Forecasting Individual Patient Response to Radiation Therapy in Head and Neck Cancer With a Dynamic Carrying Capacity Model

A mathematical model for predicting the spatiotemporal response of breast cancer cells treated with doxorubicin

Tumor heterogeneity contributes significantly to chemoresistance, a leading cause of treatment failure. To better personalize therapies, it is essential to develop tools capable of identifying and predicting intra- and inter-tumor heterogeneities. Biology-inspired mathematical models are capable of attacking this problem, but tumor heterogeneity is often overlooked in in-vivo modeling studies, while phenotypic considerations capturing spatial dynamics are not typically included in in-vitro modeling studies. We present a data assimilation-prediction pipeline with a two-phenotype model that includes a spatiotemporal component to characterize and predict the evolution of in-vitro breast cancer cells and their heterogeneous response to chemotherapy. Our model assumes that the cells can be divided into two subpopulations: surviving cells unaffected by the treatment, and irreversibly damaged cells undergoing treatment-induced death. MCF7 breast cancer cells were previously cultivated in wells for up to 1000 hours, treated with various concentrations of doxorubicin and imaged with time-resolved microscopy to record spatiotemporally-resolved cell count data. Images were used to generate cell density maps. Treatment response predictions were initialized by a training set and updated by weekly measurements. Our mathematical model successfully calibrated the spatiotemporal cell growth dynamics, achieving median [range] concordance correlation coefficients of > .99 [.88, >.99] and .73 [.58, .85] across the whole well and individual pixels, respectively. Our proposed data assimilation-prediction approach achieved values of .97 [.44, >.99] and .69 [.35, .79] for the whole well and individual pixels, respectively. Thus, our model can capture and predict the spatiotemporal dynamics of MCF7 cells treated with doxorubicin in an in-vitro setting.

Patient-Specific, Mechanistic Models of Tumor Growth Incorporating Artificial Intelligence and Big Data

Despite the remarkable advances in cancer diagnosis, treatment, and management over the past decade, malignant tumors remain a major public health problem. Further progress in combating cancer may be enabled by personalizing the delivery of therapies according to the predicted response for each individual patient. The design of personalized therapies requires the integration of patient-specific information with an appropriate mathematical model of tumor response. A fundamental barrier to realizing this paradigm is the current lack of a rigorous yet practical mathematical theory of tumor initiation, development, invasion, and response to therapy. We begin this review with an overview of different approaches to modeling tumor growth and treatment, including mechanistic as well as data-driven models based on big data and artificial intelligence. We then present illustrative examples of mathematical models manifesting their utility and discuss the limitations of stand-alone mechanistic and data-driven models. We then discuss the potential of mechanistic models for not only predicting but also optimizing response to therapy on a patient-specific basis. We describe current efforts and future possibilities to integrate mechanistic and data-driven models. We conclude by proposing five fundamental challenges that must be addressed to fully realize personalized care for cancer patients driven by computational models.

Multi-modality imaging parameters that predict rapid tumor regression in head and neck radiotherapy

Background and purpose

Volume regression during radiotherapy can indicate patient-specific treatment response. We aimed to identify pre-treatment multimodality imaging (MMI) metrics from positron emission tomography (PET), magnetic resonance imaging (MRI), and computed tomography (CT) that predict rapid tumor regression during radiotherapy in human papilloma virus (HPV) associated oropharyngeal carcinoma.

Materials and methods

Pre-treatment FDG PET-CT, diffusion-weighted MRI (DW-MRI), and intra-treatment (at 1, 2, and 3 weeks) MRI were acquired in 72 patients undergoing chemoradiation therapy for HPV+ oropharyngeal carcinoma. Nodal gross tumor volumes were delineated on longitudinal images to measure intra-treatment volume changes. Pre-treatment PET standardized uptake value (SUV), CT Hounsfield Unit (HU), and non-gaussian intravoxel incoherent motion DW-MRI metrics were computed and correlated with volume changes. Intercorrelations between MMI metrics were also assessed using network analysis. Validation was carried out on a separate cohort (N = 64) for FDG PET-CT.

