Search

Tumours are heterogeneous populations composed of different cells types: stem cells with the capacity for self-renewal and more differentiated cells lacking such ability. The overall growth behaviour of a developing neoplasm is determined largely by the combined kinetic interactions of these cells. By tracking the fate of individual cancer cells using agent-based methods in silico, we apply basic rules for cell proliferation, migration and cell death to show how these kinetic parameters interact to control, and perhaps dictate defining spatial and temporal tumour growth dynamics in tumour development. When the migration rate is small, a single cancer stem cell can only generate a small, self-limited clone because of the finite life span of progeny and spatial constraints. By contrast, a high migration rate can break this equilibrium, seeding new clones at sites outside the expanse of older clones. In this manner, the tumour continually 'self-metastasises'. Counterintuitively, when the proliferation capacity is low and the rate of cell death is high, tumour growth is accelerated because of the freeing up of space for self-metastatic expansion. Changes to proliferation and cell death that increase the rate at which cells migrate benefit tumour growth as a whole. The dominating influence of migration on tumour growth leads to unexpected dependencies of tumour growth on proliferation capacity and cell death. These dependencies stand to inform standard therapeutic approaches, which anticipate a positive response to cell killing and mitotic arrest. [ABSTRACT FROM AUTHOR]

Tumor growth and progression is a complex phenomenon dependent on the interaction of multiple intrinsic and extrinsic factors. Necessary for tumor development is a small subpopulation of potent cells, so-called cancer stem cells, that can undergo an unlimited number of cell divisions and which are proposed to divide symmetrically with a small probability to produce more cancer stem cells. We show that the majority of cells in a tumor must indeed be non-stem cancer cells with limited life span and limited replicative potential. Tumor development is dependent as well on the proliferative potential and death of these cells, and on the migratory ability of all cancer cells. With increasing number of cells in the tumor, competition for space limits tumor progression, and in agreement with in vitro observation, the majority of cancer cells become quiescent, with proliferation primarily occurring on the outer rim where space is available. We present an agent-based model of early tumor development that captures the spatial heterogeneity of stemness and proliferation status. We apply the model to simulations of radiotherapy to predict treatment outcomes for tumors with different stem cell pool sizes and different quiescence radiosensitivities. We show by first presuming homogeneous radiosensitivity throughout the tumor, and then considering the greater resistance of quiescent cells, that stem cell pool size and stem cell repopulation during treatment determine treatment success. The results for tumor cure probabilities comprise upper bounds, as there is evidence that cancer stem cells are also more radioresistant than other tumor cells. Beyond just demonstrating the influence of mass effects of stem to non-stem cell ratios and proliferating to quiescent cell ratios, we show that the spatiotemporal evolution of the developing heterogeneous population plays a pivotal role in determining radioresponse and treatment optimization. [ABSTRACT FROM AUTHOR]

A response by H. Enderling and colleagues to a letter to the editor about their article "Inflammatory breast carcinoma as a model of accelerated self-metastatic expansion by intra-vascular growth," in 2009 issue is presented.

The observed time evolution of a population is well approximated by a logistic growth function in many research fields, including oncology, ecology, chemistry, demography, economy, linguistics, and artificial neural networks. Initial growth is exponential, then decelerates as the population approaches its limit size, i.e., the carrying capacity. In mathematical oncology, the tumor carrying capacity has been postulated to be dynamically evolving as the tumor overcomes several evolutionary bottlenecks and, thus, to be patient specific. As the relative tumor-over-carrying capacity ratio may be predictive and prognostic for tumor growth and treatment response dynamics, it is paramount to estimate it from limited clinical data. We show that exploiting the logistic function's rotation symmetry can help estimate the population's growth rate and carry capacity from fewer data points than conventional regression approaches. We test this novel approach against published pan-cancer animal and human breast cancer data, achieving a 30% to 40% reduction in the time at which subsequent data collection is necessary to estimate the logistic growth rate and carrying capacity correctly. These results could improve tumor dynamics forecasting and augment the clinical decision-making process., (© 2024. The Author(s), under exclusive licence to the Society for Mathematical Biology.)

