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PDF file - 201K, The contents of the document: 1. Model equations for the vaccine and the maturing DCs 2. Formal description of the algorithm for in-treatment therapy personalization 3. Success-of-validation criteria 4. Model comparison grade and parameters for SOV criterion 5. Selecting the best performing SOV criterion 6. Table S1

Supplementary Materials from Efficacy of Weekly Docetaxel and Bevacizumab in Mesenchymal Chondrosarcoma: A New Theranostic Method Combining Xenografted Biopsies with a Mathematical Model

Supplementary Material and Methods from Cancer Immunotherapy by Interleukin-21: Potential Treatment Strategies Evaluated in a Mathematical Model

The newly characterized interleukin (IL)-21 plays a central role in the transition from innate immunity to adaptive immunity and shows substantial tumor regression in mice. IL-21 is now developed as a cancer immunotherapeutic drug, but conditions for efficacious therapy, and the conflicting immunostimulatory and immunoinhibitory influence of the cytokine, are yet to be defined. We studied the effects of IL-21 on tumor eradication in a mathematical model focusing on natural killer (NK) cell–mediated and CD8+ T-cell-mediated lysis of tumor cells. Model parameters were estimated using results in tumor-bearing mice treated with IL-21 via cytokine gene therapy (CGT), hydrodynamics-based gene delivery (HGD), or standard interval dosing (SID). Our model accurately retrieved experimental growth dynamics in the nonimmunogenic B16 melanoma and the immunogenic MethA and MCA205 fibrosarcomas, showing a strong dependence of the NK-cell/CD8+ T-cell balance on tumor immunogenicity. Moreover, in melanoma, simulations of CGT-like dosing regimens, dynamically determined according to tumor mass changes, resulted in efficient disease elimination. In contrast, in fibrosarcoma, such a strategy was not superior to that of fixed dosing regimens, HGD or SID. Our model supports clinical use of IL-21 as a potent stimulator of cellular immunity against cancer, and suggests selecting the immunotherapy strategy according to tumor immunogenicity. Nonimmunogenic tumors, but not highly immunogenic tumors, should be controlled by IL-21 dosing, which depends on tumor mass at the time of administration. This method imitates, yet amplifies, the natural anticancer immune response rather than accelerates only one of the response arms in an unbalanced manner. (Cancer Res 2006; 66(14): 7293-300)

Background: Recently, there has been a growing interest in applying immune checkpoint blockers (ICBs), so far used to treat cancer, to patients with bacterial sepsis. We aimed to develop a method for predicting the personal benefit of potential treatments for sepsis, and to apply it to therapy by meropenem, an antibiotic drug, and nivolumab, a programmed cell death-1 (PD-1) pathway inhibitor.Methods: We defined an optimization problem as a concise framework of treatment aims and formulated a fitness function for grading sepsis treatments according to their success in accomplishing the pre-defined aims. We developed a mathematical model for the interactions between the pathogen, the cellular immune system and the drugs, whose simulations under diverse combined meropenem and nivolumab schedules, and calculation of the fitness function for each schedule served to plot the fitness landscapes for each set of treatments and personal patient parameters.Results: Results show that treatment by meropenem and nivolumab has maximum benefit if the interval between the onset of the two drugs does not exceed a dose-dependent threshold, beyond which the benefit drops sharply. However, a second nivolumab application, within 7–10 days after the first, can extinguish a pathogen which the first nivolumab application failed to remove. The utility of increasing nivolumab total dose above 6 mg/kg is contingent on the patient's personal immune attributes, notably, the reinvigoration rate of exhausted CTLs and the overall suppression rates of functional CTLs. A baseline pathogen load, higher than 5,000 CFU/μL, precludes successful nivolumab and meropenem combination therapy, whereas when the initial load is lower than 3,000 CFU/μL, meropenem monotherapy suffices for removing the pathogen.Discussion: Our study shows that early administration of nivolumab, 6 mg/kg, in combination with antibiotics, can alleviate bacterial sepsis in cases where antibiotics alone are insufficient and the initial pathogen load is not too high. The study pinpoints the role of precision medicine in sepsis, suggesting that personalized therapy by ICBs can improve pathogen elimination and dampen immunosuppression. Our results highlight the importance in using reliable markers for classifying patients according to their predicted response and provides a valuable tool in personalizing the drug regimens for patients with sepsis.

