Mathematical Modeling to Simulate the Effect of Adding Radiation Therapy to Immunotherapy and Application to Hepatocellular Carcinoma

Mathematical modeling of the synergetic effect between radiotherapy and immunotherapy

The synergy between radiotherapy and immunotherapy plays a pivotal role in enhancing tumor control and treatment outcomes. To explore the underlying mechanisms of synergy, we investigated a novel treatment approach known as personalized ultra-fractionated stereotactic adaptive radiation (PULSAR) therapy, which emphasizes the impact of radiation timing. Unlike conventional daily treatments, PULSAR delivers high-dose radiation in spaced intervals over weeks or months, enabling tumors to adapt and potentially enhancing synergy with immunotherapy. Drawing on insights from small-animal radiation studies, we developed a discrete-time model based on multiple difference equations to elucidate the temporal dynamics of tumor control driven by both radiation and the adaptive immune response. By accounting for the migration and infiltration of T cells within the tumor microenvironment, we established a quantitative link between radiation therapy and immunotherapy. Model parameters were estimated using a simulated annealing algorithm applied to training data, and our model achieved high accuracy for the test data with a root mean square error of 287 mm3. Notably, our framework replicated the PULSAR effect observed in animal studies, revealing that longer intervals between radiation treatments in the context of immunotherapy yielded enhanced tumor control. Specifically, mice receiving immunotherapy alongside radiation pulses delivered at extended intervals, ten days, showed markedly improved tumor responses, whereas those treated with shorter intervals did not achieve comparable benefits. Moreover, our model offers an in-silico tool for designing future personalized ultra-fractionated stereotactic adaptive radiation trials. Overall, these findings underscore the critical importance of treatment timing in harnessing the synergy between radiotherapy and immunotherapy and highlight the potential of our model to optimize and individualize treatment protocols.

Patient-specific modeling of radiation-induced lymphopenia for head and neck cancer

BACKGROUND

Radiation-induced lymphopenia (RIL) is a frequent complication in head and neck cancer (HNC) patients undergoing radiotherapy (RT), and its severity is associated with poorer survival outcomes.

PURPOSE

This work aims to develop a patient-specific modeling method to simulate lymphocyte kinetics during and after RT and evaluate the lymphocyte-sparing effects across different RT treatment regimens.

METHODS

A cohort of 17 HNC patients receiving unilateral irradiation with protons or photons were included in this study. The dose to circulating lymphocytes was calculated using the HEDOS model, considering lymph nodes on the irradiated side, the esophagus, auto-segmented bilateral carotid arteries and jugular veins, skeletal muscle, fat, skin, compact bone, spongy bone, red marrow, and other skeleton. A patient-specific model was developed to simulate lymphocyte kinetics that account for radiation-induced damage to both circulating lymphocytes and lymph nodes. The weekly absolute lymphocyte counts (ALC) before, during and after RT, were assembled to estimate the patient-specific parameters. Four different RT treatment regimens-conventional fractionation, hypofractionation, stereotactic body radiotherapy (SBRT), and FLASH-were evaluated to compare their lymphocyte-sparing effects.

RESULTS

Patients treated with protons had 17.1% less grade 3 and 4 RIL compared to photons. The mean dose to circulating lymphocytes was 1.28 ± 0.37 Gy(RBE) for proton therapy and 3.12 ± 0.75 Gy for photon therapy. The patient-specific model captured three distinct patterns of ALC kinetics: plateau phase, normal recovery, and incomplete recovery, with a mean squared error (MSE) of 0.024 ± 0.025 (mean ± SD) between the simulated and observed ALC values. On average, 42.72% of circulating lymphocytes received more than 0.1 Gy(RBE) in proton FLASH, significantly less than the 81.94% in photon FLASH. Hypofractionated RT, SBRT, and FLASH were 6.5%, 20.2%, and 29.9%, respectively, higher than conventional RT in term of ALC levels 3 months post-RT. At 1 year post-RT, most patients achieved at least 70% recovery of baseline ALC for all treatment regimens.

CONCLUSION

A patient-specific method has been developed for modeling lymphocyte dynamics over the course of RT and the subsequent follow-up period for HNC patients.

Spatial Dose-Response Pattern Associated With Severe Radiation-Induced Lymphopenia in the Liver: A Voxel-Based Analysis

PURPOSE

This study aimed to investigate the dose-response pattern of severe radiation-induced lymphopenia (SRIL) in patients with hepatocellular carcinoma (HCC) undergoing radiation therapy (RT). We focused on identifying specific liver regions associated with SRIL development.