The reaction-diffusion equation is widely used in mathematical models of cancer. The calibration of model parameters based on limited clinical data is critical to using reaction-diffusion equation simulations for reliable predictions on a per-patient basis. Here, we focus on cell-level data as routinely available from tissue biopsies used for clinical cancer diagnosis. We analyze the spatial architecture in biopsy tissues stained with multiplex immunofluorescence. We derive a two-point correlation function and the corresponding spatial power spectral distribution. We show that this data-deduced power spectral distribution can fit the power spectrum of the solution of reaction-diffusion equations that can then identify patient-specific tumor growth and invasion rates. This approach allows the measurement of patient-specific critical tumor dynamical properties from routinely available biopsy material at a single snapshot in time., (© 2024. The Author(s).)

Background: Tumor-immune interactions shape a developing tumor and its tumor immune microenvironment (TIME) resulting in either well-infiltrated, immunologically inflamed tumor beds, or immune deserts with low levels of infiltration. The pre-treatment immune make-up of the TIME is associated with treatment outcome; immunologically inflamed tumors generally exhibit better responses to radio- and immunotherapy than non-inflamed tumors. However, radiotherapy is known to induce opposing immunological consequences, resulting in both immunostimulatory and inhibitory responses. In fact, it is thought that the radiation-induced tumoricidal immune response is curtailed by subsequent applications of radiation. It is thus conceivable that spatially fractionated radiotherapy (SFRT), administered through GRID blocks (SFRT-GRID) or lattice radiotherapy to create areas of low or high dose exposure, may create protective reservoirs of the tumor immune microenvironment, thereby preserving anti-tumor immune responses that are pivotal for radiation success., Methods: We have developed an agent-based model (ABM) of tumor-immune interactions to investigate the immunological consequences and clinical outcomes after 2 Gy × 35 whole tumor radiation therapy (WTRT) and SFRT-GRID. The ABM is conceptually calibrated such that untreated tumors escape immune surveillance and grow to clinical detection. Individual ABM simulations are initialized from four distinct multiplex immunohistochemistry (mIHC) slides, and immune related parameter rates are generated using Latin Hypercube Sampling., Results: In silico simulations suggest that radiation-induced cancer cell death alone is insufficient to clear a tumor with WTRT. However, explicit consideration of radiation-induced anti-tumor immunity synergizes with radiation cytotoxicity to eradicate tumors. Similarly, SFRT-GRID is successful with radiation-induced anti-tumor immunity, and, for some pre-treatment TIME compositions and modeling parameters, SFRT-GRID might be superior to WTRT in providing tumor control., Conclusion: This study demonstrates the pivotal role of the radiation-induced anti-tumor immunity. Prolonged fractionated treatment schedules may counteract early immune recruitment, which may be protected by SFRT-facilitated immune reservoirs. Different biological responses and treatment outcomes are observed based on pre-treatment TIME composition and model parameters. A rigorous analysis and model calibration for different tumor types and immune infiltration states is required before any conclusions can be drawn for clinical translation., (© 2024. The Author(s).)

Background: Advanced epithelial ovarian cancer (EOC) has high recurrence rates due to disseminated initial disease presentation. Cytotoxic phototherapies, such as photodynamic therapy (PDT) and photoimmunotherapy (PIT, cell-targeted PDT), have the potential to treat disseminated malignancies due to safe intraperitoneal delivery., Methods: We use in vitro measurements of EOC tumour cell and T cell responses to chemotherapy, PDT, and epidermal growth factor receptor targeted PIT as inputs to a mathematical model of non-linear tumour and immune effector cell interaction. The model outputs were used to calculate how photoimmunotherapy could be utilised for tumour control., Results: In vitro measurements of PIT dose responses revealed that although low light doses (<10 J/cm 2 ) lead to limited tumour cell killing they also increased proliferation of anti-tumour immune effector cells. Model simulations demonstrated that breaking up a larger light dose into multiple lower dose fractions (vis-à-vis fractionated radiotherapy) could be utilised to effect tumour control via stimulation of an anti-tumour immune response., Conclusions: There is promise for applying fractionated PIT in the setting of EOC. However, recommending specific fractionated PIT dosimetry and timing will require appropriate model calibration on tumour-immune interaction data in human patients and subsequent validation of model predictions in prospective clinical trials., (© 2024. The Author(s).)

Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Mathematical modeling in oncology has a long history. Recently, mathematical models and their predictions have made inroads into prospective clinical trials with encouraging results. The goal of many such modeling efforts is to make predictions, either to clinician's choice therapy or into "optimal" therapy - often for individual patients. The mathematical oncology community rightfully puts great hope into predictive modeling and mechanistic digital twins - but with this great opportunity comes great responsibility. Mathematical models need to be rigorously calibrated and validated, and their predictive performance ascertained, before conclusions about predictions into the unknown can be drawn. The recent article "Modeling tumor growth using fractal calculus: Insights into tumor dynamics" (Golmankhaneh et al., 2023), applied fractal calculus to tumor growth data. In this short commentary, I raise concerns about the study design and interpretation. In its current form, this study is poised to put cancer patients at risk if interpreted as concluded by the authors., Competing Interests: Declaration of competing interest I declare no conflict of interest., (Copyright © 2024 Elsevier B.V. All rights reserved.)

Longitudinal tumour volume data from head-and-neck cancer patients show that tumours of comparable pre-treatment size and stage may respond very differently to the same radiotherapy fractionation protocol. Mathematical models are often proposed to predict treatment outcome in this context, and have the potential to guide clinical decision-making and inform personalised fractionation protocols. Hindering effective use of models in this context is the sparsity of clinical measurements juxtaposed with the model complexity required to produce the full range of possible patient responses. In this work, we present a compartment model of tumour volume and tumour composition, which, despite relative simplicity, is capable of producing a wide range of patient responses. We then develop novel statistical methodology and leverage a cohort of existing clinical data to produce a predictive model of both tumour volume progression and the associated level of uncertainty that evolves throughout a patient's course of treatment. To capture inter-patient variability, all model parameters are patient specific, with a bootstrap particle filter-like Bayesian approach developed to model a set of training data as prior knowledge. We validate our approach against a subset of unseen data, and demonstrate both the predictive ability of our trained model and its limitations., (© 2024. The Author(s).)

From the beginning of the usage of radiotherapy (RT) for cancer treatment, mathematical modeling has been integral to understanding radiobiology and for designing treatment approaches and schedules. There has been extensive modeling of response to RT with the inclusion of various degrees of biological complexity. In this study, we compare three models of tumor volume dynamics: (1) exponential growth with RT directly reducing tumor volume, (2) logistic growth with direct tumor volume reduction, and (3) logistic growth with RT reducing the tumor carrying capacity with the objective of understanding the implications of model selection and informing the process of model calibration and parameterization. For all three models, we: examined the rates of change in tumor volume during and RT treatment course; performed parameter sensitivity and identifiability analyses; and investigated the impact of the parameter sensitivity on the tumor volume trajectories. In examining the tumor volume dynamics trends, we coined a new metric - the point of maximum reduction of tumor volume (MRV) - to quantify the magnitude and timing of the expected largest impact of RT during a treatment course. We found distinct timing differences in MRV, dependent on model selection. The parameter identifiability and sensitivity analyses revealed the interdependence of the different model parameters and that it is only possible to independently identify tumor growth and radiation response parameters if the underlying tumor growth rate is sufficiently large. Ultimately, the results of these analyses help us to better understand the implications of model selection while simultaneously generating falsifiable hypotheses about MRV timing that can be tested on longitudinal measurements of tumor volume from pre-clinical or clinical data with high acquisition frequency. Although, our study only compares three particular models, the results demonstrate that caution is necessary in selecting models of response to RT, given the artifacts imposed by each model., Competing Interests: Declaration of Competing Interest The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Heiko Enderling reports financial support was provided by National Cancer Institute., (Copyright © 2023 Elsevier Ltd. All rights reserved.)

Introduction: Radiation therapy (RT) is one of the most common anticancer therapies. Yet, current radiation oncology practice does not adapt RT dose for individual patients, despite wide interpatient variability in radiosensitivity and accompanying treatment response. We have previously shown that mechanistic mathematical modeling of tumor volume dynamics can simulate volumetric response to RT for individual patients and estimation personalized RT dose for optimal tumor volume reduction. However, understanding the implications of the choice of the underlying RT response model is critical when calculating personalized RT dose., Methods: In this study, we evaluate the mathematical implications and biological effects of 2 models of RT response on dose personalization: (1) cytotoxicity to cancer cells that lead to direct tumor volume reduction (DVR) and (2) radiation responses to the tumor microenvironment that lead to tumor carrying capacity reduction (CCR) and subsequent tumor shrinkage. Tumor growth was simulated as logistic growth with pre-treatment dynamics being described in the proliferation saturation index (PSI). The effect of RT was simulated according to each respective model for a standard schedule of fractionated RT with 2 Gy weekday fractions. Parameter sweeps were evaluated for the intrinsic tumor growth rate and the radiosensitivity parameter for both models to observe the qualitative impact of each model parameter. We then calculated the minimum RT dose required for locoregional tumor control (LRC) across all combinations of the full range of radiosensitvity and proliferation saturation values., Results: Both models estimate that patients with higher radiosensitivity will require a lower RT dose to achieve LRC. However, the two models make opposite estimates on the impact of PSI on the minimum RT dose for LRC: the DVR model estimates that tumors with higher PSI values will require a higher RT dose to achieve LRC, while the CCR model estimates that higher PSI values will require a lower RT dose to achieve LRC., Discussion: Ultimately, these results show the importance of understanding which model best describes tumor growth and treatment response in a particular setting, before using any such model to make estimates for personalized treatment recommendations., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2023 Kutuva, Caudell, Yamoah, Enderling and Zahid.)