Results

Significant correlations with volume loss were observed for baseline FDG SUVmean (Spearman ρ = 0.46, p < 0.001), CT HUmean (ρ = 0.38, p = 0.001), and DW-MRI diffusion coefficient, Dmean (ρ = -0.39, p < 0.001). Network analysis revealed 41 intercorrelations between MMI and volume loss metrics, but SUVmean remained a statistically significant predictor of volume loss in multivariate linear regression (p = 0.01). Significant correlations were also observed for SUVmean in the validation cohort in both primary (ρ = 0.30, p = 0.02) and nodal (ρ = 0.31, p = 0.02) tumors.

Conclusions

Multiple pre-treatment imaging metrics were correlated with rapid nodal gross tumor volume loss during radiotherapy. FDG-PET SUV in particular exhibited significant correlations with volume regression across the two cohorts and in multivariate analysis.

To modulate or to skip: De-escalating PARP inhibitor maintenance therapy in ovarian cancer using adaptive therapy

Toxicity and emerging drug resistance pose important challenges in poly-adenosine ribose polymerase inhibitor (PARPi) maintenance therapy of ovarian cancer. We propose that adaptive therapy, which dynamically reduces treatment based on the tumor dynamics, might alleviate both issues. Utilizing in vitro time-lapse microscopy and stepwise model selection, we calibrate and validate a differential equation mathematical model, which we leverage to test different plausible adaptive treatment schedules. Our model indicates that adjusting the dosage, rather than skipping treatments, is more effective at reducing drug use while maintaining efficacy due to a delay in cell kill and a diminishing dose-response relationship. In vivo pilot experiments confirm this conclusion. Although our focus is toxicity mitigation, reducing drug use may also delay resistance. This study enhances our understanding of PARPi treatment scheduling and illustrates the first steps in developing adaptive therapies for new treatment settings. A record of this paper's transparent peer review process is included in the supplemental information.

A Population-Based Tumor-Volume Model for Head and Neck Cancer During Radiation Therapy With a Dynamic Oxygenated Compartment

PURPOSE

With the coming era of digital medicine and healthcare technology, mathematical modeling of tumors has become a key step to optimize and realize precision radiation therapy. The purpose of this study was to develop a mathematical model for simulating the change of head and neck (HN) tumor volume during radiation therapy.

METHODS AND MATERIALS

A formula was developed to describe the dynamic change of oxygenated compartment within a tumor, which was combined with the lethal lesions model to describe various cell processes during radiation therapy, including potentially lethal lesion repair and misrepair, cell proliferation/loss, and tumor reoxygenation. Parameter sensitivity analysis was performed to evaluate the impacts of lesion- and repair-related biological factors on radiation therapy outcomes.

RESULTS

We tested our model on 14 available patients with HN cancer and compared the performance with 3 other models. The mean error of our model for the 12 good fit cases was 12.2%, which is considerably smaller than that of the linear quadratic model (19.7%), the generalized linear quadratic model (19.1%), and a 4-level cell population model (16.6%). Correlation analysis results revealed that for small tumors, there was a positive correlation (correlation coefficient r=0.9416) between hypoxic fraction (hf) and tumor volume, whereas the correlation became negative and not significant (r=-0.4365) for large tumors. It is demonstrated from sensitivity analysis that the production rate of lethal lesions (ηl) has a far greater impact on tumor volume than other parameters. The hf had an insignificant impact on tumor volume but had a notable influence on the volume of surviving cells. The final volume of surviving cells athf=0.5 was almost 8 ×102 times that of hf=0.01. The potentially lethal lesion-related parameters (the production rate of potentially lethal lessions per unit dose ηpl, the rate of correct repair per unit time εpl, and the rate of binary misrepair per unit time ε2pl) had rather small impacts (<1%) on both tumor volume and the volume of surviving cells, which indicates that the repaired and misrepaired sublethal cells only take up a small portion of the total cancer cell population.

CONCLUSIONS

A population-based tumor-volume model for HN cancer during radiation therapy with a dynamic oxygenated compartment was developed in this study. Comprehensively considering the damage process of tumor cells caused by radiation therapy, the accurate prediction of the volume change of HN tumors during treatment was revealed. Meanwhile, various cell activities and their principles in the process of antitumor treatment were reflected, which has positive clinical reference significance for radiobiology.

Fractal calculus in tumor growth simulations: The proof is in the pudding

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.

