Combining radiation with hyperthermia: a multiscale model informed by in vitro experiments

Spatio-temporal modelling of phenotypic heterogeneity in tumour tissues and its impact on radiotherapy treatment

We present a mathematical model that describes how tumour heterogeneity evolves in a tissue slice that is oxygenated by a single blood vessel. Phenotype is identified with the stemness level of a cell and determines its proliferative capacity, apoptosis propensity and response to treatment. Our study is based on numerical bifurcation analysis and dynamical simulations of a system of coupled, non-local (in phenotypic "space") partial differential equations that link the phenotypic evolution of the tumour cells to local tissue oxygen levels. In our formulation, we consider a 1D geometry where oxygen is supplied by a blood vessel located on the domain boundary and consumed by the tumour cells as it diffuses through the tissue. For biologically relevant parameter values, the system exhibits multiple steady states; in particular, depending on the initial conditions, the tumour is either eliminated ("tumour-extinction") or it persists ("tumour-invasion"). We conclude by using the model to investigate tumour responses to radiotherapy, and focus on identifying radiotherapy strategies which can eliminate the tumour. Numerical simulations reveal how phenotypic heterogeneity evolves during treatment and highlight the critical role of tissue oxygen levels on the efficacy of radiation protocols that are commonly used in the clinic.

Biological modeling in thermoradiotherapy: present status and ongoing developments toward routine clinical use

Biological modeling for anti-cancer treatments using mathematical models can be very supportive in gaining more insight into dynamic processes responsible for cellular response to treatment, and predicting, evaluating and optimizing therapeutic effects of treatment. This review presents an overview of the current status of biological modeling for hyperthermia in combination with radiotherapy (thermoradiotherapy). Various distinct models have been proposed in the literature, with varying complexity; initially aiming to model the effect of hyperthermia alone, and later on to predict the effect of the combined thermoradiotherapy treatment. Most commonly used models are based on an extension of the linear-quadratic (LQ)-model enabling an easy translation to radiotherapy where the LQ model is widely used. Basic predictions of cell survival have further progressed toward 3 D equivalent dose predictions, i.e., the radiation dose that would be needed without hyperthermia to achieve the same biological effect as the combined thermoradiotherapy treatment. This approach, with the use of temperature-dependent model parameters, allows theoretical evaluation of the effectiveness of different treatment strategies in individual patients, as well as in patient cohorts. This review discusses the significant progress that has been made in biological modeling for hyperthermia combined with radiotherapy. In the future, when adequate temperature-dependent LQ-parameters will be available for a large number of tumor sites and normal tissues, biological modeling can be expected to be of great clinical importance to further optimize combined treatments, optimize clinical protocols and guide further clinical studies.

Temperature processing and distribution in larynx thermal inhalation injury with analogy to human airway cells: a mechanism of protection

OBJECTIVE

Inhalation injuries, especially laryngeal injuries, threaten the lives of burn patients. Unlike studies on temperature distribution in the upper airway, studies on temperature development in different laryngeal layers, including the mucosa, lamina propria, cartilage, muscle, and subcutaneous layer, are lacking.

METHOD

For the in-vivo study, 16 healthy adult male beagles were divided into four groups: control, low-, medium-, and high-heat groups, inhaling dry air at 26, 80, 160, and 320°C for 20 min, with temperature probes punctured through skin into layers as mentioned, and heat energy was calculated. For the in-vitro study, we heated human lung fibroblasts and bronchial epithelial cells using a similar heating profile with heat energy of 15-90 J/g to investigate cell survival and viability for clinical comparison.

RESULTS

No statistical difference emerged between the temperatures of different laryngeal layers at each timepoint. The temperatures decreased significantly and shortly before increasing unevenly in the low- and medium-heat groups. The survival rates and viability of the two cell lines correlated negatively with heat energy. The heat energy absorbed in the low-, medium-, and high-heat groups of beagles were 12, 29, and 44 J/g, with calculated in-vitro human cell survival rates of 114%, 90%, and 69%, respectively, for the corresponding energy levels.