Fractional calculus has recently been applied to the mathematical modelling of tumour growth, but its use introduces complexities that may not be warranted. Mathematical modelling with differential equations is a standard approach to study and predict treatment outcomes for population-level and patient-specific responses. Here, we use patient data of radiation-treated tumours to discuss the benefits and limitations of introducing fractional derivatives into three standard models of tumour growth. The fractional derivative introduces a history-dependence into the growth function, which requires a continuous death-rate term for radiation treatment. This newly proposed radiation-induced death-rate term improves computational efficiency in both ordinary and fractional derivative models. This computational speed-up will benefit common simulation tasks such as model parameterization and the construction and running of virtual clinical trials., (© 2023. The Author(s).)

Acquiring sufficient data is imperative to accurately predict tumor growth dynamics and effectively treat patients. The aim of this study was to investigate the number of volume measurements necessary to predict breast tumor growth dynamics using the logistic growth model. The model was calibrated to tumor volume data from 18 untreated breast cancer patients using a varying number of measurements interpolated at clinically relevant timepoints with different levels of noise (0-20%). Error-to-model parameters and the data were compared to determine the sufficient number of measurements needed to accurately determine growth dynamics. We found that without noise, three tumor volume measurements are necessary and sufficient to estimate patient-specific model parameters. More measurements were required as the level of noise increased. Estimating the tumor growth dynamics was shown to depend on the tumor growth rate, clinical noise level, and acceptable error of the to-be-determined parameters. Understanding the relationship between these factors provides a metric by which clinicians can determine when sufficient data have been collected to confidently predict patient-specific tumor growth dynamics and recommend appropriate treatment options.

Adaptive therapy with abiraterone acetate (AA), whereby treatment is cycled on and off, has been presented as an alternative to continuous therapy for metastatic castration resistant prostate cancer (mCRPC). It is hypothesized that cycling through treatment allows sensitive cells to competitively suppress resistant cells, thereby increasing the amount of time that treatment is effective. It has been proposed that there exists a subset of patients for whom this competition can be enhanced through slight modifications. Here, we investigate how adaptive AA can be modified to extend time to progression using a simple mathematical model of stem cell, non-stem cell, and prostate-specific antigen (PSA) dynamics. The model is calibrated to longitudinal PSA data from 16 mCRPC patients undergoing adaptive AA in a pilot clinical study at Moffitt Cancer Center. Model parameters are then used to simulate range-bounded adaptive therapy (RBAT) whereby treatment is modulated to maintain PSA levels between pre-determined patient-specific bounds. Model simulations of RBAT are compared to the clinically applied adaptive therapy and show that RBAT can further extend time to progression, while reducing the cumulative dose patients received in 11/16 patients. Simulations also show that the cumulative dose can be reduced by up to 40% under RBAT. Through small modifications to the conventional adaptive therapy design, our study demonstrates that RBAT offers the opportunity to improve patient care, particularly in those patients who do not respond well to conventional adaptive therapy., Competing Interests: The authors declare no conflict of interest.

Cancer stem cells (CSCs) are key in understanding tumor growth and tumor progression. A counterintuitive effect of CSCs is the so-called tumor growth paradox: the effect where a tumor with a higher death rate may grow larger than a tumor with a lower death rate. Here we extend the modeling of the tumor growth paradox by including spatial structure and considering cancer invasion. Using agent-based modeling and a corresponding partial differential equation model, we demonstrate and prove mathematically a tumor invasion paradox: a larger cell death rate can lead to a faster invasion speed. We test this result on a generic hypothetical cancer with typical growth rates and typical treatment sensitivities. We find that the tumor invasion paradox may play a role for continuous and intermittent treatments, while it does not seem to be essential in fractionated treatments. It should be noted that no attempt was made to fit the model to a specific cancer, thus, our results are generic and theoretical., (© 2022. The Author(s).)