Designing clinical trials for patients who are not average

The heterogeneity inherent in cancer means that even a successful clinical trial merely results in a therapeutic regimen that achieves, on average, a positive result only in a subset of patients. The only way to optimize an intervention for an individual patient is to reframe their treatment as their own, personalized trial. Toward this goal, we formulate a computational framework for performing personalized trials that rely on four mathematical techniques. First, mathematical models that can be calibrated with patient-specific data to make accurate predictions of response. Second, digital twins built on these models capable of simulating the effects of interventions. Third, optimal control theory applied to the digital twins to optimize outcomes. Fourth, data assimilation to continually update and refine predictions in response to therapeutic interventions. In this perspective, we describe each of these techniques, quantify their "state of readiness", and identify use cases for personalized clinical trials.

Predicting Radiotherapy Patient Outcomes with Real-Time Clinical Data Using Mathematical Modelling

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.

Simulating tumor volume dynamics in response to radiotherapy: Implications of model selection

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.

A novel approach to predict acute radiation dermatitis in patients with head and neck cancer using a model based on Bayesian probability

PURPOSE

In this study, we aimed to establish a method for predicting the probability of each acute radiation dermatitis (ARD) grade during the head and neck Volumetric Modulated Arc Therapy (VMAT) radiotherapy planning phase based on Bayesian probability.

METHODS

The skin dose volume >50 Gy (V50), calculated using the treatment planning system, was used as a factor related to skin toxicity. The empirical distribution of each ARD grade relative to V50 was obtained from the ARD grades of 119 patients (55, 50, and 14 patients with G1, G2, and G3, respectively) determined by head and neck cancer specialists. Using Bayes' theorem, the Bayesian probabilities of G1, G2, and G3 for each value of V50 were calculated with an empirical distribution. Conversely, V50 was obtained based on the Bayesian probabilities of G1, G2, and G3.

RESULTS

The empirical distribution for each graded patient group demonstrated a normal distribution. The method predicted ARD grades with 92.4 % accuracy and provided a V50 value for each grade. For example, using the graph, we could predict that V50 should be ≤24.5 cm3 to achieve G1 with 70 % probability.

CONCLUSIONS

The Bayesian probability-based ARD prediction method could predict the ARD grade at the treatment planning stage using limited patient diagnostic data that demonstrated a normal distribution. If the probability of an ARD grade is high, skin care can be initiated in advance. Furthermore, the V50 value during treatment planning can provide radiation oncologists with data for strategies to reduce ARD.

Predicting the spatio-temporal response of recurrent glioblastoma treated with rhenium-186 labelled nanoliposomes

Rhenium-186 (186Re) labeled nanoliposome (RNL) therapy for recurrent glioblastoma patients has shown promise to improve outcomes by locally delivering radiation to affected areas. To optimize the delivery of RNL, we have developed a framework to predict patient-specific response to RNL using image-guided mathematical models.

Methods

We calibrated a family of reaction-diffusion type models with multi-modality imaging data from ten patients (NCR01906385) to predict the spatio-temporal dynamics of each patient's tumor. The data consisted of longitudinal magnetic resonance imaging (MRI) and single photon emission computed tomography (SPECT) to estimate tumor burden and local RNL activity, respectively. The optimal model from the family was selected and used to predict future growth. A simplified version of the model was used in a leave-one-out analysis to predict the development of an individual patient's tumor, based on cohort parameters.

Results

Across the cohort, predictions using patient-specific parameters with the selected model were able to achieve Spearman correlation coefficients (SCC) of 0.98 and 0.93 for tumor volume and total cell number, respectively, when compared to the measured data. Predictions utilizing the leave-one-out method achieved SCCs of 0.89 and 0.88 for volume and total cell number across the population, respectively.

Conclusion

We have shown that patient-specific calibrations of a biology-based mathematical model can be used to make early predictions of response to RNL therapy. Furthermore, the leave-one-out framework indicates that radiation doses determined by SPECT can be used to assign model parameters to make predictions directly following the conclusion of RNL treatment.