METHODS AND MATERIALS

We analyzed data from 75 patients with HCC treated with RT. Segment-wise and voxel-based analyses (VBAs) were conducted to investigate the spatial relationship between delivered dose and SRIL occurrence (absolute lymphocyte count [ALC] < 500/µL). Logistic regression was performed for segment-wise analysis, whereas generalized linear models and Mann-Whitney U tests were employed for VBAs. The liver was divided into Couinaud segments, and dose distributions were analyzed at both the segment and voxel levels.

RESULTS

Segment-wise logistic regression revealed that pre-RT ALC (odds ratio [OR], 0.006; P = .002), liver segments 1 (OR, 1.228; P = .048), and 7 (OR, 1.314; P = .016) were statistically associated with SRIL occurrence. VBAs demonstrated heterogeneous dose-response patterns across the liver, with segment 1 consistently showing the strongest association with SRIL across different statistical methods. Segment 1 contained the highest proportion of statistically significant voxels (94%) in relation to SRIL occurrence among all liver segments.

CONCLUSIONS

This study revealed an inhomogeneous dose-response pattern regarding SRIL manifestation in the liver. Our results suggest that certain regions within a single organ may require rigorous dosimetric constraints to mitigate SRIL.

Mathematical modeling in radiotherapy for cancer: a comprehensive narrative review

Mathematical modeling has long been a cornerstone of radiotherapy for cancer, guiding treatment prescription, planning, and delivery through versatile applications. As we enter the era of medical big data, where the integration of molecular, imaging, and clinical data at both the tumor and patient levels could promise more precise and personalized cancer treatment, the role of mathematical modeling has become even more critical. This comprehensive narrative review aims to summarize the main applications of mathematical modeling in radiotherapy, bridging the gap between classical models and the latest advancements. The review covers a wide range of applications, including radiobiology, clinical workflows, stereotactic radiosurgery/stereotactic body radiotherapy (SRS/SBRT), spatially fractionated radiotherapy (SFRT), FLASH radiotherapy (FLASH-RT), immune-radiotherapy, and the emerging concept of radiotherapy digital twins. Each of these areas is explored in depth, with a particular focus on how newer trends and innovations are shaping the future of radiation cancer treatment. By examining these diverse applications, this review provides a comprehensive overview of the current state of mathematical modeling in radiotherapy. It also highlights the growing importance of these models in the context of personalized medicine and multi-scale, multi-modal data integration, offering insights into how they can be leveraged to enhance treatment precision and patient outcomes. As radiotherapy continues to evolve, the insights gained from this review will help guide future research and clinical practice, ensuring that mathematical modeling continues to propel innovations in radiation cancer treatment.

Predicting Individual Tumor Response Dynamics in Locally Advanced Non-Small Cell Lung Cancer Radiation Therapy: A Mathematical Modelling Study

PURPOSE

To predict individual tumor responses to radiation therapy (RT) in non-small cell lung cancer.

MATERIALS AND METHODS

The proliferation saturation index (PSI) model, which models tumor dynamics in response to RT as an instantaneous reduction in tumor volume, was fit to n = 162 patients with 4 distinct dose fractionation schedules (30-32 fractions × 2 Gy, 23-24 fractions × 2.75 Gy, 32-42 fractions × 1.8 Gy, and 30 fractions × 1.5 Gy Bidaily, followed by 5-12 fractions × 2 Gy daily). Following initial training, the predictive power of the model was tested using only the first 3 tumor volume measurements as measured on daily imaging. The remainder of tumor volume regression during RT was simulated using the PSI model. Comparisons of the measured to the simulated volumes were made using scatter plots, coefficient of determination (R2), and Pearson correlation coefficient values.

RESULTS

The PSI model predicted tumor volume regression during RT with a high degree of accuracy. Comparison of the measured versus predicted volumes resulted in R2 values of 0.968, 0.954, 0.968, and 0.937, and Pearson correlation coefficient values of 0.984, 0.977, 0.984, and 0.968 in the 2 Gy, 1.8 Gy, 2.75 Gy, and Bidaily groups, respectively.

CONCLUSIONS

The proliferation saturation model can predict, with a high degree of accuracy, non-small cell lung cancer tumor volume regression in response to RT in 4 distinct dose fractionation schedules.