Purpose: Radiation therapy (RT) is a mainstay of cancer care, and accumulating evidence suggests the potential for synergism with components of the immune response. However, few data describe the tumor immune contexture in relation to RT sensitivity. To address this challenge, we used the radiation sensitivity index (RSI) gene signature to estimate the RT sensitivity of >10,000 primary tumors and characterized their immune microenvironments in relation to the RSI., Methods and Materials: We analyzed gene expression profiles of 10,469 primary tumors (31 types) within a prospective tissue collection protocol. The RT sensitivity of each tumor was estimated by the RSI and respective distributions were characterized. The tumor biology measured by the RSI was evaluated by differentially expressed genes combined with single sample gene set enrichment analysis. Differences in the expression of immune regulatory molecules were assessed and deconvolution algorithms were used to estimate immune cell infiltrates in relation to the RSI. A subset (n = 2368) of tumors underwent DNA sequencing for mutational frequency characterization., Results: We identified a wide range of RSI values within and across various tumor types, with several demonstrating nonunimodal distributions (eg, colon, renal, lung, prostate, esophagus, pancreas, and PAM50 breast subtypes; P < .05). Across all tumor types, stratifying RSI at a tumor type-specific median identified 7148 differentially expressed genes, of which 146 were coordinate in direction. Network topology analysis demonstrates RSI measures a coordinated STAT1, IRF1, and CCL4/MIP-1β transcriptional network. Tumors with an estimated high sensitivity to RT demonstrated distinct enrichment of interferon-associated signaling pathways and immune cell infiltrates (eg, CD8 + T cells, activated natural killer cells, M1-macrophages; q < 0.05), which was in the context of diverse expression patterns of various immunoregulatory molecules., Conclusions: This analysis describes the immune microenvironments of patient tumors in relation to the RSI gene expression signature., (Copyright © 2022 Elsevier Inc. All rights reserved.)

Immunotherapies are a major breakthrough in oncology, yielding unprecedented response rates for some cancers. Especially in combination with conventional treatments or targeted agents, immunotherapeutics offer invaluable tools to improve outcomes for many patients. However, why not all patients have a favorable response remains unclear. There is an increasing appreciation of the contributions of the complex tumor microenvironment, and the tumor-immune ecosystem in particular, to treatment outcome. To date, however, there exists no immune biomarker to explain why two patients with similar clinical stage and molecular profile would have different treatment outcomes. We hypothesize that it is critical to understand both the immune and tumor states to understand how the complex system will respond to treatment. Here, we present how integrated mathematical oncology approaches can help conceptualize the effect of various immunotherapies on a patient's tumor and local immune environment, and how combinations of immunotherapy and cytotoxic therapy may be used to improve tumor response and control and limit toxicity on a per patient basis., Competing Interests: Competing interests: None declared., (© Author(s) (or their employer(s)) 2022. Re-use permitted under CC BY-NC. No commercial re-use. See rights and permissions. Published by BMJ.)

Radiotherapy is a primary therapeutic modality widely utilized with curative intent. Traditionally tumor response was hypothesized to be due to high levels of cell death induced by irreparable DNA damage. However, the immunomodulatory aspect of radiation is now widely accepted. As such, interest into the combination of radiotherapy and immunotherapy is increasing, the synergy of which has the potential to improve tumor regression beyond that observed after either treatment alone. However, questions regarding the timing (sequential vs concurrent) and dose fractionation (hyper-, standard-, or hypo-fractionation) that result in improved anti-tumor immune responses, and thus potentially enhanced tumor inhibition, remain. Here we discuss the biological response to radiotherapy and its immunomodulatory properties before giving an overview of pre-clinical data and clinical trials concerned with answering these questions. Finally, we review published mathematical models of the impact of radiotherapy on tumor-immune interactions. Ranging from considering the impact of properties of the tumor microenvironment on the induction of anti-tumor responses, to the impact of choice of radiation site in the setting of metastatic disease, these models all have an underlying feature in common: the push towards personalized therapy., Competing Interests: Declaration of Competing Interest None., (Copyright © 2022. Published by Elsevier Inc.)