Statement of Significance

This manuscript explores the application of computational models to predict response to radionuclide therapy in glioblastoma. There are few, to our knowledge, examples of mathematical models used in clinical radionuclide therapy. We have tested a family of models to determine the applicability of different radiation coupling terms for response to the localized radiation delivery. We show that with patient-specific parameter estimation, we can make accurate predictions of future glioblastoma response to the treatment. As a comparison, we have shown that population trends in response can be used to forecast growth from the moment the treatment has been delivered.In addition to the high simulation and prediction accuracy our modeling methods have achieved, the evaluation of a family of models has given insight into the response dynamics of radionuclide therapy. These dynamics, while different than we had initially hypothesized, should encourage future imaging studies involving high dosage radiation treatments, with specific emphasis on the local immune and vascular response.

Mathematical modeling of radiotherapy: impact of model selection on estimating minimum radiation dose for tumor control

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.

An adaptive information-theoretic experimental design procedure for high-to-low fidelity calibration of prostate cancer models

The use of mathematical models to make predictions about tumor growth and response to treatment has become increasingly prevalent in the clinical setting. The level of complexity within these models ranges broadly, and the calibration of more complex models requires detailed clinical data. This raises questions about the type and quantity of data that should be collected and when, in order to maximize the information gain about the model behavior while still minimizing the total amount of data used and the time until a model can be calibrated accurately. To address these questions, we propose a Bayesian information-theoretic procedure, using an adaptive score function to determine the optimal data collection times and measurement types. The novel score function introduced in this work eliminates the need for a penalization parameter used in a previous study, while yielding model predictions that are superior to those obtained using two potential pre-determined data collection protocols for two different prostate cancer model scenarios: one in which we fit a simple ODE system to synthetic data generated from a cellular automaton model using radiotherapy as the imposed treatment, and a second scenario in which a more complex ODE system is fit to clinical patient data for patients undergoing intermittent androgen suppression therapy. We also conduct a robust analysis of the calibration results, using both error and uncertainty metrics in combination to determine when additional data acquisition may be terminated.

Logistic tumor-population growth and ghost-points symmetry

The observed time evolution of a population is well approximated by a logistic function in many research fields, including oncology, ecology, chemistry, demography, economy, linguistics, and artificial neural networks. Initial growth is exponential at a constant rate and capped at a limit size, i.e., the carrying capacity. In mathematical oncology, the carrying capacity has been postulated to be co-evolving and thus 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 a classic oncology database of logistic tumor growth, achieving a 30% to 40% reduction in the time necessary to correctly estimate the logistic growth rate and carrying capacity. Our results will improve tumor dynamics forecasting and augment the clinical decision-making process.

Modelling Radiation Cancer Treatment with a Death-Rate Term in Ordinary and Fractional Differential Equations

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.

Mathematical modelling of the dynamics of image-informed tumor habitats in a murine model of glioma

Tumors exhibit high molecular, phenotypic, and physiological heterogeneity. In this effort, we employ quantitative magnetic resonance imaging (MRI) data to capture this heterogeneity through imaging-based subregions or "habitats" in a murine model of glioma. We then demonstrate the ability to model and predict the growth of the habitats using coupled ordinary differential equations (ODEs) in the presence and absence of radiotherapy. Female Wistar rats (N = 21) were inoculated intracranially with 10⁶ C6 glioma cells, a subset of which received 20 Gy (N = 5) or 40 Gy (N = 8) of radiation. All rats underwent diffusion-weighted and dynamic contrast-enhanced MRI at up to seven time points. All MRI data at each visit were subsequently clustered using k-means to identify physiological tumor habitats. A family of four models consisting of three coupled ODEs were developed and calibrated to the habitat time series of control and treated rats and evaluated for predictive capability. The Akaike Information Criterion was used for model selection, and the normalized sum-of-square-error (SSE) was used to evaluate goodness-of-fit in model calibration and prediction. Three tumor habitats with significantly different imaging data characteristics (p < 0.05) were identified: high-vascularity high-cellularity, low-vascularity high-cellularity, and low-vascularity low-cellularity. Model selection resulted in a five-parameter model whose predictions of habitat dynamics yielded SSEs that were similar to the SSEs from the calibrated model. It is thus feasible to mathematically describe habitat dynamics in a preclinical model of glioma using biology-based ODEs, showing promise for forecasting heterogeneous tumor behavior.