We review the evolution, achievements, and limitations of the current paradigm shift in medicine, from the "one-size-fits-all" model to "Precision Medicine." Precision, or personalized, medicine-tailoring the medical treatment to the personal characteristics of each patient-engages advanced statistical methods to evaluate the relationships between static patient profiling (e.g., genomic and proteomic), and a simple clinically motivated output (e.g., yes/no responder). Today, precision medicine technologies that have facilitated groundbreaking advances in oncology, notably in cancer immunotherapy, are approaching the limits of their potential, mainly due to the scarcity of methods for integrating genomic, proteomic and clinical patient information. A different approach to treatment personalization involves methodologies focusing on the dynamic interactions in the patient-disease-drug system, as portrayed in mathematical modeling. Achievements of this scientific approach, in the form of algorithms for predicting personal disease dynamics in individual patients under immunotherapeutic drugs, are reviewed as well. The contribution of the dynamic approaches to precision medicine is limited, at present, due to insufficient applicability and validation. Yet, the time is ripe for amalgamating together these two approaches, for maximizing their joint potential to personalize and improve cancer immunotherapy. We suggest the roadmap toward achieving this goal, technologically, and urge clinicians, pharmacologists, and computational biologists to join forces along the pharmaco-clinical track of this development.

Background At present, immune checkpoint inhibitors, such as pembrolizumab, are widely used in the therapy of advanced non-resectable melanoma, as they induce more durable responses than other available treatments. However, the overall response rate does not exceed 50% and, considering the high costs and low life expectancy of nonresponding patients, there is a need to select potential responders before therapy. Our aim was to develop a new personalization algorithm which could be beneficial in the clinical setting for predicting time to disease progression under pembrolizumab treatment. Methods We developed a simple mathematical model for the interactions of an advanced melanoma tumor with both the immune system and the immunotherapy drug, pembrolizumab. We implemented the model in an algorithm which, in conjunction with clinical pretreatment data, enables prediction of the personal patient response to the drug. To develop the algorithm, we retrospectively collected clinical data of 54 patients with advanced melanoma, who had been treated by pembrolizumab, and correlated personal pretreatment measurements to the mathematical model parameters. Using the algorithm together with the longitudinal tumor burden of each patient, we identified the personal mathematical models, and simulated them to predict the patient’s time to progression. We validated the prediction capacity of the algorithm by the Leave-One-Out cross-validation methodology. Results Among the analyzed clinical parameters, the baseline tumor load, the Breslow tumor thickness, and the status of nodular melanoma were significantly correlated with the activation rate of CD8+ T cells and the net tumor growth rate. Using the measurements of these correlates to personalize the mathematical model, we predicted the time to progression of individual patients (Cohen’s κ = 0.489). Comparison of the predicted and the clinical time to progression in patients progressing during the follow-up period showed moderate accuracy (R2 = 0.505). Conclusions Our results show for the first time that a relatively simple mathematical mechanistic model, implemented in a personalization algorithm, can be personalized by clinical data, evaluated before immunotherapy onset. The algorithm, currently yielding moderately accurate predictions of individual patients’ response to pembrolizumab, can be improved by training on a larger number of patients. Algorithm validation by an independent clinical dataset will enable its use as a tool for treatment personalization.

A concise summary and explanation of the equations and parameters for all models presented in this article. (DOCX 13 kb)

Recently, cancer immunotherapy has shown considerable success, but due to the complexity of the immune-cancer interactions, clinical outcomes vary largely between patients. A possible approach to overcome this difficulty may be to develop new methodologies for personal predictions of therapy outcomes, by the integration of patient data with dynamical mathematical models of the drug-affected pathophysiological processes.This review unfolds the story of mathematical modeling in cancer immunotherapy, and examines the feasibility of using these models for immunotherapy personalization. The reviewed studies suggest that response to immunotherapy can be improved by patient-specific regimens, which can be worked out by personalized mathematical models. The studies further indicate that personalized models can be constructed and validated relatively early in treatment.The suggested methodology has the potential to raise the overall efficacy of the developed immunotherapy. If implemented already during drug development it may increase the prospects of the technology being approved for clinical use. However, schedule personalization, per se, does not comply with the current, 'one size fits all,' paradigm of clinical trials. It is worthwhile considering adjustment of the current paradigm to involve personally tailored immunotherapy regimens.

