Improving T-cell Immunotherapy for Melanoma Through a … · 2015. 6. 29. · immunotherapy, melanoma, adoptive T-cell transfer (J Immunother 2012;35:116–124) A doptive immunotherapy

Improving T-cell Immunotherapy for Melanoma Through aMathematically Motivated Strategy Efficacy in Numbers

Natalie Kronik Yuri Koganw Paul G Schlegelz and Matthias Wolflz

Summary T-cell mediated immunotherapy for malignant diseaseshas become an effective treatment option especially in malignantmelanoma Recent advances have enabled the transfer of highT-cell numbers with high functionality However with more T cellsbecoming technically available for transfer questions about dosetreatment schedule and safety become most relevant Mathema-tical oncology can simulate tumor characteristics in silico andpredict the tumor response to novel therapeutics Using similarmethods to classical pharmacokineticspharmacodynamics-typemodels mathematical oncology translates the findings into amultiparameter model system and simulates T-cell therapy formalignant diseases The tumor and immune system dynamicsmodel can provide minimal requirements (in terms of T-cell doseand T-cell functionality) depending on the tumor characteristics(growth rate residual tumor size) for a clinical study and helpselect the best treatment schedule (repetitive doses minimallyrequired duration etc) Here we present a new mathematicalmodel developed for modeling cellular immunotherapy formelanoma Computer simulations based on the new model offeran explanation for the observed finding from clinical trials that thepatients with the smallest tumor load respond better We simulatedifferent parameters critical for improvement of cellular therapy forpatients with high tumor load of fast-growing tumors We showthat tumor growth rate and tumor load are crucial in predicting theoutcome of T-cell therapy Rather than intuitively extrapolatingfrom experimental data we demonstrate how mathematicaloncology can assist in rational planning of clinical trials

Key Words mathematical oncology computer simulations cancer

immunotherapy melanoma adoptive T-cell transfer

(J Immunother 201235116ndash124)

Adoptive immunotherapy using tailored T-cell infusionsto treat malignancies has been proven to be effective in

certain types of malignancy12 However our understandingas to why certain patients respond whereas others progressis still limited Moreover clinical approaches using T-celltherapy still vary widely in issues such as how to generatelarge numbers of specific T cells how many T cells to usefor therapy and what schedule would be most effectiveThe expansion of tumor-specific T cells have been hindered

by the often low-precursor frequency in patients or healthyindividuals the loss of high-affinity T cells during ex vivoculture and the terminal differentiation of extensivelycultured and expanded T cells resulting in loss of functionand persistence upon transfer to the patient3 Recentlyprogress has been made with genetic engineering ofchimeric antigen receptors T-cell receptor transfer andsilencing of genes exerting unfavourable functions45

Furthermore use of new cytokine combinations allowsthe rapid expansion of less differentiated T cells with anenhanced functional capacity6 However recent preclinicaland clinical data also reveal the dangers of this type oftherapy with several serious adverse events related to T-cellinfusions being reported7ndash9 Therefore with high numbersof antigen-specific T cells becoming available for clinicaluse and at the same time considering the potential risks weasked whether rather than intuitively deciding on a givenT-cell regimen mathematical modeling would help todefine the prerequisites of an effective immunotherapyapproach

Integrative mathematical oncology is widely used todecode the cancerous process10 Several mechanistic ordescriptive models have been proposed to better under-stand the growth dynamics of cancerous cells embeddedin the nonmalignant environment Part of the modelshas studied 3-dimensional growth of tumors whereasothers have preferred the use of nonspatial mathematicalmodels1112

In this context modeling tumor-immune interactionshas been key issue over the past 2 decades De Boer et al13

were one of the first to model the interaction betweenT cells macrophages and tumor cells taking into accounta variable immunogenicity of the tumor cells In this insilico model small variations in specific T-cell subsetsespecially the number of activated helper T cells had alarge impact on tumor cell growth whereas calculatedrequired number of cytotoxic T cells to achieve the sameeffect was 1000-fold higher However Takayanagi andOhuchi14 provided mathematical analysis showing that anincreased number of cytotoxic T cells may ultimately tilt thebalance between tumor and immune system in favor of thelatter Other groups have investigated different aspects ofimmunotherapy such as the role of tumor dormancy thetherapeutic use of interleukin-2 (IL-2) and the effects oftumor-associated cytokines such as transforming growthfactor b (TGFb) or epidermal growth factor15ndash19 For acomprehensive review of simulation methods of tumorimmunology see Woelke et al20

We recently developed a mathematical model of T-celltherapy for glioblastoma that includes the mutual inter-actions between the immunosuppressive tumor and theexpression of major histocompatibility complex (MHC)receptors which can be induced by cytotoxic T-lymphocyte(CTL)-secreted cytokines21 The mathematical model

Received for publication June 18 2011 accepted August 28 2011From the Department of Applied Mathematics Holon Institute of

Technology Holon Israel wInstitute for Medical BioMathematicsBene Ataroth Israel and zDepartment of Pediatric HematologyOncology and Bone Marrow Transplantation University Chil-drenrsquos Hospital University of Wuerzburg Wuerzburg Germany

Reprints Natalie Kronik Department of Applied Mathematics HolonInstitute of Technology 52 Golomb St Holon Israel (e-mailkalev001umnedu)

Supplemental Digital Content is available for this article Direct URLcitations appear in the printed text and are provided in the HTMLand PDF versions of this article on the journalrsquos Websitewwwimmunotherapy-journalcom

Copyright r 2012 by Lippincott Williams amp Wilkins

BASIC STUDY

116 | wwwimmunotherapy-journalcom J Immunother Volume 35 Number 2 FebruaryndashMarch 2012

furthermore predicts the existence of a threshold value ofT-cell infusion rate which needs to be crossed before asignificant impact on the tumor growth can be observed22

