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

Histopathologic Changes after Yttrium-90 Radioembolization of Colorectal Liver Metastases: A Pilot Feasibility Study

PURPOSE

To evaluate the histopathologic changes and potential correlations of tumor absorbed dose (TAD) after yttrium-90 transarterial radioembolization (TARE) for colorectal liver metastases (CLMs).

MATERIALS AND METHODS

This prospective pilot study assessed 12 patients with 13 CLMs through positron emission tomography (PET)/computed tomography (CT)-guided biopsies before, immediately after TARE (T0), and 3 weeks after TARE (T3). Subsequent sampling from the same location was enabled by fiducial placement. Biopsy samples were evaluated with hematoxylin and eosin, TUNEL, Ki67, OxPhos, caspase-3 (CC3), and pH2AX antibodies. Proliferation changes (Ki67) and double-strand DNA breaks (DSBs) were evaluated quantitatively. TAD was calculated on post-TARE PET/CT scan of the biopsy needle location at T0 and T3.

RESULTS

Median TAD at 3 weeks after TARE was 162 Gy (interquartile range (IQR), 92-211 Gy). DSBs decreased significantly from T0 (median, 77%; IQR, 75%-100%) to T3 (median, 14%; IQR, 0%-54%; P = .028). A decrease in Ki67 was also documented (median, 73%; IQR, 70%-80% at T0 vs median, 41%; IQR, 0%-66% at T3; P = .046). There was a strong positive correlation between TAD and DSBs at T0 (r[9] = 0.68) and a strong negative correlation at T3 (r[10] = -0.855; P = .042 and P = .002, respectively). There was a strong negative correlation between TAD and Ki67 at both T0 (r[9] = -0.733; P = .025) and T3 (r[10] = -0.681; P = .030). Tumors that exhibited caspase-3 activation (8/13, 62%) at either T0 or T3 time point were more likely to develop progression (7/8 [88%] vs 1/5 [20%]; P = .015).

CONCLUSIONS

Post-TARE biopsy can be used to assess TAD and histopathologic changes. Significant decreases in DSBs and proliferation index were noted after TARE. Post-TARE CC3 activation deserves further exploration.

Theranostic digital twins: Concept, framework and roadmap towards personalized radiopharmaceutical therapies

Radiopharmaceutical therapy (RPT) is a rapidly developing field of nuclear medicine, with several RPTs already well established in the treatment of several different types of cancers. However, the current approaches to RPTs often follow a somewhat inflexible "one size fits all" paradigm, where patients are administered the same amount of radioactivity per cycle regardless of their individual characteristics and features. This approach fails to consider inter-patient variations in radiopharmacokinetics, radiation biology, and immunological factors, which can significantly impact treatment outcomes. To address this limitation, we propose the development of theranostic digital twins (TDTs) to personalize RPTs based on actual patient data. Our proposed roadmap outlines the steps needed to create and refine TDTs that can optimize radiation dose to tumors while minimizing toxicity to organs at risk. The TDT models incorporate physiologically-based radiopharmacokinetic (PBRPK) models, which are additionally linked to a radiobiological optimizer and an immunological modulator, taking into account factors that influence RPT response. By using TDT models, we envisage the ability to perform virtual clinical trials, selecting therapies towards improved treatment outcomes while minimizing risks associated with secondary effects. This framework could empower practitioners to ultimately develop tailored RPT solutions for subgroups and individual patients, thus improving the precision, accuracy, and efficacy of treatments while minimizing risks to patients. By incorporating TDT models into RPTs, we can pave the way for a new era of precision medicine in cancer treatment.

Mathematical modeling of the synergistic interplay of radiotherapy and immunotherapy in anti-cancer treatments

Introduction

While radiotherapy has long been recognized for its ability to directly ablate cancer cells through necrosis or apoptosis, radiotherapy-induced abscopal effect suggests that its impact extends beyond local tumor destruction thanks to immune response. Cellular proliferation and necrosis have been extensively studied using mathematical models that simulate tumor growth, such as Gompertz law, and the radiation effects, such as the linear-quadratic model. However, the effectiveness of radiotherapy-induced immune responses may vary among patients due to individual differences in radiation sensitivity and other factors.

Methods

We present a novel macroscopic approach designed to quantitatively analyze the intricate dynamics governing the interactions among the immune system, radiotherapy, and tumor progression. Building upon previous research demonstrating the synergistic effects of radiotherapy and immunotherapy in cancer treatment, we provide a comprehensive mathematical framework for understanding the underlying mechanisms driving these interactions.

Results

Our method leverages macroscopic observations and mathematical modeling to capture the overarching dynamics of this interplay, offering valuable insights for optimizing cancer treatment strategies. One shows that Gompertz law can describe therapy effects with two effective parameters. This result permits quantitative data analyses, which give useful indications for the disease progression and clinical decisions.