Background Despite considerable investigational efforts, no method to overcome the pathogenesis caused by loss of function (LoF) mutations in tumor suppressor genes has been successfully translated to the clinic. The most frequent LoF mutation in human cancers is Adenomatous polyposis coli (APC), causing aberrant activation of the Wnt pathway. In nearly all colon cancer tumors, the APC protein is truncated, but still retains partial binding abilities. Objective & methods Here, we tested the hypothesis that extracellular inhibitors of the Wnt pathway, although acting upstream of the APC mutation, can restore normal levels of pathway activity in colon cancer cells. To this end, we developed and simulated a mathematical model for the Wnt pathway in different APC mutants, with or without the effects of the extracellular inhibitors, Secreted Frizzled-Related Protein1 (sFRP1) and Dickhopf1 (Dkk1). We compared our model predictions to experimental data in the literature. Results Our model accurately predicts T-cell factor (TCF) activity in mutant cells that vary in APC mutation. Model simulations suggest that both sFRP1 and DKK1 can reduce TCF activity in APC1638N/1572T and Apcmin/min mutants, but restoration of normal activity levels is possible only in the former. When applied in combination, synergism between the two inhibitors can reduce their effective doses to one-fourth of the doses required under single inhibitor application. Overall, re-establishment of normal Wnt pathway activity is predicted for every APC mutant in whom TCF activity is increased by up to 11 fold. Conclusions Our work suggests that extracellular inhibitors can effectively restore normal Wnt pathway activity in APC-truncated cancer cells, even though these LoF mutations occur downstream of the inhibitory action. The insufficient activity of the truncated APC can be quantitatively balanced by the upstream intervention. This new concept of upstream intervention to control the effects of downstream mutations may be considered also for other partial LoF mutations in other signaling pathways.

645 Background: In advanced cancers, predicting disease progression just before its clinical manifestation enables an earlier switch to the next treatment line, preventing deterioration in the patient's state and potentially improving survival. Yet, given the ambiguity of current tumor markers in alerting to progression, physicians are unable to forecast this key event. We developed a diagnostic algorithm for announcing an approaching disease progression in late-stage colorectal cancer (CRC) patients by processing continuous carcinoembryonic antigen (CEA) input. Methods: Longitudinally measured CEA data of advanced CRC patients treated by standard 1st line chemotherapies, collected from 2 clinical trials (projectdatasphere.org), served for algorithm development by machine-learning and training assisted by receiver-operating-characteristic (ROC) analysis and correlation tests. Performance was validated by cross-validation techniques. Results: CEA and response evaluations of 489 CRC patients (median follow-up time: 168 days) were processed by the algorithm, predicting disease progression with 57% sensitivity (100/175 progression events) and 88% specificity (21/175 false positives). Positive and negative predictive values, accuracy and Cohen’s kappa were 64%, 84%, 79% and 0.46, respectively. The algorithm’s predictive power was superior to that of standard statistical analyses of these CEA data (e.g., ROC). Conclusions: Our study offers a new approach to using tumor markers as prognosticators. The algorithm-amplified ability of CEA to predict progression in CRC complements our recent findings in lung cancer, where integration of CEA and 4 other markers provided 66% sensitivity in predicting progression, surpassing the low capacity of each separate marker. Conceivably, future algorithm-integration of multiple markers in CRC may also exceed the limited signal of a single marker. Clinical use of our algorithm, amplifying weak marker signals of imminent progression, should allow physicians to reliably harness tumor markers for improving treatment and potentially extending survival in cancer patients.

Aggressive cancers develop immune suppression mechanisms, allowing them to evade specific immune responses. Patients with active melanoma are polarized towards a T helper (Th) 2-type immune phenotype, which subverts effective anticancer Th1-type cellular immunity. The pro-inflammatory factor, interleukin (IL)-12, can potentially restore Th1 responses in such patients, but still shows limited clinical efficacy and substantial side effects. We developed a model for the Th1/Th2 imbalance in melanoma patients and its regulation via IL-12 treatment. The model focuses on the interactions between the two Th cell types as mediated by their respective key cytokines, interferon (IFN)-$\gamma$ and IL-10. Theoretical and numerical analysis showed a landscape consisting of a single, globally attracting steady state, which is stable under large ranges of relevant parameter values. Our results suggest that in melanoma, the cellular arm of the immune system cannot reverse tumor immunotolerance naturally, and that immunotherapy may be the only way to overturn tumor dominance. We have shown that given a toxicity threshold for IFN$\gamma$, the maximal allowable IL-12 concentration to yield a Th1-polarized state can be estimated. Moreover, our analysis pinpoints the IL-10 secretion rate as a significant factor influencing the Th1:Th2 balance, suggesting its use as a personal immunomarker for prognosis.