In this study we present a mathematical model forimmunotherapy in the context of published clinical dataWe chose immunotherapy by transfer of ex vivo expandedtumor-specific T cells for melanoma patients as thistherapeutic strategy has been shown to be especiallyeffective in this patient population At the same time littleis known about the actual numbers of T cells required fortherapeutic treatment resulting in a wide variation in T-cellnumbers across clinical studies In fact T-cell dosing isoften calculated based on body surface areamdasha conceptwhich stems from pharmacological substances which relyon renal excretionmdashor on body weight rather than on theestimated tumor burden However this is exactly wheremathematical modeling may help to design an individua-lized treatment schedule for each patient On the basis ofreported parameters in the literature a mathematical modelwas built by transferring a descriptive model into mathe-matical equations Using experimental quantitative datareported recently the model was then retrospectivelyvalidated We then analyzed treatment schedules usedpreviously in clinical trials to assess the magnitude of afunctional T cells response required to efficiently targetmalignant melanoma We show that even high T-cellnumbers used for therapy will unlikely influence large andfast-growing tumors unless the functional capacity of eachT-cell product is improved Furthermore finer quantifica-tion of residual tumor load may assist in identifyingpatients which will benefit from this type of therapy

METHODOLOGYIn our previous study21 a simplified mechanism for

alloreactive cellular therapy for glioblastoma was intro-duced Partially based on this previous study we developeda new model with special adaptation to melanoma andmelanoma immunotherapy parameters Figure 1 shows ascheme of the model The mathematical equations are

Mathematical Equations

Tfrac14 rT 1

T

K

aT

MI

eT thornMI

aT bFbthorn eT b

Fbthorn eT b

CT

hT

hT thornTeth1THORN

Equation (1) describes the tumor cell T dynamics(the dot is the time derivative) as influenced by tumor cellmaximal number K CTL population C killing efficacy ofthe CTLs aT presence of MHC class I receptors MI andthe level of TGFb secretion For full explanations here andhereafter and list of parameters see Appendix Supple-mental Digital Content 1 httplinkslwwcomJITA157

Cfrac14 mCCthorn I eth2THORN

Equation (2) describes the dynamics of the CTLs Cby the death rate of CTLs proportional to the population ofCTLs with coefficient mC and finally I the CTL infusionrate

F bfrac14 abT T mbFb eth3THORN

Equation (3) describes the dynamics of TGFb Fb asproportional to the tumor cell population T with abT as aproportion coefficient and is destroyed at a rate of mb

proportional to FbF gfrac14 agC C mg Fg eth4THORN

Equation (4) describes the dynamics of IFNg Fg asproportional to the population of CTLs C with propor-tion coefficient agc and is destroyed at a rate mgproportional to the amount of Fg

MI frac14 gMI thorn

aMI g Fg

Fgthorn eMI g mMI MI eth5THORN

Equation (5) describes the dynamics of MHC class Imolecules MI are presented on the tumor cell surface at arate gMI this rate is augmented by a Michaelis-type termdependent on Fg The MI molecules are internalized at arate mg

Model AssumptionsThe current model assumes that a primary tumor cell

population and a metastatic tumor cell population areindistinguishable by size alone or level of malignancy permetastatic population We feel it is a safe assumption tomake for most of the patients at least at this fundamentalstage of model development

FIGURE 1 A simplified model for the interaction of melanomacells and cytotoxic T cells and the respective cytokinesMelanoma cells express immunogenic antigens in the contextof the MHC I complex but also secrete TGFb which inhibitsT-cell activity Upon contact with melanoma cells exogenouslyinfused CTLs lyse their target and secrete IFN-g IFN-g leads toupregulation of MHC class I in the melanoma cells which inreturn increases the CTL-mediated effect IL-2 injections prolongpersitence of infused CTLs Endogenous cytotoxic T cells areincluded as constant influx to the T-cell effector compartmentCTL indicates cytotoxic T lymphocyte IFN interferon ILinterleukin MHC major histocompatibility class TGFb trans-forming growth factor b

J Immunother Volume 35 Number 2 FebruaryndashMarch 2012 Improving T-cell Immunotherapy

r 2012 Lippincott Williams amp Wilkins wwwimmunotherapy-journalcom | 117

COMPUTER SIMULATIONSComputer simulations were performed using Matlab

For all computer simulations tumor initial population sizewas determined between 11010 to 51011 cells We divi-ded this range into 50 equal intervals Tumor growth rateswere set between 00001 to 001hour In the same mannerthat range was divided into 10 equal intervals Allcombinatorial possibilities were then crossed creating5010=500 combinations of tumor initial populationsize and tumor growth rates The crossing imitates a virtualpopulation of patients with a wide range of personal diseasecharacteristics Computer simulations predicting tumorpopulation size under different adoptive T-cell therapy regi-mens over 300 days were run with these initial conditionsOf this 500 virtual patientsrsquo grid (or data set) 100 patientswere selected randomly and their simulation results werepresented in plots and summary statistics The results ofrandomly selected 100 patients were plotted

Clinical Interpretation of ComputerSimulation Results

Response Evaluation Criteria in Solid Tumors arebeing adopted in many clinical studies to help harmoniza-tion of data analysis for clinical outcome23 We adoptedthese criteria for the definition of progressionnonrespon-ders (larger than 120 of original size) stable disease (70to 120) and partial (30 decrease) or complete response(disappearance)

RESULTS

Description of the ModelThis mathematical model simulates the effect of cyto-

toxic lymphocytes on melanoma cells (Fig1) It consists of5 differential equations describing the dynamics of thetumor growth CTL persistence cytokine secretion andMHC class-I expression The exact dynamics is controlledby the following key parameters cytolytic activity of theT cells tumor growth rate survival of the T cells and thecollective sensitivity of the tumor cells to killing (hT) It is arefined model of our previous study modeling immunother-apy for glioblastoma patients2122 A detailed description ofthe model and all the relevant parameters is given in theAppendix Supplemental Digital Content 1 httplinkslwwcomJITA157