Discussion

Through validation against diverse data sets from the literature, we demonstrate the reliability and versatility of our approach in predicting the time evolution of the disease and assessing the potential efficacy of radiotherapy-immunotherapy combinations. This further supports the promising potential of the abscopal effect, suggesting that in select cases, depending on tumor size, it may confer full efficacy to radiotherapy.

Designing combination therapies for cancer treatment: application of a mathematical framework combining CAR T-cell immunotherapy and targeted radionuclide therapy

Introduction

Cancer combination treatments involving immunotherapies with targeted radiation therapy are at the forefront of treating cancers. However, dosing and scheduling of these therapies pose a challenge. Mathematical models provide a unique way of optimizing these therapies.

Methods

Using a preclinical model of multiple myeloma as an example, we demonstrate the capability of a mathematical model to combine these therapies to achieve maximum response, defined as delay in tumor growth. Data from mice studies with targeted radionuclide therapy (TRT) and chimeric antigen receptor (CAR)-T cell monotherapies and combinations with different intervals between them was used to calibrate mathematical model parameters. The dependence of progression-free survival (PFS), overall survival (OS), and the time to minimum tumor burden on dosing and scheduling was evaluated. Different dosing and scheduling schemes were evaluated to maximize the PFS and optimize timings of TRT and CAR-T cell therapies.

Results

Therapy intervals that were too close or too far apart are shown to be detrimental to the therapeutic efficacy, as TRT too close to CAR-T cell therapy results in radiation related CAR-T cell killing while the therapies being too far apart result in tumor regrowth, negatively impacting tumor control and survival. We show that splitting a dose of TRT or CAR-T cells when administered in combination is advantageous only if the first therapy delivered can produce a significant benefit as a monotherapy.

Discussion

Mathematical models are crucial tools for optimizing the delivery of cancer combination therapy regimens with application along the lines of achieving cure, maximizing survival or minimizing toxicity.

An AI-based approach for modeling the synergy between radiotherapy and immunotherapy

Personalized, ultra-fractionated stereotactic adaptive radiotherapy (PULSAR) is designed to administer tumoricidal doses in a pulsed mode with extended intervals, spanning weeks or months. This approach leverages longer intervals to adapt the treatment plan based on tumor changes and enhance immune-modulated effects. In this investigation, we seek to elucidate the potential synergy between combined PULSAR and PD-L1 blockade immunotherapy using experimental data from a Lewis Lung Carcinoma (LLC) syngeneic murine cancer model. Employing a long short-term memory (LSTM) recurrent neural network (RNN) model, we simulated the treatment response by treating irradiation and anti-PD-L1 as external stimuli occurring in a temporal sequence. Our findings demonstrate that: (1) The model can simulate tumor growth by integrating various parameters such as timing and dose, and (2) The model provides mechanistic interpretations of a "causal relationship" in combined treatment, offering a completely novel perspective. The model can be utilized for in-silico modeling, facilitating exploration of innovative treatment combinations to optimize therapeutic outcomes. Advanced modeling techniques, coupled with additional efforts in biomarker identification, may deepen our understanding of the biological mechanisms underlying the combined treatment.

The Next Chapter in Immunotherapy and Radiation Combination Therapy: Cancer-Specific Perspectives

Immunotherapeutic agents have revolutionized cancer treatment over the past decade. However, most patients fail to respond to immunotherapy alone. A growing body of preclinical studies highlights the potential for synergy between radiation therapy and immunotherapy, but the outcomes of clinical studies have been mixed. This review summarizes the current state of immunotherapy and radiation combination therapy across cancers, highlighting existing challenges and promising areas for future investigation.

Modeling the Synergistic Impact of Yttrium 90 Radioembolization and Immune Checkpoint Inhibitors on Hepatocellular Carcinoma

The impact of yttrium 90 radioembolization (Y90-RE) in combination with immune checkpoint inhibitors (ICIs) has recently gained attention. However, it is unclear how sequencing and dosage affect therapeutic efficacy. The purpose of this study was to develop a mathematical model to simulate the synergistic effects of Y90-RE and ICI combination therapy and find the optimal treatment sequences and dosages. We generated a hypothetical patient cohort and conducted simulations to apply different treatments to the same patient. The compartment of models is described with ordinary differential equations (ODEs), which represent targeted tumors, non-targeted tumors, and lymphocytes. We considered Y90-RE as a local treatment and ICIs as a systemic treatment. The model simulations show that Y90-RE and ICIs administered simultaneously yield greater benefits than subsequent sequential therapy. In addition, applying Y90-RE before ICIs has more benefits than applying ICIs before Y90-RE. Moreover, we also observed that the median PFS increased up to 31~36 months, and the DM rates at 3 years decreased up to 36~48% as the dosage of the two drugs increased (p < 0.05). The proposed model predicts a significant benefit of Y90-RE with ICIs from the results of the reduced irradiated tumor burden and the associated immune activation and suppression. Our model is expected to help optimize complex strategies and predict the efficacy of clinical trials for HCC patients.