Mechanistic in silico explorations of the immunogenic and synergistic effects of radiotherapy and immunotherapy: a critical review

Immunotherapy is a rapidly evolving field, with many models attempting to describe its impact on the immune system, especially when paired with radiotherapy. Tumor response to this combination involves a complex spatiotemporal dynamic which makes either clinical or pre-clinical in vivo investigation across the resulting extensive solution space extremely difficult. In this review, several in silico models of the interaction between radiotherapy, immunotherapy, and the patient's immune system are examined. The study included only mathematical models published in English that investigated the effects of radiotherapy on the immune system, or the effect of immuno-radiotherapy with immune checkpoint inhibitors. The findings indicate that treatment efficacy was predicted to improve when both radiotherapy and immunotherapy were administered, compared to radiotherapy or immunotherapy alone. However, the models do not agree on the optimal schedule and fractionation of radiotherapy and immunotherapy. This corresponds to relevant clinical trials, which report an improved treatment efficacy with combination therapy, however, the optimal scheduling varies between clinical trials. This discrepancy between the models can be attributed to the variation in model approach and the specific cancer types modeled, making the determination of the optimum general treatment schedule and model challenging. Further research needs to be conducted with similar data sets to evaluate the best model and treatment schedule for a specific cancer type and stage.

Ten challenges and opportunities in computational immuno-oncology

Immuno-oncology has transformed the treatment of cancer, with several immunotherapies becoming the standard treatment across histologies. Despite these advancements, the majority of patients do not experience durable clinical benefits, highlighting the imperative for ongoing advancement in immuno-oncology. Computational immuno-oncology emerges as a forefront discipline that draws on biomedical data science and intersects with oncology, immunology, and clinical research, with the overarching goal to accelerate the development of effective and safe immuno-oncology treatments from the laboratory to the clinic. In this review, we outline 10 critical challenges and opportunities in computational immuno-oncology, emphasizing the importance of robust computational strategies and interdisciplinary collaborations amid the constantly evolving interplay between clinical needs and technological innovation.

Modelling radiobiology

Radiotherapy has played an essential role in cancer treatment for over a century, and remains one of the best-studied methods of cancer treatment. Because of its close links with the physical sciences, it has been the subject of extensive quantitative mathematical modelling, but a complete understanding of the mechanisms of radiotherapy has remained elusive. In part this is because of the complexity and range of scales involved in radiotherapy-from physical radiation interactions occurring over nanometres to evolution of patient responses over months and years. This review presents the current status and ongoing research in modelling radiotherapy responses across these scales, including basic physical mechanisms of DNA damage, the immediate biological responses this triggers, and genetic- and patient-level determinants of response. Finally, some of the major challenges in this field and potential avenues for future improvements are also discussed.

Particle Beam Radiobiology Status and Challenges: A PTCOG Radiobiology Subcommittee Report

Particle therapy (PT) represents a significant advancement in cancer treatment, precisely targeting tumor cells while sparing surrounding healthy tissues thanks to the unique depth-dose profiles of the charged particles. Furthermore, their linear energy transfer and relative biological effectiveness enhance their capability to treat radioresistant tumors, including hypoxic ones. Over the years, extensive research has paved the way for PT's clinical application, and current efforts aim to refine its efficacy and precision, minimizing the toxicities. In this regard, radiobiology research is evolving toward integrating biotechnology to advance drug discovery and radiation therapy optimization. This shift from basic radiobiology to understanding the molecular mechanisms of PT aims to expand the therapeutic window through innovative dose delivery regimens and combined therapy approaches. This review, written by over 30 contributors from various countries, provides a comprehensive look at key research areas and new developments in PT radiobiology, emphasizing the innovations and techniques transforming the field, ranging from the radiobiology of new irradiation modalities to multimodal radiation therapy and modeling efforts. We highlight both advancements and knowledge gaps, with the aim of improving the understanding and application of PT in oncology.