Although therapeutic vaccination often induces markers of tumor-specific immunity, therapeutic responses remain rare. An improved understanding of patient-specific dynamic interactions of immunity and tumor progression, combined with personalized application of immune therapeutics would increase the efficacy of immunotherapy. Here, we developed a method to predict and enhance the individual response to immunotherapy by using personalized mathematical models, constructed in the early phase of treatment. Our approach includes an iterative real-time in-treatment evaluation of patient-specific parameters from the accruing clinical data, construction of personalized models and their validation, model-based simulation of subsequent response to ongoing therapy, and suggestion of potentially more effective patient-specific modified treatment. Using a mathematical model of prostate cancer immunotherapy, we applied our model to data obtained in a clinical investigation of an allogeneic whole-cell therapeutic prostate cancer vaccine. Personalized models for the patients who responded to treatment were derived and validated by data collected before treatment and during its early phase. Simulations, based on personalized models, suggested that an increase in vaccine dose and administration frequency would stabilize the disease in most patients. Together, our findings suggest that application of our method could facilitate development of a new paradigm for studies of in-treatment personalization of the immune agent administration regimens (P-trials), with treatment modifications restricted to an approved range, resulting in more efficacious immunotherapies. Cancer Res; 72(9); 2218–27. ©2012 AACR.

The cancer stem cell (CSC) hypothesis states that only a small fraction of a malignant cell population is responsible for tumor growth and relapse. Understanding the relationships between CSC dynamics and cancer progression may contribute to improvements in cancer treatment. Analysis of a simple discrete mathematical model has suggested that homeostasis in developing tissues is governed by a "quorum sensing" control mechanism, in which stem cells differentiate or proliferate according to feedback they receive from neighboring cell populations. Further analysis of the same model has indicated that excessive stem cell proliferation leading to malignant transformation mainly results from altered sensitivity to such micro-environmental signals. Our aim in this work is to expand the analysis to the dynamics of established populations of cancer cells and to examine possible therapeutic avenues for eliminating CSCs. The proposed model considers two populations of cells: CSCs, which can divide indefinitely, and differentiated cancer cells, which do not divide and have a limited lifespan. We assume that total cell density has negative feedback on CSC proliferation and that high CSC density activates CSC differentiation. We show that neither stimulation of CSC differentiation nor inhibition of CSC proliferation alone is sufficient for complete CSC elimination and cancer cure, since each of these two therapies affects a different subpopulation of CSCs. However, a combination of these two strategies can substantially reduce the population sizes and densities of all types of cancer cells. Therefore, we propose that in clinical trials, CSC differentiation therapy should only be examined in combination with chemotherapy. Our conclusions are corroborated by clinical experience with differentiating agents in acute promyelocytic leukemia and neuroblastoma.

e21114Background: Extending survival in advanced non-small cell lung cancer (NSCLC) is of great importance. Finding survival predictors and assessing the potential for improving patient outcomes th...

e21190Background: Non-small cell lung cancer (NSCLC) is the leading cause of cancer death in America. Predicting disease progression just prior to its clinical manifestation would allow an earlier ...

To date, no effective cure has been found for high grade malignant glioma (HGG), current median survival for HGG patients under treatment ranging from 18 months (grade IV) to 5 years (grade III). Recently, T cell therapy for HGG has been suggested as a promising avenue for treating such resistant tumors, but clinical outcome has not been conclusive. For studying this new therapy option, a mathematical model for tumor–T cell interactions was developed, where tumor immune response was modeled by six coupled ordinary differential equations describing tumor cells, T cells, and their respective secreted cytokines and immune mediating receptors. Here we mathematically analyze the model in an untreated case and under T cell immunotherapy. For both settings we classify steady states, determine stability properties, and explore the global behavior of the model. Analysis suggests that in untreated patients, the system always converges to a steady state of a large tumor mass. An increase in the patient's pro-inflamm...

Recently, adult stem cells have become a focus of intensive biomedical research, but the complex regulation that allows a small population of stem cells to replenish depleted tissues is still unknown. It has been suggested that specific tissue structures delimit the spaces where stem cells undergo unlimited proliferation (stem cell niche). In contrast, mathematical analysis suggests that a feedback control of stem cells on their own proliferation and differentiation (denoted Quorum Sensing) suffices for preserving homeostasis in developing tissues. In the present work we examine this discrepancy by analyzing a mathematical model of signalling pathways in a mammary stem cell. Our work shows that the model has a unique equilibrium depending on the environmental conditions, which is stable for appropriate parameter values. We show how this dependence on the micro-environment can control the cell decision to either proliferate or differentiate. Our work further suggests that this description is sufficient for the creation of niche conditions, with no need of additional structures. The analysis also pinpoints the pathways that may serve as the Quorum Sensing mechanism.