CONCLUSIONS

The abnormal temperature processing and lack of a difference between layers indicate an effective self-protective mechanism of heat conduction in larynx. The in-vitro results demonstrate a high survival rate of lung cells at comparable heat energy levels to those measured in the larynx.

A Multi-Compartment Model of Glioma Response to Fractionated Radiation Therapy Parameterized via Time-Resolved Microscopy Data

Purpose

Conventional radiobiology models, including the linear-quadratic model, do not explicitly account for the temporal effects of radiation, thereby making it difficult to make time-resolved predictions of tumor response to fractionated radiation. To overcome this limitation, we propose and validate an experimental-computational approach that predicts the changes in cell number over time in response to fractionated radiation.

Methods

We irradiated 9L and C6 glioma cells with six different fractionation schemes yielding a total dose of either 16 Gy or 20 Gy, and then observed their response via time-resolved microscopy. Phase-contrast images and Cytotox Red images (to label dead cells) were collected every 4 to 6 hours up to 330 hours post-radiation. Using 75% of the total data (i.e., 262 9L curves and 211 C6 curves), we calibrated a two-species model describing proliferative and senescent cells. We then applied the calibrated parameters to a validation dataset (the remaining 25% of the data, i.e., 91 9L curves and 74 C6 curves) to predict radiation response. Model predictions were compared to the microscopy measurements using the Pearson correlation coefficient (PCC) and the concordance correlation coefficient (CCC).

Results

For the 9L cells, we observed PCCs and CCCs between the model predictions and validation data of (mean ± standard error) 0.96 ± 0.007 and 0.88 ± 0.013, respectively, across all fractionation schemes. For the C6 cells, we observed PCCs and CCCs between model predictions and the validation data were 0.89 ± 0.008 and 0.75 ± 0.017, respectively, across all fractionation schemes.

Conclusion

By proposing a time-resolved mathematical model of fractionated radiation response that can be experimentally verified in vitro, this study is the first to establish a framework for quantitative characterization and prediction of the dynamic radiobiological response of 9L and C6 gliomas to fractionated radiotherapy.

Targeting Cellular DNA Damage Responses in Cancer: An In Vitro-Calibrated Agent-Based Model Simulating Monolayer and Spheroid Treatment Responses to ATR-Inhibiting Drugs

We combine a systems pharmacology approach with an agent-based modelling approach to simulate LoVo cells subjected to AZD6738, an ATR (ataxia–telangiectasia-mutated and rad3-related kinase) inhibiting anti-cancer drug that can hinder tumour proliferation by targeting cellular DNA damage responses. The agent-based model used in this study is governed by a set of empirically observable rules. By adjusting only the rules when moving between monolayer and multi-cellular tumour spheroid simulations, whilst keeping the fundamental mathematical model and parameters intact, the agent-based model is first parameterised by monolayer in vitro data and is thereafter used to simulate treatment responses in in vitro tumour spheroids subjected to dynamic drug delivery. Spheroid simulations are subsequently compared to in vivo data from xenografts in mice. The spheroid simulations are able to capture the dynamics of in vivo tumour growth and regression for approximately 8 days post-tumour injection. Translating quantitative information between in vitro and in vivo research remains a scientifically and financially challenging step in preclinical drug development processes. However, well-developed in silico tools can be used to facilitate this in vitro to in vivo translation, and in this article, we exemplify how data-driven, agent-based models can be used to bridge the gap between in vitro and in vivo research. We further highlight how agent-based models, that are currently underutilised in pharmaceutical contexts, can be used in preclinical drug development.