A data assimilation framework to predict the response of glioma cells to radiation

We incorporate a practical data assimilation methodology into our previously established experimental-computational framework to predict the heterogeneous response of glioma cells receiving fractionated radiation treatment. Replicates of 9L and C6 glioma cells grown in 96-well plates were irradiated with six different fractionation schemes and imaged via time-resolved microscopy to yield 360- and 286-time courses for the 9L and C6 lines, respectively. These data were used to calibrate a biology-based mathematical model and then make predictions within two different scenarios. For Scenario 1, 70% of the time courses are fit to the model and the resulting parameter values are averaged. These average values, along with the initial cell number, initialize the model to predict the temporal evolution for each test time course (10% of the data). In Scenario 2, the predictions for the test cases are made with model parameters initially assigned from the training data, but then updated with new measurements every 24 hours via four versions of a data assimilation framework. We then compare the predictions made from Scenario 1 and the best version of Scenario 2 to the experimentally measured microscopy measurements using the concordance correlation coefficient (CCC). Across all fractionation schemes, Scenario 1 achieved a CCC value (mean ± standard deviation) of 0.845 ± 0.185 and 0.726 ± 0.195 for the 9L and C6 cell lines, respectively. For the best data assimilation version from Scenario 2 (validated with the last 20% of the data), the CCC values significantly increased to 0.954 ± 0.056 (p = 0.002) and 0.901 ± 0.061 (p = 8.9e-5) for the 9L and C6 cell lines, respectively. Thus, we have developed a data assimilation approach that incorporates an experimental-computational system to accurately predict the in vitro response of glioma cells to fractionated radiation therapy.

Sources of inter-individual variability leading to significant changes in anti-PD-1 and anti-PD-L1 efficacy identified in mouse tumor models using a QSP framework

While anti-PD-1 and anti-PD-L1 [anti-PD-(L)1] monotherapies are effective treatments for many types of cancer, high variability in patient responses is observed in clinical trials. Understanding the sources of response variability can help prospectively identify potential responsive patient populations. Preclinical data may offer insights to this point and, in combination with modeling, may be predictive of sources of variability and their impact on efficacy. Herein, a quantitative systems pharmacology (QSP) model of anti-PD-(L)1 was developed to account for the known pharmacokinetic properties of anti-PD-(L)1 antibodies, their impact on CD8⁺ T cell activation and influx into the tumor microenvironment, and subsequent anti-tumor effects in CT26 tumor syngeneic mouse model. The QSP model was sufficient to describe the variability inherent in the anti-tumor responses post anti-PD-(L)1 treatments. Local sensitivity analysis identified tumor cell proliferation rate, PD-1 expression on CD8⁺ T cells, PD-L1 expression on tumor cells, and the binding affinity of PD-1:PD-L1 as strong influencers of tumor growth. It also suggested that treatment-mediated tumor growth inhibition is sensitive to T cell properties including the CD8⁺ T cell proliferation half-life, CD8⁺ T cell half-life, cytotoxic T-lymphocyte (CTL)-mediated tumor cell killing rate, and maximum rate of CD8⁺ T cell influx into the tumor microenvironment. Each of these parameters alone could not predict anti-PD-(L)1 treatment response but they could shift an individual mouse's treatment response when perturbed. The presented preclinical QSP modeling framework provides a path to incorporate potential sources of response variability in human translation modeling of anti-PD-(L)1.

Opportunities for improving brain cancer treatment outcomes through imaging-based mathematical modeling of the delivery of radiotherapy and immunotherapy

Immunotherapy has become a fourth pillar in the treatment of brain tumors and, when combined with radiation therapy, may improve patient outcomes and reduce the neurotoxicity. As with other combination therapies, the identification of a treatment schedule that maximizes the synergistic effect of radiation- and immune-therapy is a fundamental challenge. Mechanism-based mathematical modeling is one promising approach to systematically investigate therapeutic combinations to maximize positive outcomes within a rigorous framework. However, successful clinical translation of model-generated combinations of treatment requires patient-specific data to allow the models to be meaningfully initialized and parameterized. Quantitative imaging techniques have emerged as a promising source of high quality, spatially and temporally resolved data for the development and validation of mathematical models. In this review, we will present approaches to personalize mechanism-based modeling frameworks with patient data, and then discuss how these techniques could be leveraged to improve brain cancer outcomes through patient-specific modeling and optimization of treatment strategies.

Rethinking the immunotherapy numbers game

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.