Mathematical model predicts tumor control patterns induced by fast and slow cytotoxic T lymphocyte killing mechanisms

Immunotherapy has dramatically transformed the cancer treatment landscape largely due to the efficacy of immune checkpoint inhibitors (ICIs). Although ICIs have shown promising results for many patients, the low response rates in many cancers highlight the ongoing challenges in cancer treatment. Cytotoxic T lymphocytes (CTLs) execute their cell-killing function via two distinct mechanisms: a fast-acting, perforin-mediated process and a slower, Fas ligand (FasL)-driven pathway. Evidence also suggests that the preferred killing mechanism of CTLs depends on the antigenicity of tumor cells. To determine the critical factors affecting responses to ICIs, we construct an ordinary differential equation model describing in vivo tumor-immune dynamics in the presence of active or blocked PD-1/PD-L1 immune checkpoint. Specifically, we identify important aspects of the tumor-immune landscape that affect tumor size and composition in the short and long term. We also generate a virtual cohort of mice with diverse tumor and immune attributes to simulate the outcomes of immune checkpoint blockade in a heterogeneous population. By identifying key tumor and immune characteristics associated with tumor elimination, dormancy, and escape, we predict which fraction of a population potentially responds well to ICIs and ways to enhance therapeutic outcomes with combination therapy.

Mathematical Modeling Support for Lung Cancer Therapy-A Short Review

The paper presents a review of models that can be used to describe dynamics of lung cancer growth and its response to treatment at both cell population and intracellular processes levels. To address the latter, models of signaling pathways associated with cellular responses to treatment are overviewed. First, treatment options for lung cancer are discussed, and main signaling pathways and regulatory networks are briefly reviewed. Then, approaches used to model specific therapies are discussed. Following that, models of intracellular processes that are crucial in responses to therapies are presented. The paper is concluded with a discussion of the applicability of the presented approaches in the context of lung cancer.

Generating missing patient anatomy from partially acquired cone-beam computed tomography images using deep learning: a proof of concept

The patient setup technique currently in practice in most radiotherapy departments utilises on-couch cone-beam computed tomography (CBCT) imaging. Patients are positioned on the treatment couch using visual markers, followed by fine adjustments to the treatment couch position depending on the shift observed between the computed tomography (CT) image acquired for treatment planning and the CBCT image acquired immediately before commencing treatment. The field of view of CBCT images is limited to the size of the kV imager which leads to the acquisition of partial CBCT scans for lateralised tumors. The cone-beam geometry results in high amounts of streaking artifacts and in conjunction with limited anatomical information reduces the registration accuracy between planning CT and the CBCT image. This study proposes a methodology that can improve radiotherapy patient setup CBCT images by removing streaking artifacts and generating the missing patient anatomy with patient-specific precision. This research was split into two separate studies. In Study A, synthetic CBCT (sCBCT) data was created and used to train two machine learning models, one for removing streaking artifacts and the other for generating the missing patient anatomy. In Study B, planning CT and on-couch CBCT data from several patients was used to train a base model, from which a transfer of learning was performed using imagery from a single patient, producing a patient-specific model. The models developed for Study A performed well at removing streaking artifacts and generating the missing anatomy. The outputs yielded in Study B show that the model understands the individual patient and can generate the missing anatomy from partial CBCT datasets. The outputs generated demonstrate that there is utility in the proposed methodology which could improve the patient setup and ultimately lead to improving overall treatment quality.

Radio-immune response modelling for spatially fractionated radiotherapy

Objective.Radiation-induced cell death is a complex process influenced by physical, chemical and biological phenomena. Although consensus on the nature and the mechanism of the bystander effect were not yet made, the immune process presumably plays an important role in many aspects of the radiotherapy including the bystander effect. A mathematical model of immune response during and after radiation therapy is presented.Approach.Immune response of host body and immune suppression of tumor cells are modelled with four compartments in this study; viable tumor cells, T cell lymphocytes, immune triggering cells, and doomed cells. The growth of tumor was analyzed in two distinctive modes of tumor status (immune limited and immune escape) and its bifurcation condition.Main results.Tumors in the immune limited mode can grow only up to a finite size, named as terminal tumor volume analytically calculated from the model. The dynamics of the tumor growth in the immune escape mode is much more complex than the tumors in the immune limited mode especially when the status of tumor is close to the bifurcation condition. Radiation can kill tumor cells not only by radiation damage but also by boosting immune reaction.Significance.The model demonstrated that the highly heterogeneous dose distribution in spatially fractionated radiotherapy (SFRT) can make a drastic difference in tumor cell killing compared to the homogeneous dose distribution. SFRT cannot only enhance but also moderate the cell killing depending on the immune response triggered by many factors such as dose prescription parameters, tumor volume at the time of treatment and tumor characteristics. The model was applied to the lifted data of 67NR tumors on mice and a sarcoma patient treated multiple times over 1200 days for the treatment of tumor recurrence as a demonstration.