Towards an Image-Informed Mathematical Model of In Vivo Response to Fractionated Radiation Therapy

Simple Summary

Using medical imaging data and computational models, we develop a modeling framework to provide personalized treatment response forecasts to fractionated radiation therapy for individual tumors. We evaluate this approach in an animal model of brain cancer and forecast changes in tumor cellularity and vasculature.

Abstract

Fractionated radiation therapy is central to the treatment of numerous malignancies, including high-grade gliomas where complete surgical resection is often impractical due to its highly invasive nature. Development of approaches to forecast response to fractionated radiation therapy may provide the ability to optimize or adapt treatment plans for radiotherapy. Towards this end, we have developed a family of 18 biologically-based mathematical models describing the response of both tumor and vasculature to fractionated radiation therapy. Importantly, these models can be personalized for individual tumors via quantitative imaging measurements. To evaluate this family of models, rats (n = 7) with U-87 glioblastomas were imaged with magnetic resonance imaging (MRI) before, during, and after treatment with fractionated radiotherapy (with doses of either 2 Gy/day or 4 Gy/day for up to 10 days). Estimates of tumor and blood volume fractions, provided by diffusion-weighted MRI and dynamic contrast-enhanced MRI, respectively, were used to calibrate tumor-specific model parameters. The Akaike Information Criterion was employed to select the most parsimonious model and determine an ensemble averaged model, and the resulting forecasts were evaluated at the global and local level. At the global level, the selected model’s forecast resulted in less than 16.2% error in tumor volume estimates. At the local (voxel) level, the median Pearson correlation coefficient across all prediction time points ranged from 0.57 to 0.87 for all animals. While the ensemble average forecast resulted in increased error (ranging from 4.0% to 1063%) in tumor volume predictions over the selected model, it increased the voxel wise correlation (by greater than 12.3%) for three of the animals. This study demonstrates the feasibility of calibrating a model of response by serial quantitative MRI data collected during fractionated radiotherapy to predict response at the conclusion of treatment.

Mathematical model for the thermal enhancement of radiation response: thermodynamic approach

Radiotherapy can effectively kill malignant cells, but the doses required to cure cancer patients may inflict severe collateral damage to adjacent healthy tissues. Recent technological advances in the clinical application has revitalized hyperthermia treatment (HT) as an option to improve radiotherapy (RT) outcomes. Understanding the synergistic effect of simultaneous thermoradiotherapy via mathematical modelling is essential for treatment planning. We here propose a theoretical model in which the thermal enhancement ratio (TER) relates to the cell fraction being radiosensitised by the infliction of sublethal damage through HT. Further damage finally kills the cell or abrogates its proliferative capacity in a non-reversible process. We suggest the TER to be proportional to the energy invested in the sensitisation, which is modelled as a simple rate process. Assuming protein denaturation as the main driver of HT-induced sublethal damage and considering the temperature dependence of the heat capacity of cellular proteins, the sensitisation rates were found to depend exponentially on temperature; in agreement with previous empirical observations. Our findings point towards an improved definition of thermal dose in concordance with the thermodynamics of protein denaturation. Our predictions well reproduce experimental in vitro and in vivo data, explaining the thermal modulation of cellular radioresponse for simultaneous thermoradiotherapy.

The interplay of blood flow and temperature in regional hyperthermia: a mathematical approach

In recent decades, hyperthermia has been used to raise oxygenation levels in tumours undergoing other therapeutic modalities, of which radiotherapy is the most prominent one. It has been hypothesized that oxygenation increases would come from improved blood flow associated with vasodilation. However, no test has determined whether this is a relevant assumption or other mechanisms might be acting. Additionally, since hyperthermia and radiotherapy are not usually co-administered, the crucial question arises as to how temperature and perfusion in tumours will change during and after hyperthermia. Overall, it would seem necessary to find a research framework that clarifies the current knowledge, delimits the scope of the different effects and guides future research. Here, we propose a simple mathematical model to account for temperature and perfusion dynamics in brain tumours subjected to regional hyperthermia. Our results indicate that tumours in well-perfused organs like the brain might only reach therapeutic temperatures if their vasculature is highly disrupted. Furthermore, the characteristic times of return to normal temperature levels are markedly shorter than those required to deliver adjuvant radiotherapy. According to this, a mechanistic coupling of perfusion and temperature would not explain any major oxygenation boost in brain tumours immediately after hyperthermia.