This work is based on a previous model of Z. Agur, Y. Daniel and Y. Ginosar (2002), retrieving the essential properties of homeostatic tissue development, as reflected by the bone marrow. The original model, represented by cellular automata on a connected, locally finite undirected graph, identifies the minimal basic properties essential for maintaining tissue homeostasis and for guaranteeing the ability of a few stem cells to repopulate the tissue following its depletion. However, this model is too general to ensure a relative “stability” of stem cell numbers in the tissue, a prerequisite for the integrity of biological systems. In the present work, some natural limitations on the model are introduced, under which a formula for the state of a given cell at any given time is obtained, as well as for the proportion of stem cells as a function of model parameters. For tube-like graphs, defined for modeling tissue engineering scaffolds and known tumor geometries, the system obtains a fixed cellular composition, interpreted as homeostasis, thus enabling precise calculation of the necessary conditions for tissue reconstruction. These results also can shed light on conditions for disrupting homeostasis in cancerous tissues.

Glioblastoma (GBM), a highly aggressive (WHO grade IV) primary brain tumor, is refractory to traditional treatments, such as surgery, radiation or chemotherapy. This study aims at aiding in the design of more efficacious GBM therapies. We constructed a mathematical model for glioma and the immune system interactions, that may ensue upon direct intra-tumoral administration of ex vivo activated alloreactive cytotoxic-T-lymphocytes (aCTL). Our model encompasses considerations of the interactive dynamics of aCTL, tumor cells, major histocompatibility complex (MHC) class I and MHC class II molecules, as well as cytokines, such as TGF-beta and IFN-gamma, which dampen or increase the pro-inflammatory environment, respectively. Computer simulations were used for model verification and for retrieving putative treatment scenarios. The mathematical model successfully retrieved clinical trial results of efficacious aCTL immunotherapy for recurrent anaplastic oligodendroglioma and anaplastic astrocytoma (WHO grade III). It predicted that cellular adoptive immunotherapy failed in GBM because the administered dose was 20-fold lower than required for therapeutic efficacy. Model analysis suggests that GBM may be eradicated by new dose-intensive strategies, e.g., 3 x 10(8) aCTL every 4 days for small tumor burden, or 2 x 10(9) aCTL, infused every 5 days for larger tumor burden. Further analysis pinpoints crucial bio-markers relating to tumor growth rate, tumor size, and tumor sensitivity to the immune system, whose estimation enables regimen personalization. We propose that adoptive cellular immunotherapy was prematurely abandoned. It may prove efficacious for GBM, if dose intensity is augmented, as prescribed by the mathematical model. Re-initiation of clinical trials, using calculated individualized regimens for grade III-IV malignant glioma, is suggested.

Despite recent advances, treatment of patients with aggressive Non-Hodgkin's lymphoma (NHL 2 ) has yet to be optimally designed. Notwithstanding the contribution of molecular treatments, intensiflcation of chemotherapeutic regimens may still be beneflcial. Hoping to aid in the design of intensifled chemotherapy, we put forward a mathematical and computational model that analyses the efiect of Doxorubicin on NHL over a wide range of patho-physiological conditions. The model represents tumour growth both in difiusion-limited settings, that is, in small avascular tumours and tumour cords, and in perfusion-limited settings, e.g. in well-vascularized tumours. Model simulations indicated the presence of a critical regimen intensity below which treatment will fall short of tumour elimination. Taking this critical intensity into account, we compared two regimen intensiflcation strategies: Dose escalation and regimen densiflcation, i.e. reducing the inter-dosing interval. In the difiusion-limited setting, dose escalation was somewhat more e-cient than regimen densiflcation. In the perfusion-limited setting, both intensiflcation strategies yielded similar results. The present study coupled with a realistic myelotoxicity model may add insight on the optimisation of NHL intensifled chemotherapy design.