Predicting regrowth of low-grade gliomas after radiotherapy

Diffuse low grade gliomas are invasive and incurable brain tumors that inevitably transform into higher grade ones. A classical treatment to delay this transition is radiotherapy (RT). Following RT, the tumor gradually shrinks during a period of typically 6 months to 4 years before regrowing. To improve the patient’s health-related quality of life and help clinicians build personalized follow-ups, one would benefit from predictions of the time during which the tumor is expected to decrease. The challenge is to provide a reliable estimate of this regrowth time shortly after RT (i.e. with few data), although patients react differently to the treatment. To this end, we analyze the tumor size dynamics from a batch of 20 high-quality longitudinal data, and propose a simple and robust analytical model, with just 4 parameters. From the study of their correlations, we build a statistical constraint that helps determine the regrowth time even for patients for which we have only a few measurements of the tumor size. We validate the procedure on the data and predict the regrowth time at the moment of the first MRI after RT, with precision of, typically, 6 months. Using virtual patients, we study whether some forecast is still possible just three months after RT. We obtain some reliable estimates of the regrowth time in 75% of the cases, in particular for all “fast-responders”. The remaining 25% represent cases where the actual regrowth time is large and can be safely estimated with another measurement a year later. These results show the feasibility of making personalized predictions of the tumor regrowth time shortly after RT.

Mathematical Model for Evaluation of Tumor Response in Targeted Radionuclide Therapy with 211At Using Implanted Mouse Tumor

Recent introduction of alpha-emitting radionuclides in targeted radionuclide therapy has stimulated the development of new radiopharmaceuticals. Preclinical evaluation using an animal experiment with an implanted tumor model is frequently used to examine the efficiency of the treatment method and to predict the treatment response before clinical trials. Here, we propose a mathematical model for evaluation of the tumor response in an implanted tumor model and apply it to the data obtained from the previous experiment of ²¹¹At treatment in a thyroid cancer mouse model. The proposed model is based on the set of differential equations, describing the kinetics of radiopharmaceuticals, the tumor growth, and the treatment response. First, the tumor growth rate was estimated from the control data without injection of ²¹¹At. The kinetic behavior of the injected radionuclide was used to estimate the radiation dose profile to the target tumor, which can suppress the tumor growth in a dose-dependent manner. An additional two factors, including the time delay for the reduction of tumor volume and the impaired recovery of tumor regrowth after the treatment, were needed to simulate the temporal changes of tumor size after treatment. Finally, the parameters obtained from the simulated tumor growth curve were able to predict the tumor response in other experimental settings. The model can provide valuable information for planning the administration dose of radiopharmaceuticals in clinical trials, especially to determine the starting dose at which efficacy can be expected with a sufficient safety margin.

Toward Precision Radiotherapy: A Nonlinear Optimization Framework and an Accelerated Machine Learning Algorithm for the Deconvolution of Tumor-Infiltrating Immune Cells

Tumor-infiltrating immune cells (TIICs) form a critical part of the ecosystem surrounding a cancerous tumor. Recent advances in radiobiology have shown that, in addition to damaging cancerous cells, radiotherapy drives the upregulation of immunosuppressive and immunostimulatory TIICs, which in turn impacts treatment response. Quantifying TIICs in tumor samples could form an important predictive biomarker guiding patient stratification and the design of radiotherapy regimens and combined immune-radiation treatments. As a result of several limitations associated with experimental methods for quantifying TIICs and the availability of extensive gene sequencing data, deconvolution-based computational methods have appeared as a suitable alternative for quantifying TIICs. Accordingly, we introduce and discuss a nonlinear regression approach (remarkably different from the traditional linear modeling approach of current deconvolution-based methods) and a machine learning algorithm for approximating the solution of the resulting constrained optimization problem. This way, the deconvolution problem is treated naturally, given that the gene expression levels of pure and heterogenous samples do not have a strictly linear relationship. When applied across transcriptomics datasets, our approach, which also allows the coupling of different loss functions, yields results that closely match ground-truth values from experimental methods and exhibits superior performance over popular deconvolution-based methods.