With a widely attended virtual kickoff event on January 29, 2021, the National Cancer Institute (NCI) and the Department of Energy (DOE) launched a series of 4 interactive, interdisciplinary workshops-and a final concluding "World Café" on March 29, 2021-focused on advancing computational approaches for predictive oncology in the clinical and research domains of radiation oncology. These events reflect 3,870 human hours of virtual engagement with representation from 8 DOE national laboratories and the Frederick National Laboratory for Cancer Research (FNL), 4 research institutes, 5 cancer centers, 17 medical schools and teaching hospitals, 5 companies, 5 federal agencies, 3 research centers, and 27 universities. Here we summarize the workshops by first describing the background for the workshops. Participants identified twelve key questions-and collaborative parallel ideas-as the focus of work going forward to advance the field. These were then used to define short-term and longer-term "Blue Sky" goals. In addition, the group determined key success factors for predictive oncology in the context of radiation oncology, if not the future of all of medicine. These are: cross-discipline collaboration, targeted talent development, development of mechanistic mathematical and computational models and tools, and access to high-quality multiscale data that bridges mechanisms to phenotype. The workshop participants reported feeling energized and highly motivated to pursue next steps together to address the unmet needs in radiation oncology specifically and in cancer research generally and that NCI and DOE project goals align at the convergence of radiation therapy and advanced computing., (©2022 by Radiation Research Society. All rights of reproduction in any form reserved.)

Objectives: Recurrent and/or metastatic (R/M) head and neck squamous cell carcinoma (HNSCC) is currently an incurable disease. To improve treatment strategies, combinations of cetuximab plus nivolumab or pembrolizumab were evaluated for efficacy and safety for incurable R/M HNSCC. While some patients had a significant clinical benefit with complete or partial response, most patients had stable or progressive disease (PD). To identify patients with a high likelihood of treatment failure and prevent futile treatments, we developed a mathematical model of early response dynamics as an early biomarker of treatment failure., Materials and Methods: Demographics, RECIST assessment, and outcome were obtained from patients who were treated with combination of cetuximab and nivolumab on a previously published phase I/II clinical trial. We trained a tumor growth inhibition (TGI) ordinary differential equation (ODE) model describing patient-specific pre-treatment growth rate and uniform initial treatment sensitivity and rate of evolution of resistance. In a leave-one-out approach, we forecasted tumor burden and predicted time to progression (TTP) and PD., Results: The TGI model accurately represented tumor burden dynamics (R 2 =0.98; RMSE=0.57 cm) and predicted PD with accuracy=0.71,sensitivity=1.00, and specificity=0.69 after three serial response assessment scans. Patient-specific pre-treatment growth rate correlated negatively with TTP (Spearman's ρ=-0.67,p=5.7e-05)., Conclusion: The TGI model can identify patients with high likelihood of PD based on early dynamics. Further studies including prospective validation are warranted., (Copyright © 2022. Published by Elsevier Ltd.)

Competing Interests: Declaration of Competing Interest The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Heiko Enderling has filed provisional patent applications for different mathematical modeling approaches to support clinical decision making (63/010,327, 62/944,804, 62/040,579, 62/900,003, 62/040,579, 63/279,994).

Classical mathematical models of tumor growth have shaped our understanding of cancer and have broad practical implications for treatment scheduling and dosage. However, even the simplest textbook models have been barely validated in real world-data of human patients. In this study, we fitted a range of differential equation models to tumor volume measurements of patients undergoing chemotherapy or cancer immunotherapy for solid tumors. We used a large dataset of 1472 patients with three or more measurements per target lesion, of which 652 patients had six or more data points. We show that the early treatment response shows only moderate correlation with the final treatment response, demonstrating the need for nuanced models. We then perform a head-to-head comparison of six classical models which are widely used in the field: the Exponential, Logistic, Classic Bertalanffy, General Bertalanffy, Classic Gompertz and General Gompertz model. Several models provide a good fit to tumor volume measurements, with the Gompertz model providing the best balance between goodness of fit and number of parameters. Similarly, when fitting to early treatment data, the general Bertalanffy and Gompertz models yield the lowest mean absolute error to forecasted data, indicating that these models could potentially be effective at predicting treatment outcome. In summary, we provide a quantitative benchmark for classical textbook models and state-of-the art models of human tumor growth. We publicly release an anonymized version of our original data, providing the first benchmark set of human tumor growth data for evaluation of mathematical models., Competing Interests: I have read the journal’s policy and the authors of this manuscript have the following competing interests: JNK declares consulting services for Owkin, France and Panakeia, UK. No other potential conflicts of interest are reported by any of the authors.