Selection of Studies Simulated With This ModelWe wanted to simulate 4 representative immunother-

apy studies based on the data obtained from publishedliterature to model the greatly varying treatment schedulesand results24ndash26 The 4 studies were selected using the

following criteria clinical trials (phase III) using antigen-specific T cells to target malignant melanoma dataavailable in the literature to model treatment schedule interms of dose and timing different research groups withonly 1 study per group

The 4 selected studies are summarized in Table 1illustrating the significant variation in terms of T-cellnumbers administered frequency of infusions and initialtumor load Therefore these main factors were analyzedwith this model

Polyclonal T-cell Lines in Stage III MelanomaKhammari et al24 compared infusions of ex vivo

expanded tumor infiltrating lymphocytes (TILs) with IL-2versus IL-2 treatment alone Eighty-eight patients wereenrolled and equally distributed into each arm of the studyThese patients had not received earlier systemic treatmentand were enrolled when regional lymph node recurrenceoccurred after surgery (stage III T1-4N recurrent M0) Thegroup reports on a long follow-up of more than 10 years

Patients with 1 invaded lymph node were comparedwith patients with multiple lymph node metastasis Patientswith only 1 invaded lymph node receiving TIL and IL-2had a striking survival advantage over patients receivingIL-2 only (333 vs 6842 relapse percentage) Thisdifference was not seen in patients with multiple lymphnode metastases suggesting that tumor load impactsefficacy of the treatment Tumor load and tumor growthrate for each individual patient however are not reportedin the study2122 To model this study we therefore chose arange of initial tumor sizes and tumor growth rates (seeMethodology section for details) and simulated thepotential outcome for 500 different combinations of initialtumor load and growth rate values (Fig 2) In analogyto the clinical protocol we simulated a treatment regimenwith 2 infusions given 1 month apart Simulations wereperformed using the reported median cell dose of 171010

TILs (Fig 2A) and the lowest (22109 Fig 2B) andhighest (271010 Fig 2C) doses As the best reportedvalue of tumor specific T cells was 138 T-cell dose wascorrected for 10

Simulated response rate (all the patients but thenonresponders) varied between 1 and 25 (Figs 2BC) depending mainly on TIL dose However even withthe highest T-cell dose and assuming favorable conditionsfor the T cells only tumors with the lowest size couldbe delayed significantly in their growth or reduced insize reflecting complete remission according to ResponseEvaluation Criteria in Solid Tumorsrsquo criteria Thusthe mathematical model predicts that repetitive lysis oftumor cells by each T-cell infused results only in rare

TABLE 1 Actual Treatments Chosen for Simulation

Study Stage Type and Number of Infused T Cells Schedule IL-2

Khammari et al24 III TIL 171010 Two infusions 1 month apart 6106 IUm2 5 dwk 2wkYee et al26 IV T-cell clones 33109m2 Four infusions every 2wk 025-1106 IUm2 for 2wkMackensen et al25 IV T-cell lines 21108 Three infusions every 2wk 3106 IUm2 for 6 dDudley et al27 IV TIL 31010-91010 One bolus infusion 72105 IUkg intravenously every

8 hours to tolerance up to 15doses days1-3

IL indicates interleukin TIL tumor infiltrating lymphocyte

Kronik et al J Immunother Volume 35 Number 2 FebruaryndashMarch 2012

118 | wwwimmunotherapy-journalcom r 2012 Lippincott Williams amp Wilkins

circumstances such as low residual tumor size in a signifi-cant impact on the tumor

The fact that only patients with involvement of a singlelymph node showed a benefit in this study suggested a qua-ntitative effect of the T cells in the tumor load However ina subgroup analysis of the 27 patients for whom data on thecontent of tumor-reactive T cells were available no cor-relation was found between clinical outcome (as indicatedby relapse vs no relapse) and the applied dose of antigen-specific T cells28 One likely explanation may be the smallsample size Computer simulation offers an alternativeexplanation Figure 3 plots initial tumor size versussimulated final tumor size Simulations are shown for thesame 3 different T-cell doses For tumors larger than11011 no correlation can be seen between outcome (finaltumor size) and initial tumor volume regardless of theT-cell dose infused This is in line with the clinical observ-ation Only when the initial tumor burden is sufficientlysmall a dose-effect relationship of the T cells can beestablished suggesting that rather than clinical staging aswas done in this trial a detailed volumetric analysis ofresidual tumor massesmdashif at all possiblemdashmay representbetter correlation with clinical effectiveness of a T-cellresponse TIL dose-effect relationship can be seen only forsmall initial tumor size and completely vanishes for largeinitial tumor cell numbers (Fig 3)

T-cell Clones With Defined SpecificityThe exact fraction of antigen-specific T cells within the

infused T-cell lines remained unknown in the study byKhammari et al24 To address better the actual numberof antigen-specific T cells we simulated a different studyin which clonally expanded antigen-specific T cells thussuggesting similar tumor reactivity were used26 Tenstage IV melanoma patients (metastatic disease) weretreated with 33109m2 CTLs given in biweekly in-fusions 4 timesmdashwith 2 patients receiving 6 and 7 infusionsrespectively and 2 patients receiving only 3 infusionsDetailed data on initial tumor burden are not availableYee et alrsquos26 clinical data report on 7 of 10 patients ashaving partial responses 5 of which reaching stable diseasewith a mean duration of approximately 1 year and 2patients with progressive disease Mathematical modelingsuggests a 59 response rate (complete and partialresponses) at 300 days posttreatment (Fig 4) Bearing inmind that the actual tumor burden or tumor growth ratesof the patients were not available the agreement betweenthe clinical trial and the simulations is good The number ofantigen-specific T-cell numbers of each infusion in Yeeet alrsquos26 trial was comparable to the highest T-cell doseinfused in the Khammari study however 4 infusions weregiven in Yee et alrsquos study as opposed to 2 infusions in theKhammari trial This may account for the higher response