Prostate cancer (PCa) is a leading cause of cancer death of men worldwide. In hormone-sensitive prostate cancer (HSPC), androgen deprivation therapy (ADT) is widely used, but an eventual failure on ADT heralds the passage to the castration-resistant prostate cancer (CRPC) stage. Because predicting time to failure on ADT would allow improved planning of personal treatment strategy, we aimed to develop a predictive personalization algorithm for ADT efficacy in HSPC patients.A mathematical mechanistic model for HSPC progression and treatment was developed based on the underlying disease dynamics (represented by prostate-specific antigen; PSA) as affected by ADT. Following fine-tuning by a dataset of ADT-treated HSPC patients, the model was embedded in an algorithm, which predicts the patient's time to biochemical failure (BF) based on clinical metrics obtained before or early in-treatment.The mechanistic model, including a tumor growth law with a dynamic power and an elaborate ADT-resistance mechanism, successfully retrieved individual time-courses of PSA (R(2) = 0.783). Using the personal Gleason score (GS) and PSA at diagnosis, as well as PSA dynamics from 6 months after ADT onset, and given the full ADT regimen, the personalization algorithm accurately predicted the individual time to BF of ADT in 90% of patients in the retrospective cohort (R(2) = 0.98).The algorithm we have developed, predicting biochemical failure based on routine clinical tests, could be especially useful for patients destined for short-lived ADT responses and quick progression to CRPC. Prospective studies must validate the utility of the algorithm for clinical decision-making.

We develop a method for computing efficient patient-specific drug protocols. Using this method, we identify two general categories of anticancer drug protocols, depending on the temporal cycle parameters of the host and cancer cells: a one-time intensive treatment, or a series of nonintensive treatments. Our method is based on a theoretical and experimental work showing that treatment efficacy can be improved by determining the dosing frequency on the drug-susceptible target and host cell-cycle parameters. Simulating the patient's pharmaco-dynamics in a simple model for cell population growth, we calculate the number of drug susceptible cells at every moment of therapy. Local search heuristics are then used to conduct a search for the desired solution, as defined by our criteria. These criteria include the patient's state at the end of a predetermined time period, the number of cancer and host cells at the end of treatment, and the time to the patient's cure. The process suggested here does not depend on the exact biological assumptions of the model, thus enabling its use in a more complex description of the system. We test three solution methods. Simulated annealing is compared to threshold acceptance and old bachelor acceptance, which are less known variants to this method. The conclusions concerning the three approximation methods are that good results can be achieved by choosing the proper parameters for each of the methods, but the computational effort required for achieving good results is much greater in simulated annealing than in the other methods. Also, a large number of iterations does not guarantee better solution quality, and resources would be better used in several short searches with different parameter values than in one long search.

The newly characterized interleukin (IL)-21 plays a central role in the transition from innate immunity to adaptive immunity and shows substantial tumor regression in mice. IL-21 is now developed as a cancer immunotherapeutic drug, but conditions for efficacious therapy, and the conflicting immunostimulatory and immunoinhibitory influence of the cytokine, are yet to be defined. We studied the effects of IL-21 on tumor eradication in a mathematical model focusing on natural killer (NK) cell–mediated and CD8+ T-cell-mediated lysis of tumor cells. Model parameters were estimated using results in tumor-bearing mice treated with IL-21 via cytokine gene therapy (CGT), hydrodynamics-based gene delivery (HGD), or standard interval dosing (SID). Our model accurately retrieved experimental growth dynamics in the nonimmunogenic B16 melanoma and the immunogenic MethA and MCA205 fibrosarcomas, showing a strong dependence of the NK-cell/CD8+ T-cell balance on tumor immunogenicity. Moreover, in melanoma, simulations of CGT-like dosing regimens, dynamically determined according to tumor mass changes, resulted in efficient disease elimination. In contrast, in fibrosarcoma, such a strategy was not superior to that of fixed dosing regimens, HGD or SID. Our model supports clinical use of IL-21 as a potent stimulator of cellular immunity against cancer, and suggests selecting the immunotherapy strategy according to tumor immunogenicity. Nonimmunogenic tumors, but not highly immunogenic tumors, should be controlled by IL-21 dosing, which depends on tumor mass at the time of administration. This method imitates, yet amplifies, the natural anticancer immune response rather than accelerates only one of the response arms in an unbalanced manner. (Cancer Res 2006; 66(14): 7293-300)

Zvia Agur is an internationally known biomathematician whose research focuses on the dynamics of cancer and infectious diseases, and on mathematical methods for identifying improved drug regimens and improved vaccination programs. She is President of the Institute for Medical BioMathematics, Israel, and the Founder, Chairperson and Chief Scientific Officer of Optimata Ltd, Israel. Professor Agur is a former president of the Israeli Society of Theoretical and Mathematical Biology (1995–2001) and a former member of the Board of Directors of the European Society of Mathematical and Theoretical Biology (1996–2002). Her innovative research has won national awards, has been published in a long list of leading scientific journals and is recognized by the academic community worldwide. She serves on the editorial board of several scientific publications, and holds a PhD from the Hebrew University, Jerusalem, and the Université Libre, Brussels.