Mathematical modeling and analysis of cancer treatment with radiation and anti-PD-L1

In cancer treatment, radiation therapy (RT) induces direct tumor cell death due to DNA damage, but it also enhances the deaths of radiosensitive immune cells and is followed by local relapse and up-regulation of immune checkpoint ligand PD-L1. Since the binding between PD-1 and PD-L1 curtails anti-tumor immunities, combining RT and PD-L1 inhibitor, anti-PD-L1, is a potential method to improve the treatment efficacy by RT. Some experiments support this hypothesis by showing that the combination of ionizing irradiation (IR) and anti-PD-L1 improves tumor reduction comparing to the monotherapy of IR or anti-PD-L1. In this work, we create a simplified ODE model to study the order of tumor growths under treatments of IR and anti-PD-L1. Our synergy analysis indicates that both IR and anti-PD-L1 improve the tumor reduction of each other, when IR and anti-PD-L1 are given simultaneously. When giving IR and anti-PD-L1 separately, a high dosage of IR should be given first to efficiently reduce tumor load and then followed by anti-PD-L1 with strong efficacy to maintain the tumor reduction and slow down the relapse. Increasing the duration of anti-PD-L1 improves the tumor reduction, but it cannot prolong the duration that tumor relapses to the level of the control case. Under some simplification, we also prove that the model has an unstable tumor free equilibrium and a locally asymptotically stable tumor persistent equilibrium. Our bifurcation diagram reveals a transition from tumor elimination to tumor persistence, as the tumor growth rate increases. In the tumor persistent case, both anti-PD-L1 and IR can reduce tumor amount in the long term.

Normal Tissue Complication Probability Modeling of Severe Radiation-Induced Lymphopenia Using Blood Dose for Patients With Hepatocellular Carcinoma

PURPOSE

This study aimed to develop a normal tissue complication probability (NTCP) model to estimate the risk of severe radiation-induced lymphopenia (SRIL; absolute lymphocyte count [ALC] < 500/μL) by using the blood dose of patients with hepatocellular carcinoma (HCC).

METHODS AND MATERIALS

We retrospectively collected data from 75 patients with HCC who received radiation therapy (RT) between 2015 and 2018. The hematological dose framework calculated blood dose-volume histograms (DVHs) using a predefined blood flow model, organ DVHs, the number of treatment fractions, and beam delivery time. A Lyman-Kutcher-Burman model with a generalized equivalent dose was used to establish the NTCP model, reflecting the whole-blood DVHs. Optimization of the Lyman-Kutcher-Burman parameters was conducted by minimizing a negative log-likelihood function.

RESULTS

There were 6, 4, 18, 33, and 14 patients in the groups with radiation-induced lymphopenia grades 0, 1, 2, 3, and 4, respectively. The median pre- and post-RT ALC values were 1410/μL (range, 520-3710/μL) and 470/μL (range, 60-1760/μL), respectively. There was a correlation between mean blood dose and ALC depletion (Pearson r = -0.664; P < .001). The average mean blood doses in each radiation-induced lymphopenia group were 2.90 Gy (95% CI, 1.96-3.85 Gy) for grade 0 to 1, 5.29 Gy (95% CI, 4.12-6.45 Gy) for grade 2, 8.81 Gy (95% CI, 7.55-10.07 Gy) for grade 3, and 11.69 Gy (95% CI, 9.82-17.57 Gy) for grade 4. When applying the developed NTCP model to predict SRIL, the area under the receiver operating characteristic curve and Brier score values were 0.89 and 0.12, respectively.

CONCLUSIONS

We developed the first NTCP model based on whole-blood DVHs for estimating SRIL after abdominal RT in patients with HCC. Our results showed a strong correlation between blood dose and ALC depletion, suggesting the potential to predict the risk of SRIL occurrence using blood dose.

A Novel Nomogram to Predict Prognosis of Advanced Hepatocellular Carcinoma Treated with Intensity-Modulated Radiotherapy Plus Anti-PD1

Purpose

The combination of radiotherapy and monoclonal antibody against programmed cell death 1 (anti-PD1) showed preliminary efficacy in hepatocellular carcinoma (HCC). This study aimed to identify the prognostic factors and construct a nomogram to predict the overall survival (OS) of patients with advanced HCC after treatment with intensity-modulated radiotherapy (IMRT) plus anti-PD1.

Patients and Methods

The OS and progression-free survival (PFS) of 102 patients with BCLC stage C HCC was analyzed using the Kaplan-Meier method. Potential independent prognostic factors were determined using univariate and multivariate Cox regression analyses. A nomogram was established to predict prognosis whose accuracy and reliability was verified by a calibration curve and area under the receiver operating characteristic curve (AUROC).