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FIGURE 2 Simulations of tumor cell number and TIL dose in the Khammari et al24 clinical trial A to C Simulations of time-dependenttumor cell number dynamics of 100 random simulations are shown Virtual tumors with randomly chosen initial tumor sizes (1010

to 51011 cells) and different growth rates (00001 to 0001h) are simulated with (A) 0851010 TILs given twice 1 month apart(B) 0111010 TILs twice 1 month apart and (C) 1351010 TILs twice 1 month apart Tumors that have reduced in size to practical 0(RECIST complete response CR) are marked in red (thin solid line) tumors that have reduced by 30 (RECIST partial response PR) aremarked in blue (thick solid line) Tumors that have stabilized between 70 and 120 of their original size (RECIST stable disease SD)are marked in green Black (dotted line) marks time-dependent tumor cell numbers simulations that were nonresponsive NR The2 ripples observed up to day 44 are due to the IL-2 treatment given for 2 weeks after each TIL transfusion IL indicates interleukinRECIST Response Evaluation Criteria in Solid Tumors TIL tumor infiltrating lymphocyte



ratesmdashobserved clinically and simulated mathematicallymdashin Yee et alrsquos trial

Multiple Infusions With Short-term CulturedT-cell Lines

To address the question how the number of infusionsaffects treatment success we chose a study performed byMackensen et al25 Polyclonal T-cell lines were generatedagainst a single epitope (MelanAMART1) and infused(average 21108 T cells) Three T-cell infusions werescheduled 2 weeks apart followed by up to 10 infusions in4-week intervals IL-2 was administered for 6 days aftereach infusion Eleven patients were treated25 One patientachieved a complete response and 1 patient achieved partialresponse 2 others had stable disease and mixed reactionsComputer simulations of randomly selected virtual patientsshowed a positive response rate of 10 (at day 300posttreatment) which is lower than the reported clinicaldata (36 3mo minimal observation time) (Fig 5A)Next we used the model to search for more effectiveregimens which were not observed in Mackensen clinicaltrial Figure 5B shows that all other parameters beingequal increasing the T-cell dose to 5108 cells (which isstill 10 times less than the dose apllied in Yee et al26)increases response rates within the simulation to 20When T-cell mediated tumor lysis parameter was increased2-fold (Table 1 in Supplemental Appendix SupplementalDigital Content 1 httplinkslwwcomJITA157 ) a posi-tive effect was observed on 24 of the simulated patients

(Fig 5C) combining higher lytic capacity and increasedT-cell dose lead to a greatly increased efficacy of 34(Fig 5D)

Excessive T-cell Numbers Combined WithChemotherapy

Whereas experimentally it is possible but difficult toassess differences in lytic capacity between different clinicalstudies due to differences in handling the T cells and per-forming the assays T-cell numbers are more comparableA correlation between cell numbers and clinical efficacy wasalready established with the aforementioned simulationsHowever the magnitude of the T-cell dose needed toachieve durable responses in most of the patients wasunclear We therefore analyzed data of a clinical trialperformed by Steve Rosenberg group in which a very highnumber of T cells were usedmdashin fact to the best of ourknowledge it is the highest number of T cells used andreported for adoptive T-cell therapy2729 These studies haveused nonmyeloablative chemotherapy before the TILinfusion A total of 11011 cells were given in 1 bolusinfusion and more importantly total body irradiation (TBI)therapy in a low dosage (2Gy) and in high dosage (12Gy)was added to the therapy29 The positive response rate was13 of 25 (52) and 18 of 25 (72) respectively In thesimulations we show here we chose to simulate the high-dose treatment assuming antigen specificity of 10 basedon Table 3 in Dudley et alrsquos study29 When this high dosewas given alone a positive response in 52 of the patients

0 05 1 15 2 25 3 35 4 45 5

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FIGURE 3 Predictions of the final tumor cell number as a result of TIL dosage according to data derived from Khammari et al24 Onehundred virtual patients were simulated as in Figure 2 except that TIL dose was also randomly chosen from 5 different dosages between0111010 to 1351010 given twice 1 month apart Upper illustration shows simulated treatment results using the lowest TIL dosemiddle illustration shows simulated results using intermediate TIL dose (0731010) and lower illustration shows simulated treatmentresults with the highest TIL dose Red dashed line delineates the separation between responsive tumor sizes to its left and nonresponsivetumor sizes to its right TIL indicates tumor infiltrating lymphocyte



was predicted (Fig 6A) Next we simulated a possible effectof low intensity TBI immediately before the TIL infusionWe assumed that such a treatment could decrease tumorload Figure 6B shows that reducing tumor load by 10increased positive responses to 56 To simulate the highTBI treatment we assumed that in addition to tumor sizereduction the high dose TBI sensitizes tumor cells to CTL-mediated lysis (eg by an increase in tumor accessibility dueto proinflammatory signals) Such a change in the tumor-CTL accessibility is reflected in the parameter hT A simu-lated increase of 33 results in a similar positive responsein 71 of the virtual patients (Fig 6C) The accessibilityparameter hT is used in modeling tumor-immune inter-actions to attenuate the killing efficacy of CTLs as thetumor increases (for instance de Pillis et al30) Of allparameters used it is the most difficult parameter to assessexperimentally as multiple events leading to a potentialincrease in sensitivity of the tumor cells for T-cell-mediatedlysis may be represented by this parameter (eg theelimination of regulatory T cells) However it is a validalternative explanation to increased efficiency of T-cellimmunotherapy through a general effect on tumor sensi-tivity due to the preparative chemotherapyradiotherapywhich results in higher response rates

