In this work,104 they were able to visualizequite well most of the cysts that could be seen on ultrasoundimages; however, fibroadenomas could not be visualized ex-

    FIG. 9. rf penetration depths in various tissues.Downloaded 30 Jul 2006 to 165.91.48.1. Redistribution subject to Acept in the case of a fibroadenoma with associated atypicalhyperplasia. The group attributed the lack of visualization ofcancers to inadequate imaging quality, etc. We believe themain problem in their system was that the rf absorption at434 MHz is too weak and the SNR was not high enough.Figure 10a shows a diagram of their recent setup Patent6633774.101 A triplanar array, consisting of a total of 128rectangular elements, was designed to approximate a spheri-cal surface with a diameter of 170 mm. The distribution ofthe detector elements was chosen to provide approximatelyuniform coverage over the surface of a hemisphere when it isrotated to a plurality of angles about the vertical axis. Eachelement is 7 mm wide and 8 mm high and has a wide band-width with a center frequency of 1 MHz. rf pulses with a0.7 s duration were directed toward the breast via eightwaveguides arrayed radially around the breast, which re-mained stationary. Figure 10b shows a TCT image of anormal breast. The field of view of the image is 2020 cm2 and has a 0.78 mm thickness because each voxel isa 0.78 mm cube. Tissues with higher water concentrationse.g., skin and glandular tissue display greater rf absorptionthan tissues with lower water concentrations e.g., fat.

    Our own group developed a prototype of an imagingsystem utilizing 3 GHz microwaves.73,76,85,90,98 rf absorptionat this frequency is about twofold stronger than that at434 MHz, according to the data shown in Fig. 9. Figure11a shows a diagram of the circular measurement configu-ration in our initial study.98 An ultrasound transducer drivenby a step motor scanned around the sample on a horizontalx-y plane; this mechanical scanning will eventually be re-placed by a circular transducer array. Both the transducer andthe sample under study were immersed in a container filledwith a coupling medium such as mineral oil. The microwavepulses transmitted from a 3 GHz microwave generator had apulse energy of 10 mJ and a pulse width of 0.5 s. Micro-wave energy was delivered to the sample by a rectangularwaveguide with a cross section of 7234 mm2 that was re-cently replaced by a waveguide horn to provide a larger il-lumination area. Figure 11b shows the image of a phantomsample with five gel absorbers made of gelatin and waterburied in a fat base, which was acquired by a 2.25 MHzunfocused ultrasonic transducer. The high contrast is due tohigh rf absorption in gel high water content and low rfabsorption in fat low water content. A preliminary study ofbreast cancer imaging was reported,105,106 in which excised

    FIG. 10. a Side view schematic of abreast imager with spherical scans. bTCT image of a normal breast Cour-tesy of OptoSonics, Inc..IP license or copyright, see http://rsi.aip.org/rsi/copyright.jsp

  • 041101-17 Photoacoustic imaging in biomedicine Rev. Sci. Instrum. 77, 041101 2006breast specimens were imaged and tumor regions wereclearly located. An example of the TAT image of a mastec-tomy specimen, which was acquired by a 1 MHz cylindri-cally focused ultrasonic transducer, is shown in Fig. 11c.106

    In summary, for breast imaging, the first challenge ofTAT is the delivery of rf energy to the breast. Because of itslong wavelength, rf energy does not readily focus into asmall region of interest for the scanning rf focuses to gener-ate images with good resolution. A better approach is to usemultiple rf sources, coming from different directions, to illu-minate a larger region as homogeneously as possible, so thatthe reconstructed images truly reflect the differential rf ab-sorption. The second challenge is to choose a proper ultra-sound frequency for the detection. Due to the large size of abreast, typically around 15 cm in diameter and the increasein ultrasound attenuation at high frequencies, optimal ultra-sound frequencies should be between 1 and 3 MHz, which

    FIG. 11. a Diagram of circular scan. b Reconstructed thermoacousticimage. c TAT image of a breast mastectomy specimen Ref. 106.can be initiated by rf pulses with a duration of submicrosec-

    Downloaded 30 Jul 2006 to 165.91.48.1. Redistribution subject to Aonds. In addition, the selection of a proper rf wavelengthwith which to initiate the process is another key to achievinggood contrast and signal-to-noise ratio.

    2. Laser-based imagingA tumor typically has more