The prostate is an exocrine gland of the male reproductive system dependent on androgens (testosterone and dihydrotestosterone) for development and maintenance. First-line therapy for prostate cancer includes androgen deprivation therapy (ADT), depriving both the normal and malignant prostate cells of androgens required for proliferation and survival. A significant problem with continuous ADT at the maximum tolerable dose is the insurgence of cancer cell resistance. In recent years, intermittent ADT has been proposed as an alternative to continuous ADT, limiting toxicities and delaying time-to-progression. Several mathematical models with different biological resistance mechanisms have been considered to simulate intermittent ADT response dynamics. We present a comparison between 13 of these intermittent dynamical models and assess their ability to describe prostate-specific antigen (PSA) dynamics. The models are calibrated to longitudinal PSA data from the Canadian Prospective Phase II Trial of intermittent ADT for locally advanced prostate cancer. We perform Bayesian inference and model analysis over the models' space of parameters on- and off-treatment to determine each model's strength and weakness in describing the patient-specific PSA dynamics. Additionally, we carry out a classical Bayesian model comparison on the models' evidence to determine the models with the highest likelihood to simulate the clinically observed dynamics. Our analysis identifies several models with critical abilities to disentangle between relapsing and not relapsing patients, together with parameter intervals where the critical points' basin of attraction might be exploited for clinical purposes. Finally, within the Bayesian model comparison framework, we identify the most compelling models in the description of the clinical data., (© 2021. The Author(s).)

Radiotherapy efficacy is the result of radiation-mediated cytotoxicity coupled with stimulation of antitumor immune responses. We develop an in silico 3-dimensional agent-based model of diverse tumor-immune ecosystems (TIES) represented as anti- or pro-tumor immune phenotypes. We validate the model in 10,469 patients across 31 tumor types by demonstrating that clinically detected tumors have pro-tumor TIES. We then quantify the likelihood radiation induces antitumor TIES shifts toward immune-mediated tumor elimination by developing the individual Radiation Immune Score (iRIS). We show iRIS distribution across 31 tumor types is consistent with the clinical effectiveness of radiotherapy, and in combination with a molecular radiosensitivity index (RSI) combines to predict pan-cancer radiocurability. We show that iRIS correlates with local control and survival in a separate cohort of 59 lung cancer patients treated with radiation. In combination, iRIS and RSI predict radiation-induced TIES shifts in individual patients and identify candidates for radiation de-escalation and treatment escalation. This is the first clinically and biologically validated computational model to simulate and predict pan-cancer response and outcomes via the perturbation of the TIES by radiotherapy., (Copyright © 2021. Published by Elsevier Inc.)

Purpose: To model and predict individual patient responses to radiation therapy., Methods and Materials: We modeled tumor dynamics as logistic growth and the effect of radiation as a reduction in the tumor carrying capacity, motivated by the effect of radiation on the tumor microenvironment. The model was assessed on weekly tumor volume data collected for 2 independent cohorts of patients with head and neck cancer from the H. Lee Moffitt Cancer Center (MCC) and the MD Anderson Cancer Center (MDACC) who received 66 to 70 Gy in standard daily fractions or with accelerated fractionation. To predict response to radiation therapy for individual patients, we developed a new forecasting framework that combined the learned tumor growth rate and carrying capacity reduction fraction (δ) distribution with weekly measurements of tumor volume reduction for a given test patient to estimate δ, which was used to predict patient-specific outcomes., Results: The model fit data from MCC with high accuracy with patient-specific δ and a fixed tumor growth rate across all patients. The model fit data from an independent cohort from MDACC with comparable accuracy using the tumor growth rate learned from the MCC cohort, showing transferability of the growth rate. The forecasting framework predicted patient-specific outcomes with 76% sensitivity and 83% specificity for locoregional control and 68% sensitivity and 85% specificity for disease-free survival with the inclusion of 4 on-treatment tumor volume measurements., Conclusions: These results demonstrate that our simple mathematical model can describe a variety of tumor volume dynamics. Furthermore, combining historically observed patient responses with a few patient-specific tumor volume measurements allowed for the accurate prediction of patient outcomes, which may inform treatment adaptation and personalization., (Copyright © 2021 The Authors. Published by Elsevier Inc. All rights reserved.)