DISCUSSIONThis new mathematical model simulating 4 indepen-

dent clinical trials emphasizes 3 critical issues for this typeof therapy (1) cellular therapy is based on the functionalcapacity of each individually transferred cell (2) even highT-cell numbers used for therapy will unlikely influence largeand fast-growing tumors and (3) the current classification

of tumors (stage and grade) needs to be refined for properestimation of the residual tumor cell mass Future modelmodifications may include classification of tumors by themetastatic sites and their malignancy scores Currently wefeel however that even population size alone can provideus with ample insights and predictions as to the success ofT-cell therapy

Absolute tumor burden and growth dynamics can beestimated within a certain degree of certainty at the start ofcellular therapy taking into account size stage and gradeof the tumor As demonstrated here low initial tumor cellmass is critical for the success of T-cell therapy Forinstance although Mackensen et al25 do not report exacttumor burden it is hard to ignore the fact that all patientsthat showed any response at all (mixed partial or stabledisease) were the ones with only one disease site (Table 1 inMackensen et al study) which is consistent with Kham-marirsquos findings This underlines the importance of quanti-tative effects in cancer progression and the existence of awindow of opportunities for efficacious treatment

In the simulations presented here both tumor cellnumbers and growth rates were randomly chosen within apreset range to simulate various biological preconditionsThis hands-on way of simulating variable and parameterranges is uncommon in mathematical articles modelingimmunotherapy However we believe such simulations arecloser to the clinical situation and this way of presentingmathematical modeling may be more tangible for physicianscientists This model is based on the assumption thatT cells lyse tumor cells repetitively throughout their lifespan Therefore it is logical that a T-cell dose effect will beobserved but the extent of this effect could not be foreseenHowever what is becoming evident by mathematicalmodeling and computer simulation is the degree to whichcellular therapy needs to be augmented to expect asignificant impact The data clearly illustrates the quanti-tative effects for clinical trials the T-cell dose rangedthroughout all 4 studies from 1108 to 11011 T cellsAssuming the lytic activity of the cells being equal therewas little chance of a tumor response using Mackensenrsquosapproach whereas the use of a 1000 times higher T-celldose combined with synergistic measures (such as TBIbefore therapy) increased the likelihood of a responsesignificantly Delving deeper into Dudley et alrsquos29 data thepercentage of CD8+ cells of TILs is consistently higher forresponders than for nonresponder patients (821 vs749 in the 2Gy treatment and 860 vs 605 in the12Gy treatment) When comparing the percentage ofspecific Mart-1 of CD8+ cells we find the same trend asbefore as responder patients were administered with ahigher percentage of Mart-1 cells (196 vs 34 in the2Gy treatment and 28 vs 16 in theGy treatment)Therefore the responder patients clearly received higherdosage of effective Mart-1 cells Therefore taking amechanistic view of the T-cell effect the broad range alonecan explain success or failure of the respective regimen Thismodel allows for the first time to compare unrelated studieswith immensely varying treatment schedules

Very little data is available on the exact numbersrequired for an efficient immune response against tumorantigens As shown in Figure 3 simulation suggests theexistence of a threshold of T-cell dose that has to be crossedbefore an effect on the tumor can be observed Theexistence of such a threshold in a tumor T-cell therapytype of system was predicted by Kogan et al22 Its clinical

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FIGURE 4 Simulations of time-dependent tumor cell numberdynamics as a result of the Greenberg protocol (Yee et al)26

Infusions of 59109 (3310918 m2 surface area of ahuman) were given at days 0 14 35 and 56 Tumors that havereduced in size to practical 0 (RECIST complete response CR) aremarked in red (thin solid line) tumors that have reduced by 30(RECIST partial response PR) are marked in blue (thick solid line)Tumors that have stabilized between 70 and 120 of theiroriginal size (RECIST stable disease SD) are marked in greenBlack (dotted line) marks time dependent tumor cell numberssimulations that were nonresponsive NR RECIST indicatesResponse Evaluation Criteria in Solid Tumors



meaning is that the high renewal potential of the tumorrenders any trial to just reduce the tumor and keep it incheck futile Unless the tumor is eradicated no long-termstable equilibrium can exist If the doses used are just belowand above the threshold this effect will be most strikingin the smallest tumors as can be seen in Figure 3

In a recent study by Budhu et al31 the efficiency ofT-cell-mediated killing has been carefully correlated withthe T-cell concentration It is shown that the efficacy ofsuch killing significantly increases once the T-cell dose isbeyond a certain threshold In Budhu et alrsquos study it isdemonstrated thatmdashin an in vitro settingmdasha ratio of 10001to 101 of effector-to-tumor cells ensures the elimination ofa tumor cell population of 1104 to 1106 respectivelyWhen the researchers incubated melanoma B16 cells withT cells at roughly 11 ratio for 7 days in the presence of IL-2 they received nearly 100 killing Without the presenceof IL-2 the researchers required a 201 ratio to achievetumor eradication and the functionality of the T cells lastedfor only 5 days A distinct threshold value of T cells isapparent below which the effect of T-cells is very weak andabove which it is dramatic (Budhu et al 2010 Fig 5) Theexistence of a numerical threshold effect has recently beenpredicted in a mathematical analysis of the immunotherapy

for treatment of glioblastoma22 Such stepwise function ofimmunotherapy is counter intuitive for the physicianmdashalthough not entirely unfamiliar when thinking of pharma-cokinetics and pharmacodynamics Identifying this step onthe basis of mathematical modeling may increase thesuccess rate of cellular immunotherapy

In a clinical setting a T-cell dose in the orderadministered by the Rosenberg group (11011) whichmay be called a supraphysiological T-cell dose may inducea cytokine stormmdashwith release of interferon-g IL-8 tumornecrosis factor-a etc Ultimately the inhibitory milieu ofthe tumor environment might be overcome leading toupregulation of MHC class-I expression on the tumor cellsand consequently increased tumor cell lysis