Data-Driven Simulation of Fisher-Kolmogorov Tumor Growth Models Using Dynamic Mode Decomposition

The computer simulation of organ-scale biomechanistic models of cancer personalized via routinely collected clinical and imaging data enables to obtain patient-specific predictions of tumor growth and treatment response over the anatomy of the patient's affected organ. However, the simulation of the underlying spatiotemporal models can entail a prohibitive computational cost, which constitutes a barrier to the successful development of clinically-actionable computational technologies for personalized tumor forecasting. Here we propose to utilize Dynamic-Mode Decomposition (DMD), an unsupervised machine learning method, to construct a low-dimensional representation of cancer models and accelerate their simulation. We show that DMD may be applied to Fisher-Kolmogorov models, which constitute an established formulation to represent untreated solid tumor growth that can further accommodate other relevant cancer phenomena. Our results show that a DMD implementation of this model over a clinically-relevant parameter space can yield impressive predictions, with short to medium-term errors remaining under 1% and long-term errors remaining under 20%, despite very short training periods. In particular, we have found that, for moderate to high tumor cell diffusivity and low to moderate tumor cell proliferation rate, DMD reconstructions provide accurate, bounded-error reconstructions for all tested training periods. We posit that this data-driven approach has the potential to greatly reduce the computational overhead of personalized simulations of cancer models, thereby facilitating tumor forecasting, parameter identification, uncertainty quantification, and treatment optimization.

Retrospective Clinical Evaluation of a Decision-Support Software for Adaptive Radiotherapy of Head and Neck Cancer Patients

Purpose

This study aimed to evaluate the clinical need for an automated decision-support software platform for adaptive radiation therapy (ART) of head and neck cancer (HNC) patients.

Methods

We tested RTapp (SegAna), a new ART software platform for deciding when a treatment replan is needed, to investigate a set of 27 HNC patients’ data retrospectively. For each fraction, the software estimated key components of ART such as daily dose distribution and cumulative doses received by targets and organs at risk (OARs) from daily 3D imaging in real-time. RTapp also included a prediction algorithm that analyzed dosimetric parameter (DP) trends against user-specified thresholds to proactively trigger adaptive re-planning up to four fractions ahead. The DPs evaluated for ART were based on treatment planning dose constraints. Warning (V₉₅<95%) and adaptation (V₉₅<93%) thresholds were set for PTVs, while OAR adaptation dosimetric endpoints of +10% (DE₁₀) were set for all D_max and D_mean DPs. Any threshold violation at end of treatment (EOT) triggered a review of the DP trends to determine the threshold-crossing fraction Fx when the violations occurred. The prediction model accuracy was determined as the difference between calculated and predicted DP values with 95% confidence intervals (CI₉₅).

Results

RTapp was able to address the needs of treatment adaptation. Specifically, we identified 18/27 studies (67%) for violating PTV coverage or parotid D_mean at EOT. Twelve PTVs had V₉₅<95% (mean coverage decrease of −6.8 ± 2.9%) including six flagged for adaptation at median Fx= 6 (range, 1–16). Seventeen parotids were flagged for exceeding D_mean dose constraints with a median increase of +2.60 Gy (range, 0.99–6.31 Gy) at EOT, including nine with DP>DE₁₀. The differences between predicted and calculated PTV V₉₅ and parotid D_mean was up to 7.6% (mean ± CI₉₅, −2.7 ± 4.1%) and 5 Gy (mean ± CI₉₅, 0.3 ± 1.6 Gy), respectively. The most accurate predictions were obtained closest to the threshold-crossing fraction. For parotids, the results showed that Fx ranged between fractions 1 and 23, with a lack of specific trend demonstrating that the need for treatment adaptation may be verified for every fraction.

Conclusion

Integrated in an ART clinical workflow, RTapp aids in predicting whether specific treatment would require adaptation up to four fractions ahead of time.

Mathematical modeling of radiotherapy and its impact on tumor interactions with the immune system

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.