Results

The median PFS and OS rates of the 102 patients with advanced HCC were 9.9 months and 14.3 months, respectively. Ninety-three patients were evaluated for efficacy, including five (5.38%) with complete response and 48 (51.61%) with partial response, with an overall response rate of 56.99%. Grade 3 and 4 adverse reactions (AEs) were observed in 32.35% of patients; no grade 5 AEs occurred. Multivariate Cox analysis revealed albumin and alpha-fetoprotein levels, neutrophil counts 3-4 weeks after IMRT initiation, and platelet-to-lymphocyte ratio 3-4 weeks after IMRT initiation to be independent prognostic factors. The nomogram model constructed using these factors had good consistency and accuracy with 1-3 years AUROC of 78.7, 78.6, and 93.5, respectively.

Conclusion

IMRT plus anti-PD1 showed promising efficacy and controllable adverse reactions in treating advanced HCC. The nomogram model demonstrated good reliability and clinical applicability.

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.

A review of mechanistic learning in mathematical oncology

Mechanistic learning refers to the synergistic combination of mechanistic mathematical modeling and data-driven machine or deep learning. This emerging field finds increasing applications in (mathematical) oncology. This review aims to capture the current state of the field and provides a perspective on how mechanistic learning may progress in the oncology domain. We highlight the synergistic potential of mechanistic learning and point out similarities and differences between purely data-driven and mechanistic approaches concerning model complexity, data requirements, outputs generated, and interpretability of the algorithms and their results. Four categories of mechanistic learning (sequential, parallel, extrinsic, intrinsic) of mechanistic learning are presented with specific examples. We discuss a range of techniques including physics-informed neural networks, surrogate model learning, and digital twins. Example applications address complex problems predominantly from the domain of oncology research such as longitudinal tumor response predictions or time-to-event modeling. As the field of mechanistic learning advances, we aim for this review and proposed categorization framework to foster additional collaboration between the data- and knowledge-driven modeling fields. Further collaboration will help address difficult issues in oncology such as limited data availability, requirements of model transparency, and complex input data which are embraced in a mechanistic learning framework.

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.

How Can We Use Mathematical Modeling of Amyloid-β in Alzheimer's Disease Research and Clinical Practices?

The accumulation of amyloid-β (Aβ) plaques in the brain is considered a hallmark of Alzheimer's disease (AD). Mathematical modeling, capable of predicting the motion and accumulation of Aβ, has obtained increasing interest as a potential alternative to aid the diagnosis of AD and predict disease prognosis. These mathematical models have provided insights into the pathogenesis and progression of AD that are difficult to obtain through experimental studies alone. Mathematical modeling can also simulate the effects of therapeutics on brain Aβ levels, thereby holding potential for drug efficacy simulation and the optimization of personalized treatment approaches. In this review, we provide an overview of the mathematical models that have been used to simulate brain levels of Aβ (oligomers, protofibrils, and/or plaques). We classify the models into five categories: the general ordinary differential equation models, the general partial differential equation models, the network models, the linear optimal ordinary differential equation models, and the modified partial differential equation models (i.e., Smoluchowski equation models). The assumptions, advantages and limitations of these models are discussed. Given the popularity of using the Smoluchowski equation models to simulate brain levels of Aβ, our review summarizes the history and major advancements in these models (e.g., their application to predict the onset of AD and their combined use with network models). This review is intended to bring mathematical modeling to the attention of more scientists and clinical researchers working on AD to promote cross-disciplinary research.

Radiation and Immune Checkpoint Inhibitors: Combination Therapy for Treatment of Hepatocellular Carcinoma

The liver tumor immune microenvironment has been thought to possess a critical role in the development and progression of hepatocellular carcinoma (HCC). Despite the approval of immune checkpoint inhibitors (ICIs), such as programmed cell death receptor 1 (PD-1)/programmed cell death ligand 1 (PD-L1) and cytotoxic T lymphocyte associated protein 4 (CTLA-4) inhibitors, for several types of cancers, including HCC, liver metastases have shown evidence of resistance or poor response to immunotherapies. Radiation therapy (RT) has displayed evidence of immunosuppressive effects through the upregulation of immune checkpoint molecules post-treatment. However, it was revealed that the limitations of ICIs can be overcome through the use of RT, as it can reshape the liver immune microenvironment. Moreover, ICIs are able to overcome the RT-induced inhibitory signals, effectively restoring anti-tumor activity. Owing to the synergetic effect believed to arise from the combination of ICIs with RT, several clinical trials are currently ongoing to assess the efficacy and safety of this treatment for patients with HCC.