In summary mathematical modeling holds the promisethat immunologymdashand especially human immunologymdashisnot just a black box where the effects of a certain treatmentare unpredictable but that before a clinical trial theinterplay between crucial parameters can be analyzed andpredicted The model is dependent on quantitative datasome of the parameters implemented in the model arededuced from diverse sources The accuracy of modelprediction can be improved when such quantitative dataare available for each individual study It seems therefore

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BA

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FIGURE 5 Simulations of time-dependent tumor cell number dynamics as a result of the Mackensen et al25 clinical trial (A) andsimulated improvement to the trial (B) (C) and (D) Simulations of time-dependent tumor cell number dynamics of 100 randomsimulations are shown Virtual tumors with randomly chosen initial tumor sizes (1010 to 51011 cells) and different growth rates(00001 to 0001h) are simulated with (A) a presumed general Mackensen regimen (21108 cell given 10 times at intervals indicatedin the text) B All parameters the same as in (A) except CTL dose simulated here to be 5108 (A) C All parameter the same as in (A)except the CTL-induced tumor cell kill rate is simulated here to be twice as in (A) D Combined effect of intensified regimens in (B) and(C) Tumors that have reduced in size to practical 0 (RECIST complete response) are marked in red (thin solid line) tumors that havereduced by 30 (RECIST partial response) are marked in blue (thick solid line) Black (dotted line) marks time-dependent tumor cellnumbers simulations that were nonresponsive RECIST indicates Response Evaluation Criteria in Solid Tumors



necessary to raise the awareness of cellular therapists forthe potential of mathematical modeling and improve thequality of quantitative data

But even without exact data on tumor size and growthrate we tried to account for biological variability byallowing a range of initial tumor sizes and growth ratesThe efficacy of the T cellsmdashbeing regarded as ldquoserialkillersrdquo in this modelmdashmay be lower than the values usedfor simulation thus if anything required T-cell doseswould even be higher

Proliferation of tumor-specific T cells may be crucialto solve the need for large amounts of T cells as simulatedin this study The proliferative capacity of antigen-primedT cells depends on the differentiation state late stageeffector cells have a good lytic capacity but poor proli-ferative capacity and little in vivo persistence whereas earlyeffector memory T cells or central memory T cells have thecapacity to further expand in vivo Exciting new studiespoint toward differentiation pathways that can be manipu-lated ex vivo to maintain or induce a central memoryphenotype thus increasing the persistence functionalityand the potential efficacy of such T cells32ndash34

Biomathematical modeling of T-cell immunotherapyhas its greatest value when sufficient numbers of T cells areavailable In fact we recently calculated for a glioblastomamodel thatmdashtechnical challenges asidemdasha constant rate of

T-cell infusions directly into the tumor bed over a pro-longed time (weeks) may defeat even large tumors22 suchregimen also avoids peak T-cell load Mathematical model-ing can also predict the minimum number of T cells neededto have a reasonable chance to have an impact onto theresidual tumor masses In other words mathematicalmodeling can provide the order of magnitude of theT-cell treatment required

We are aware of the technical challenges of generationand application of such large numbers of antigen-specificT cells However for some antigens such as Melan-A usingimproved protocols the T cells can already be expanded tovery high numbers within a short culture time6 ormdashforantigens with a lower T-cell precursor frequencymdashlargenumbers of peripheral blood mononuclear cell can betransduced to express modified and functionally improvedtumor-specific T-cell receptors4 At the same time recentreports on severe adverse events after adoptive immuno-therapy7 and preclinical animal models showing significanttoxicity after transferring TCR gene transferred peripheralblood mononuclear cell also emphasize the risks of T-cellimmunotherapy and stress the need for meticulous pre-clinical evaluation including mathematical modeling Math-ematical modeling can help rationalize the design of eitherappropriate dose per patient or alternatively determineexclusion criteria for patients with large tumor burden in

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FIGURE 6 Simulations of time-dependent tumor cell number dynamics as a result of the Rosenberg intensive protocol29 A 11011

(multiplied by 01 assumed antigen specificity ratio) antigen-specific T cells given in a 1 time bolus infusion B The same treatment as in(A) given to tumors 20 smaller than the initial tumor size in (A) C The same treatment as in (A) given to tumors 20 smaller than theinitial tumor size in (A) and hT larger by 33 Tumors that have reduced in size to practical 0 (RECIST complete response) are marked inred (thin solid line) tumors that have reduced by 30 (RECIST partial response) are marked in blue (thick solid line) Black (dotted line)marks time dependent tumor cell numbers simulations that were nonresponsive RECIST indicates Response Evaluation Criteria in SolidTumors



case large CTL (or TIL) dose is unavailable In summarymathematical modeling can help pick the right schedule forthe right patient and thus hopefully improve treatmentsuccess

ACKNOWLEDGMENTS

The authors thank Dr Michal Besser of the Ella Institutefor the Treatment and Research of Melanoma and SkinCancer at the Sheba Medical Center for helpful discussions

CONFLICTS OF INTERESTFINANCIAL DISCLOSURES

NK and YK were supported by the Chai foundationMW is the recipient of a postdoctoral stipend from the Child-Philipp-Foundation (T237165862007) Germany This studywas supported by a Program Project Grant from BayImmuNet(to MW and PGS) (F2-F51217111312009)

All authors have declared there are no financial conflictsof interest in regard to this work

REFERENCES

1 June CH Adoptive T cell therapy for cancer in the clinicJ Clin Invest 20071171466ndash1476

2 Disis ML Bernhard H Jaffee EM Use of tumour-responsiveT cells as cancer treatment Lancet 2009373673ndash683

3 June CH Principles of adoptive T cell cancer therapy J ClinInvest 20071171204ndash1212

4 KershawMH TengMW Smyth MJ et al Supernatural T cellsgenetic modification of T cells for cancer therapy Nat RevImmunol 20055928ndash940 [Doinri1729 [pii] 101038nri1729