Neutropenia is a significant dose-limiting toxicity of cancer chemotherapy, especially in dose-intensified regimens. It is widely treated by injections of Granulocyte Colony-Stimulating Factor (G-CSF). However, optimal schedules of G-CSF administration are still not determined. In order to aid in identifying more efficacious and less neutropenic treatment protocols, we studied a detailed physiologically-based computer model of granulopoiesis, as affected by different treatment schedules of doxorubicin and/or Granulocyte Colony-Stimulating Factor (G-CSF). We validated the model as evident from accurate prediction of clinical data on human granulopoiesis in healthy individuals and in doxorubicin-treated cancer patients, with or without G-CSF support. Based on our model, we suggest new G-CSF administration regimens. These regimens include reduced G-CSF doses, optimally timed post-chemotherapy. Application of these regimens can lead to minimization of G-CSF side effects, as well as more cost-effective and less myelotoxic protocols. Currently clinical trials are being designed in order to test these new treatment regimens.

We analysed measurements of tumour growth, neovascular maturation and function in human epithelial ovarian carcinoma xenografts, studied noninvasively by magnetic resonance imaging. Results suggest that vascular maturation and mature and immature vessel regression occur continuously during tumour neovascularisation. Moreover, in these spheroids, a high tumour growth-rate is associated with monotonic changes in vessel density (VD) and with large proportions of mature blood vessels, whereas a lower tumour growth-rate is associated with fluctuating VD and lower proportions of mature vessels. These results corroborate a mathematical model for tumour dynamics, including vascular maturation and immature and mature vessel regression. The model predicts that rapid tumour growth may result from a high maturation-rate of neo-vasculatures, due to substantial mature VD in the microenvironment, while a slower tumour growth is an outcome of a lower background VD, leading to a lower vessel maturation-rate, larger proportion of immature vessels and, consequently, to regression-driven instabilities. The generality of these results for other tumour types should be validated.

In this paper we present several ODE systems encoding the most essential observations and assumptions about the complex hierarchical inter- active processes of tumor neo-vascularization (angiogenesis). From experi- mental results we infer that a significant marker of tumor aggressiveness is the oscillatory behavior of tumor size, which is driven by its vascularization dynamics. To study the forces underlying these oscillations we perform a Hopf point analysis of the angiogenesis models. In the analyzed models Hopf points appear if and only if a nontrivial set of time-delays is introduced into the tu- mor proliferation or the neo-vascularization process. We suggest to examine in laboratory experiments how to employ these results for containing cancer growth.

Summary. Thrombopoietin (TPO) immunogenicity hampers its development as a therapeutic agent for attenuating thrombocytopenia and improving platelet harvest in donors. This work was aimed at validating, in mouse and in monkey experiments, a thrombopoiesis computer-model prediction that platelet counts, similar to those obtained with accepted TPO dose scheduling, can also be achieved by new and safer schedules of significantly reduced doses. To this end we compared, in a two-arm mouse experiment, platelet increases obtained with a single intraperitoneal dosing of recombinant mouse TPO (17·5 μg/kg), with those obtained by the model-suggested protocol of a significantly reduced dose (2 μg/kg on 4 consecutive days). The two TPO regimens generated similar platelet profiles, peaking at ca. 2700 × 109/l platelets. In rhesus monkeys, treated by rhesus monkey recombinant TPO (5 μg/kg on 4 consecutive days), the suggested protocol yielded effective platelet stimulation with significantly reduced immunogenicity. The model's ability to predict individual monkey responses to several new TPO administration protocols was further validated, proving sufficient robustness in providing good predictions with limited input data. The simulation tool could be used for testing the effects of different therapeutic agents on thrombopoiesis. Human trials are warranted for testing the suggested improved TPO protocol, possibly in conjunction with chemotherapy.

The ability of a few stem-cells to repopulate a severely damaged bone marrow (BM) guarantees the stability of our physical existence, and facilitates successful BM transplantations. What are the basic properties of stem cells that enable the maintenance of the system's homeostasis? In the present work we attempt to answer this question by investigating a discrete (in time and phase-space) dynamical system. The model we present is shown to retrieve the essential properties of homeostasis, as reflected in BM functioning, namely, (a) to produce a constant amount of mature cells, and (b) to be capable of returning to this production after very large perturbations. The mechanism guaranteeing the fulfillment of these properties is extrinsic--negative feedback control in the micro-environment--and does not need additional stochastic assumptions. Nevertheless, the existence of a simple intrinsic control mechanism, a clock which determines the switch to differentiation, ascertains that the system does not admit non-trivial extinction states. This result may help clarifying some of the controversy about extrinsic versus intrinsic control over stem cell fate. It should be stressed that all conclusions are valid for any system containing progenitor and maturing cells.