Combination Therapy of Immune Checkpoint Inhibitors with Locoregional Therapy for Hepatocellular Carcinoma

Hepatocellular carcinoma (HCC) is estimated to be the fourth leading cause of cancer-related deaths globally, and its overall prognosis is dismal because most cases are diagnosed at a late stage and are unamenable to curative treatment. The emergence of immune checkpoint inhibitors (ICIs) has dramatically improved the therapeutic efficacy for advanced hepatocellular carcinoma; however, their response rates remain unsatisfactory, partly because >50% of HCC exhibit an ICI-nonresponsive tumor microenvironment characterized by a paucity of cytotoxic T cells (immune-cold), as well as difficulty in their infiltration into tumor sites (immune excluded). To overcome this limitation, combination therapies with locoregional therapies, including ablation, transarterial embolization, and radiotherapy, which are usually used for early stage HCCs, have been actively explored to enhance ICI efficacy by promoting the release of tumor-associated antigens and cytokines, and eventually accelerating the so-called cancer-immunity cycle. Various combination therapies have been investigated in early- to late-phase clinical trials, and some have shown promising results. This comprehensive article provides an overview of the immune landscape for HCC to understand ICI efficacy and its limitations and, subsequently, reviews the status of combinatorial therapies of ICIs with locoregional therapy for HCC.

Advances in radiotherapy and immunity in hepatocellular carcinoma

Primary liver cancer is one of the most common malignant tumours worldwide; it caused approximately 830,000 deaths in 2020. Hepatocellular carcinoma (HCC) is the most common type of primary liver cancer, accounting for over 80% of all cases. Various methods, including surgery, chemotherapy, radiotherapy, and radiofrequency ablation, have been widely used in the treatment of HCC. With the advancement of technology, radiotherapy has become increasingly important in the comprehensive treatment of HCC. However, due to the insufficient sensitivity of tumour cells to radiation, there are still multiple limitation in clinical application of radiotherapy. In recent years, the role of immunotherapy in cancer has been increasingly revealed, and more researchers have turned their attention to the combined application of immunotherapy and radiotherapy in the hope of achieving better treatment outcomes. This article reviews the progress on radiation therapy in HCC and the current status of its combined application with immunotherapy, and discusses the prospects and value of radioimmunotherapy in HCC.

Mathematical prediction with pretreatment growth rate of metastatic cancer on outcomes: implications for the characterization of oligometastatic disease

Background

Oligometastatic disease (OMD) represents an indolent cancer status characterized by slow tumor growth and limited metastatic potential. The use of local therapy in the management of the condition continues to rise. This study aimed to investigate the advantage of pretreatment tumor growth rate in addition to baseline disease burden in characterizing OMDs, generally defined by the presence of ≤ 5 metastatic lesions.

Methods

The study included patients with metastatic melanoma treated with pembrolizumab. Gross tumor volume of all metastases was contoured on imaging before (TP_-1) and at the initiation of pembrolizumab (TP₀). Pretreatment tumor growth rate was calculated by an exponential ordinary differential equation model using the sum of tumor volumes at TP_-1 and TP₀ and the time interval between TP_-1. and TP₀. Patients were divided into interquartile groups based on pretreatment growth rate. Overall survival, progression-free survival, and subsequent progression-free survival were the study outcomes.

Results

At baseline, median cumulative volume and number of metastases were 28.4 cc (range, 0.4-1194.8 cc) and 7 (range, 1-73), respectively. The median interval between TP_-1 and TP₀ was -90 days and pretreatment tumor growth rate (×10^-2 days^-1) was median 4.71 (range -0.62 to 44.1). The slow-paced group (pretreatment tumor growth rate ≤ 7.6 ×10^-2 days^-1, the upper quartile) had a significantly higher overall survival rate, progression-free survival, and subsequent progression-free survival compared to those of the fast-paced group (pretreatment tumor growth rate > 7.6 ×10^-2 days^-1). Notably, these differences were prominent in the subgroup with >5 metastases.

Conclusion

Pretreatment tumor growth rate is a novel prognostic metric associated with overall survival, progression-free survival, and subsequent progression-free survival among metastatic melanoma patients, especially patients with >5 metastases. Future prospective studies should validate the advantage of disease growth rate plus disease burden in better defining OMDs.