5 Stromnes IM Blattman JN Tan X et al Abrogating cbl-b ineffector CD8(+) T cells improves the efficacy of adoptivetherapy of leukemia in mice J Clin Invest 120 (10)3722-3734Doi41991 [pii] 101172JCI41991

6 Wolfl M Merker K Morbach H et al Primed tumor-reactive multifunctional CD62l(+) human CD8 (+) T cells forimmunotherapy Cancer Immunol Immunother [Doi101007s00262-010-0928-8]

7 Morgan RA Yang JC Kitano M et al Case report of a seriousadverse event following the administration of T cells transducedwith a chimeric antigen receptor recognizing erbb2 Mol Ther 18(4)843-851 Doimt201024 [pii] 101038mt201024

8 Warren EH Fujii N Akatsuka Y et al Therapy of relapsedleukemia after allogeneic hematopoietic cell transplantationwith T cells specific for minor histocompatibility antigensBlood 115 (19)3869-3878 Doiblood-2009-10-248997 [pii]101182blood-2009-10-248997

9 Yeh S Karne NK Kerkar SP et al Ocular and systemicautoimmunity after successful tumor-infiltrating lymphocyteimmunotherapy for recurrent metastatic melanoma Ophthal-mology 2009116981ndash989 e981

10 Anderson AR Quaranta V Integrative mathematical onco-logy Nat Rev Cancer 20088227ndash234

11 Itik M Banks SP Chaos in a three-dimensional cancer modelInt J Bifurcation Chaos 20102071ndash79

12 Eftimie R Bramson JL Earn DJ Interactions between theimmune system and cancer a brief review of non-spatial mathe-matical models Bull Math Biol Doi101007s11538-010-9526-3

13 De Boer RJ Hogeweg P Dullens HF et al MacrophageT lymphocyte interactions in the anti-tumor immune responsea mathematical model J Immunol 19851342748ndash2758

14 Takayanagi T Ohuchi A A mathematical analysis of theinteractions between immunogenic tumor cells and cytotoxicT lymphocytes Microbiol Immunol 200145709ndash715

15 Kuznetsov VA Makalkin IA Taylor MA et al Nonlineardynamics of immunogenic tumors parameter estimation andglobal bifurcation analysis Bull Math Biol 199456295ndash321

16 Joshi B Wang X Banerjee S et al On immunotherapies andcancer vaccination protocols a mathematical modellingapproach J Theor Biol 2009259820ndash827

17 drsquoOnofrio A Gatti F Cerrai P et al Delay-induced OscillatoryDynamics of Tumour-immune System Interaction Mathematicaland Computer Modelling 200951572ndash591

18 Kirschner D Panetta JC Modeling immunotherapy of thetumor-immune interaction J Math Biol 199837235ndash252

19 Wang Z Birch CM Sagotsky J et al Cross-pathwayevaluation using an agent-based non-small cell lung cancermodel Bioinformatics 2009252389ndash2396

20 Woelke AL Murgueitio MS Preissner R Theoretical model-ing techniques and their impact on tumor immunologyClin Dev Immunol 2010271794 Doi1011552010271794

21 Kronik N Kogan Y Vainstein V et al Improving alloreactiveCTL immunotherapy for malignant gliomas using a simulationmodel of their interactive dynamics Cancer Immunol Immun-other 200857425ndash439 Doi101007s00262-007-0387-z

22 Kogan Y Forys U Shukron O et al Cellular immunotherapyfor high grade gliomas mathematical analysis derivingefficacous infusion rates based on patient requirements SIAMJ App Mathematics 2010701953ndash1976

23 Eisenhauer EA Therasse P Bogaerts J et al New responseevaluation criteria in solid tumours revised RECIST guideline(version 11) Eur J Cancer 200945228ndash247

24 Khammari A Nguyen JM Pandolfino MC et al Long-term follow-up of patients treated by adoptive transfer ofmelanoma tumor-infiltrating lymphocytes as adjuvant therapyfor stage iii melanoma Cancer Immunol Immunother 2007561853ndash1860

25 Mackensen A Meidenbauer N Vogl S et al Phase I studyof adoptive T-cell therapy using antigen-specific CD8+ T cellsfor the treatment of patients with metastatic melanoma J ClinOncol 2006245060ndash5069

26 Yee C Thompson JA Byrd D et al Adoptive T cell therapyusing antigen-specific CD8+ T cell clones for the treatmentof patients with metastatic melanoma in vivo persistencemigration and antitumor effect of transferred t cells Proc NatlAcad Sci U S A 20029916168ndash16173

27 Dudley ME Wunderlich JR Yang JC et al A phase I studyof nonmyeloablative chemotherapy and adoptive transferof autologous tumor antigen-specific T lymphocytes in pa-tients with metastatic melanoma J Immunother 200225243ndash251

28 Benlalam H Vignard V Khammari A et al Infusion ofmelan-amart-1 specific tumor-infiltrating lymphocytes en-hanced relapse-free survival of melanoma patients CancerImmunol Immunother 200756515ndash526

29 Dudley ME Yang JC Sherry R et al Adoptive cell therapyfor patients with metastatic melanoma evaluation of intensivemyeloablative chemoradiation preparative regimens J ClinOncol 2008265233ndash5239

30 de Pillis LG Radunskaya AE Wiseman CL A validatedmathematical model of cell-mediated immune response totumor growth Cancer Res 2005657950ndash7958

31 Budhu S Loike JD Pandolfi A et al CD8+ T cell con-centration determines their efficiency in killing cognateantigen-expressing syngeneic mammalian cells in vitro and inmouse tissues J Exp Med 207223-235 Doijem20091279 [pii]101084jem20091279