Inflammation underlies many diseases and is an undesired effect of several therapy modalities. Biomathematical modeling can help unravel the complex inflammatory processes and the mechanisms triggering their emergence. We developed a model for induction of C-reactive protein (CRP), a clinically reliable marker of inflammation, by interleukin (IL)-11, an approved cytokine for treatment of chemotherapy-induced thrombocytopenia. Due to paucity of information on the mechanisms underlying inflammation-induced CRP dynamics, our model was developed by systematically evaluating several models for their ability to retrieve variable CRP profiles observed in IL-11-treated breast cancer patients. The preliminary semi-mechanistic models were designed by non-linear mixed-effects modeling, and were evaluated by various performance criteria, which test goodness-of-fit, parsimony and uniqueness. The best-performing model, a robust population model with minimal inter-individual variability, uncovers new aspects of inflammation dynamics. It shows that CRP clearance is a nonlinear self-controlled process, indicating an adaptive anti-inflammatory reaction in humans. The model also reveals a dual IL-11 effect on CRP elevation, whereby the drug has not only a potent immediate influence on CRP incline, but also a long-term influence inducing elevated CRP levels for several months. Consistent with this, model simulations suggest that periodic IL-11 therapy may result in prolonged low-grade (chronic) inflammation post treatment. Future application of the model can therefore help design improved IL-11 regimens with minimized long-term CRP toxicity. Our study illuminates the dynamics of inflammation and its control, and provides a prototype for progressive modeling of complex biological processes in the medical realm and beyond.

The theory of resonance in population persistence proposes that the survival of a population that is exposed to externally inflicted loss processes (disturbances) during part of its life cycle is dependent on the relation between the average period of the disturbances and the average generation time of the population. This suggests that the size of a population can be controlled by manipulating the period between external disturbances. This theory, first formalized in a study of intertidal Red Sea mollusks exposed to periodic storms, has been found to apply to such seemingly disparate phenomena as the spread of a pathogen among susceptible individuals and the response of malignant cancer cells to chemotherapy. The current article provides a brief review of the evolution of the resonance theory into a tool that can be applied to designing vaccination policies – specifically, in preparedness for bio-terrorism attacks – and in personalized medicine. A personalized protocol based on the resonance theory was applied to a cancer patient, stabilizing his tumor progression, relieving his hematopoietic toxicity, and extending his survival

Based on a theory of population dynamics in perturbed environments, it was hypothesized that measles epidemics can be more efficiently controlled by pulse vaccination, i.e., by a vaccination effort that is pulsed over time [1]. Here, we analyze the rationale of the pulse vaccination strategy in the simple SIR epidemic model. We show that repeatedly vaccinating the susceptible population in a series of 'pulses,' it is possible to eradicate the measles infection from the entire model population. We derive the conditions for epidemic eradication under various constraints and show their dependence on the parameters of the epidemic model.

The fundamental strategy of chemotherapy is to maximize tumor eradication within the limits of tolerable toxicity to the organism. To demonstrate the use of mathematical models in designing treatment protocols, we modeled the effect of chemotherapy on tumor mass and simulated the outcome of several neoadjuvant protocols for breast cancer disease. The model assumes unperturbed tumor growth, superimposed by periods of tumor regression during treatment applications. It takes into account both cell cycle specific (CCS) and cell-cycle non specific drugs (CCNS). Three possible modes of growth (exponential, Gompertz and power laws) were simulated in the study. The model parameters (such as cytotoxic activity of a given protocol) were estimated by best fit procedure from the clinical data of tumor regression following neoadjuvant treatments. The estimated parameters were then used to simulate various regimens that are employed today in the treatment of adjuvant and metastatic breast cancer. Our results suggest that although high dose chemotherapy (HDT) cannot eradicate overt metastatic disease, it may lead to cure if applied early in the natural history of breast cancer. Moreover, the simulations predict a better response for a rather toxic dose dense regimen, as compared to a more conventional protocol. However, our simulations suggest that a well tolerable continuous protocol is no less efficient. The results of the study provide insights into the effectivity of chemotherapy and may assist in designing better protocols.