A Mathematical Model for Predicting Patient Responses to Combined Radiotherapy with CTLA-4 Immune Checkpoint Inhibitors

The purpose of this study was to develop a cell-cell interaction model that could predict a tumor's response to radiotherapy (RT) combined with CTLA-4 immune checkpoint inhibition (ICI) in patients with hepatocellular carcinoma (HCC). The previously developed model was extended by adding a new term representing tremelimumab, an inhibitor of CTLA-4. The distribution of the new immune activation term was derived from the results of a clinical trial for tremelimumab monotherapy (NCT01008358). The proposed model successfully reproduced longitudinal tumor diameter changes in HCC patients treated with tremelimumab (complete response = 0%, partial response = 17.6%, stable disease = 58.8%, and progressive disease = 23.6%). For the non-irradiated tumor control group, adding ICI to RT increased the clinical benefit rate from 8% to 32%. The simulation predicts that it is beneficial to start CTLA-4 blockade before RT in terms of treatment sequences. We developed a mathematical model that can predict the response of patients to the combined CTLA-4 blockade with radiation therapy. We anticipate that the developed model will be helpful for designing clinical trials with the ultimate aim of maximizing the efficacy of ICI-RT combination therapy.

Are charged particles a good match for combination with immunotherapy? Current knowledge and perspectives

Charged particle radiotherapy, mainly using protons and carbon ions, provides physical characteristics allowing for a volume conformal irradiation and a reduction of the integral dose to normal tissue. Carbon ion therapy additionally features an increased biological effectiveness resulting in peculiar molecular effects. Immunotherapy, mostly performed with immune checkpoint inhibitors, is nowadays considered a pillar in cancer therapy. Based on the advantageous features of charged particle radiotherapy, we review pre-clinical evidence revealing a strong potential of its combination with immunotherapy. We argue that the combination therapy deserves further investigation with the aim of translation in clinics, where a few studies have been set up already.

Radiation therapy in the era of immune treatment for hepatocellular carcinoma

Immune checkpoint inhibitors (ICIs) have revolutionized cancer treatment in recent years and provide new opportunities to treat hepatocellular carcinoma (HCC). To date, several ICIs have been approved by the FDA for advanced HCC in first-line or second-line therapy. Downstaging conversion therapy for potentially resectable HCC to provide opportunities for surgical intervention is challenging. ICIs have become a hot spot in this field due to their high response rate. However, HCC has various etiologies and can evade the immune system through multiple mechanisms, which limit the efficacy of ICI monotherapy and demand novel combination strategies. Radiation therapy (RT) is also a candidate for conversion therapy in HCC and is currently gaining increasing attention as a good combination partner with ICIs due to its ability to modulate the tumor microenvironment. In this review, we illustrate the current indications for ICIs and RT in HCC, the rationale for their synergistic combination, and the current clinical trials in combination therapy. We also speculate on predictive biomarkers and novel future strategies to further enhance the efficacy of this combination. This review aims to provide references for future research on radiation and immunotherapy to arrive at a promising new era of HCC treatment.

Mathematical modeling of cancer immunotherapy for personalized clinical translation

Encouraging advances are being made in cancer immunotherapy modeling, especially in the key areas of developing personalized treatment strategies based on individual patient parameters, predicting treatment outcomes and optimizing immunotherapy synergy when used in combination with other treatment approaches. Here we present a focused review of the most recent mathematical modeling work on cancer immunotherapy with a focus on clinical translatability. It can be seen that this field is transitioning from pure basic science to applications that can make impactful differences in patients' lives. We discuss how researchers are integrating experimental and clinical data to fully inform models so that they can be applied for clinical predictions, and present the challenges that remain to be overcome if widespread clinical adaptation is to be realized. Lastly, we discuss the most promising future applications and areas that are expected to be the focus of extensive upcoming modeling studies.

New Challenges Facing Systemic Therapies of Advanced HCC in the Era of Different First-Line Immunotherapy-Based Combinations

The standard of care of first-line systemic therapy for advanced hepatocellular carcinoma (HCC) is currently changing with the results of the IMbrave150 trial which are demonstrating superiority of the atezolizumab-bevacizumab combination over sorafenib, modifying this line of treatment for the first time in over 10 years. Recently, other immunotherapy-based combinations (durvalumab-tremelimumab, lenvatinib-pembrolizumab, cabozantinib-atezolizumab, and camrelizumab-rivoceranib) reported results in phase III studies, and might challenge this new standard of care. This revolution will lead to a considerable change in practice, and highlight challenges for future drug development. In this review, we will, firstly, describe results of the different combinations, and discuss the difficulties in selecting the first-line treatment. We will then present the different recommendations about second-line treatment following the first-line immunotherapy-based combination, discussing the rationale for the differences in existing recommendations. We will finally discuss the challenges for future drug development in advanced HCC.