32 Araki K Turner AP Shaffer VO et al Ahmed RMtorregulates memory CD8 T-cell differentiation Nature2009460108ndash112

33 Rao RR Li Q Odunsi K et al The mtor kinase determineseffector versus memory CD8+ T cell fate by regulating theexpression of transcription factors t-bet and eomesoderminImmunity 32 (1)67-78 DoiS1074-7613(09)00545-7 [pii]101016jimmuni200910010

34 Butler MO Friedlander P Milstein MI et al Establishment ofantitumor memory in humans using in vitro-educated CD8+T cells Sci Transl Med 2011380ra34



furthermore predicts the existence of a threshold value ofT-cell infusion rate which needs to be crossed before asignificant impact on the tumor growth can be observed22

In this study we present a mathematical model forimmunotherapy in the context of published clinical dataWe chose immunotherapy by transfer of ex vivo expandedtumor-specific T cells for melanoma patients as thistherapeutic strategy has been shown to be especiallyeffective in this patient population At the same time littleis known about the actual numbers of T cells required fortherapeutic treatment resulting in a wide variation in T-cellnumbers across clinical studies In fact T-cell dosing isoften calculated based on body surface areamdasha conceptwhich stems from pharmacological substances which relyon renal excretionmdashor on body weight rather than on theestimated tumor burden However this is exactly wheremathematical modeling may help to design an individua-lized treatment schedule for each patient On the basis ofreported parameters in the literature a mathematical modelwas built by transferring a descriptive model into mathe-matical equations Using experimental quantitative datareported recently the model was then retrospectivelyvalidated We then analyzed treatment schedules usedpreviously in clinical trials to assess the magnitude of afunctional T cells response required to efficiently targetmalignant melanoma We show that even high T-cellnumbers used for therapy will unlikely influence large andfast-growing tumors unless the functional capacity of eachT-cell product is improved Furthermore finer quantifica-tion of residual tumor load may assist in identifyingpatients which will benefit from this type of therapy

METHODOLOGYIn our previous study21 a simplified mechanism for

alloreactive cellular therapy for glioblastoma was intro-duced Partially based on this previous study we developeda new model with special adaptation to melanoma andmelanoma immunotherapy parameters Figure 1 shows ascheme of the model The mathematical equations are

Mathematical Equations

Tfrac14 rT 1

T

K

aT

MI

eT thornMI

aT bFbthorn eT b

Fbthorn eT b

CT

hT

hT thornTeth1THORN

Equation (1) describes the tumor cell T dynamics(the dot is the time derivative) as influenced by tumor cellmaximal number K CTL population C killing efficacy ofthe CTLs aT presence of MHC class I receptors MI andthe level of TGFb secretion For full explanations here andhereafter and list of parameters see Appendix Supple-mental Digital Content 1 httplinkslwwcomJITA157

Cfrac14 mCCthorn I eth2THORN

Equation (2) describes the dynamics of the CTLs Cby the death rate of CTLs proportional to the population ofCTLs with coefficient mC and finally I the CTL infusionrate

F bfrac14 abT T mbFb eth3THORN

Equation (3) describes the dynamics of TGFb Fb asproportional to the tumor cell population T with abT as aproportion coefficient and is destroyed at a rate of mb

proportional to FbF gfrac14 agC C mg Fg eth4THORN

Equation (4) describes the dynamics of IFNg Fg asproportional to the population of CTLs C with propor-tion coefficient agc and is destroyed at a rate mgproportional to the amount of Fg

MI frac14 gMI thorn

aMI g Fg

Fgthorn eMI g mMI MI eth5THORN

Equation (5) describes the dynamics of MHC class Imolecules MI are presented on the tumor cell surface at arate gMI this rate is augmented by a Michaelis-type termdependent on Fg The MI molecules are internalized at arate mg

Model AssumptionsThe current model assumes that a primary tumor cell

population and a metastatic tumor cell population areindistinguishable by size alone or level of malignancy permetastatic population We feel it is a safe assumption tomake for most of the patients at least at this fundamentalstage of model development

FIGURE 1 A simplified model for the interaction of melanomacells and cytotoxic T cells and the respective cytokinesMelanoma cells express immunogenic antigens in the contextof the MHC I complex but also secrete TGFb which inhibitsT-cell activity Upon contact with melanoma cells exogenouslyinfused CTLs lyse their target and secrete IFN-g IFN-g leads toupregulation of MHC class I in the melanoma cells which inreturn increases the CTL-mediated effect IL-2 injections prolongpersitence of infused CTLs Endogenous cytotoxic T cells areincluded as constant influx to the T-cell effector compartmentCTL indicates cytotoxic T lymphocyte IFN interferon ILinterleukin MHC major histocompatibility class TGFb trans-forming growth factor b







RESULTS























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ACKNOWLEDGMENTS





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0 50 100 150 200 250 3000

2

4

6

8

10x 10

11

Time (days)

Tum

or c

ell n

umbe

r

CR=43 PR=6 SD=3 NR=48

0 50 100 150 200 250 3000

2

4

6

8

10x 10

11

Time (days)

Tum

or c

ell n

umbe

r

CR=49 PR=6 SD=1 NR=44

0 50 100 150 200 250 3000

2

4

6

8

10x 10

11

Time (days)

Tum

or c

ell n

umbe

r

CR=63 PR=6 SD=2 NR=29

A B

C






ACKNOWLEDGMENTS





REFERENCES






































ACKNOWLEDGMENTS





REFERENCES





































Documents

Improving T-cell Immunotherapy for Melanoma Through a … · 2015. 6. 29. · immunotherapy, melanoma, adoptive T-cell transfer (J Immunother 2012;35:116–124) A doptive immunotherapy