Integrating mechanism-based modeling with biomedical imaging to build practical digital twins for clinical oncology

Digital twins employ mathematical and computational models to virtually represent a physical object (e.g., planes and human organs), predict the behavior of the object, and enable decision-making to optimize the future behavior of the object. While digital twins have been widely used in engineering for decades, their applications to oncology are only just emerging. Due to advances in experimental techniques quantitatively characterizing cancer, as well as advances in the mathematical and computational sciences, the notion of building and applying digital twins to understand tumor dynamics and personalize the care of cancer patients has been increasingly appreciated. In this review, we present the opportunities and challenges of applying digital twins in clinical oncology, with a particular focus on integrating medical imaging with mechanism-based, tissue-scale mathematical modeling. Specifically, we first introduce the general digital twin framework and then illustrate existing applications of image-guided digital twins in healthcare. Next, we detail both the imaging and modeling techniques that provide practical opportunities to build patient-specific digital twins for oncology. We then describe the current challenges and limitations in developing image-guided, mechanism-based digital twins for oncology along with potential solutions. We conclude by outlining five fundamental questions that can serve as a roadmap when designing and building a practical digital twin for oncology and attempt to provide answers for a specific application to brain cancer. We hope that this contribution provides motivation for the imaging science, oncology, and computational communities to develop practical digital twin technologies to improve the care of patients battling cancer.

From Fitting the Average to Fitting the Individual: A Cautionary Tale for Mathematical Modelers

An outstanding challenge in the clinical care of cancer is moving from a one-size-fits-all approach that relies on population-level statistics towards personalized therapeutic design. Mathematical modeling is a powerful tool in treatment personalization, as it allows for the incorporation of patient-specific data so that treatment can be tailor-designed to the individual. Herein, we work with a mathematical model of murine cancer immunotherapy that has been previously-validated against the average of an experimental dataset. We ask the question: what happens if we try to use this same model to perform personalized fits, and therefore make individualized treatment recommendations? Typically, this would be done by choosing a single fitting methodology, and a single cost function, identifying the individualized best-fit parameters, and extrapolating from there to make personalized treatment recommendations. Our analyses show the potentially problematic nature of this approach, as predicted personalized treatment response proved to be sensitive to the fitting methodology utilized. We also demonstrate how a small amount of the right additional experimental measurements could go a long way to improve consistency in personalized fits. Finally, we show how quantifying the robustness of the average response could also help improve confidence in personalized treatment recommendations.

Tumor Volume Regression during and after Radiochemotherapy: A Macroscopic Description

Tumor volume regression during and after chemo and radio therapy is a useful information for clinical decisions. Indeed, a quantitative, patient oriented, description of the response to treatment can guide towards the modification of the scheduled doses or the evaluation of the best time for surgery. We propose a macroscopic algorithm which permits to follow quantitatively the time evolution of the tumor volume during and after radiochemotherapy. The method, initially validated with different cell-lines implanted in mice, is then successfully applied to the available data for partially responding and complete recovery patients.

Predictive Radiation Oncology - A New NCI-DOE Scientific Space and Community

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.

Dynamics-Adapted Radiotherapy Dose (DARD) for Head and Neck Cancer Radiotherapy Dose Personalization

Standard of care radiotherapy (RT) doses have been developed as a one-size-fits all approach designed to maximize tumor control rates across a population. Although this has led to high control rates for head and neck cancer with 66-70 Gy, this is done without considering patient heterogeneity. We present a framework to estimate a personalized RT dose for individual patients, based on pre- and early on-treatment tumor volume dynamics-a dynamics-adapted radiotherapy dose (D_DARD). We also present the results of an in silico trial of this dose personalization using retrospective data from a combined cohort of n = 39 head and neck cancer patients from the Moffitt and MD Anderson Cancer Centers that received 66-70 Gy RT in 2-2.12 Gy weekday fractions. This trial was repeated constraining D_DARD between (54, 82) Gy to test more moderate dose adjustment. D_DARD was estimated to range from 8 to 186 Gy, and our in silico trial estimated that 77% of patients treated with standard of care were overdosed by an average dose of 39 Gy, and 23% underdosed by an average dose of 32 Gy. The in silico trial with constrained dose adjustment estimated that locoregional control could be improved by >10%. We demonstrated the feasibility of using early treatment tumor volume dynamics to inform dose personalization and stratification for dose escalation and de-escalation. These results demonstrate the potential to both de-escalate most patients, while still improving population-level control rates.

Tumor-immune ecosystem dynamics define an individual Radiation Immune Score to predict pan-cancer radiocurability

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.