Combining stereotactic body radiotherapy with camrelizumab for unresectable hepatocellular carcinoma: a single-arm trial

PURPOSE

Stereotactic body radiotherapy (SBRT) may have significant immunomodulatory effects that enhance tumor response to immune checkpoint inhibitors. This phase 2 clinical trial was conducted to evaluate the safety and efficacy of combining palliative SBRT with camrelizumab (an anti-PD1 monoclonal antibody) in patients with unresectable hepatocellular carcinoma (uHCC).

METHODS

Patients with uHCC, Child-Pugh A/B liver function, and at least one measurable lesion were enrolled between April 2020 and August 2022. Patients were administered 200 mg camrelizumab intravenously from the first day of palliative SBRT and then every 3 weeks. Palliative SBRT was delivered daily over five fractions per week, with a dose range of 30-50 Gy. The primary endpoints were objective response rate (ORR) and safety. This trial was registered at ClinicalTrials.gov (NCT04193696).

RESULTS

Twenty-one patients were enrolled; the median radiation dose was 40 Gy, and the median number of cycles of camrelizumab was five. The ORR was 52.4%. After a median follow-up of 19.7 months, the median progression-free and overall survival were 5.8 and 14.2 months, respectively. The overall survival probability was 85.7% at 6 months, 76.2% at 9 months, and 59.9% at 12 months. All grade 3 treatment-related adverse events (TRAEs) occurred in five patients (23.8%) and were manageable. No grade 4/5 TRAEs were observed.

CONCLUSION

Palliative SBRT plus camrelizumab showed promising antitumor activity against uHCC. Toxicities were manageable with no unexpected safety issues. This study provides evidence of a new therapeutic method for the treatment of uHCC.

Systematic review of adjuvant external beam radiotherapy for hepatocellular carcinoma following radical hepatectomy

BACKGROUND AND AIM

Recurrence remains the main bottleneck hindering outcomes of hepatectomy for hepatocellular carcinoma (HCC). Owing to technological advances, external beam radiotherapy (EBRT) is being increasingly used in the management of HCC; however, there is no consensus on the role of adjuvant EBRT following hepatectomy.

METHODS

A systematic review was conducted according to the guidelines of the Preferred Reporting Items for Systematic Reviews and Meta-Analysis. PubMed, MedLine, Embase, the Cochrane Library, Web of Knowledge were used to screen eligible studies (published as of May 1st, 2022) that evaluated the clinical safety and efficacy of EBRT for HCC receiving hepatectomy. The endpoints were disease-free survival (DFS), overall survival (OS), and adverse events (AEs).

RESULTS

A total of ten studies were eligible (three randomized controlled trials, one phase II trial, and six retrospective comparative studies). The pooled hazard ratio (HR) for median DFS and OS were both in favor of adjuvant EBRT compared with surgery alone (all P<0.05), and the advantage of adjuvant EBRT was also confirmed in subgroups stratified by different populations (narrow margin, P<0.05; microvascular invasion, P<0.05; portal vein tumor thrombus, P<0.05) and study designs (prospective studies, P<0.05; retrospective studies, P<0.05). Adjuvant EBRT was also found to be superior to adjuvant TACE (P<0.05). Pooled rates of overall AEs and severe AEs were 65.3% and 12.2%, but no fatal AEs were reported.

CONCLUSION

Adjuvant EBRT can be considered for HCC patients, especially those with a high risk of recurrence. Further studies are required for validation of these findings.

Modeling of radiation effects to immune system: a review

Cancer metastasis is the major cause of cancer mortality and accounts for about 90% of cancer death. Although radiation therapy has been considered to reduce the localized cancer burden, emerging evidence that radiation can potentially turn tumors into an in situ vaccine has raised significant interest in combining radiation with immunotherapy. However, the combination approach might be limited by the radiation-induced immunosuppression. Assessment of radiation effects on the immune system at the patient level is critical to maximize the systemic antitumor response of radiation. In this review, we summarize the developed solutions in three different categories for systemic radiation therapy: blood dose, radiation-induced lymphopenia, and tumor control. Furthermore, we address how they could be combined to optimize radiotherapy regimens and maximize their synergy with immunotherapy.