Mathematical modelling reveals cellular dynamics within tumour spheroids

Tumour spheroids are widely used as an in vitro assay for characterising the dynamics and response to treatment of different cancer cell lines. Their popularity is largely due to the reproducible manner in which spheroids grow: the diffusion of nutrients and oxygen from the surrounding culture medium, and their consumption by tumour cells, causes proliferation to be localised at the spheroid boundary. As the spheroid grows, cells at the spheroid centre may become hypoxic and die, forming a necrotic core. The pressure created by the localisation of tumour cell proliferation and death generates an cellular flow of tumour cells from the spheroid rim towards its core. Experiments by Dorie et al. showed that this flow causes inert microspheres to infiltrate into tumour spheroids via advection from the spheroid surface, by adding microbeads to the surface of tumour spheroids and observing the distribution over time. We use an off-lattice hybrid agent-based model to re-assess these experiments and establish the extent to which the spatio-temporal data generated by microspheres can be used to infer kinetic parameters associated with the tumour spheroids that they infiltrate. Variation in these parameters, such as the rate of tumour cell proliferation or sensitivity to hypoxia, can produce spheroids with similar bulk growth dynamics but differing internal compositions (the proportion of the tumour which is proliferating, hypoxic/quiescent and necrotic/nutrient-deficient). We use this model to show that the types of experiment conducted by Dorie et al. could be used to infer spheroid composition and parameters associated with tumour cell lines such as their sensitivity to hypoxia or average rate of proliferation, and note that these observations cannot be conducted within previous continuum models of microbead infiltration into tumour spheroids as they rely on resolving the trajectories of individual microbeads.

Tumour spheroids are an experimental assay used to characterise the dynamics and response to treatment of different cancer cell lines. Previous experiments have demonstrated that the localisation of tumour cell proliferation to the spheroid edge (due to the gradient formed by nutrient diffusing from the surrounding medium) causes cells to be pushed from the proliferative rim towards the nutrient-deficient necrotic core. This movement allows inert particles to infiltrate tumour spheroids. We use a hybrid agent-based model to reproduce this data. We show further how data from individual microbead trajectories can be used to infer the composition of simulated tumour spheroids, and to estimate model parameters pertaining to tumour cell proliferation rates and their responses to hypoxia. Since these measurements are possible using modern imaging techniques, this could motivate new experiments in which spheroid composition could be inferred by observing passive infiltration of inert particles.

Combining hypoxia-activated prodrugs and radiotherapy in silico: Impact of treatment scheduling and the intra-tumoural oxygen landscape

Hypoxia-activated prodrugs (HAPs) present a conceptually elegant approach to not only overcome, but better yet, exploit intra-tumoural hypoxia. Despite being successful in vitro and in vivo, HAPs are yet to achieve successful results in clinical settings. It has been hypothesised that this lack of clinical success can, in part, be explained by the insufficiently stringent clinical screening selection of determining which tumours are suitable for HAP treatments. Taking a mathematical modelling approach, we investigate how tumour properties and HAP-radiation scheduling influence treatment outcomes in simulated tumours. The following key results are demonstrated in silico: (i) HAP and ionising radiation (IR) monotherapies may attack tumours in dissimilar, and complementary, ways. (ii) HAP-IR scheduling may impact treatment efficacy. (iii) HAPs may function as IR treatment intensifiers. (iv) The spatio-temporal intra-tumoural oxygen landscape may impact HAP efficacy. Our in silico framework is based on an on-lattice, hybrid, multiscale cellular automaton spanning three spatial dimensions. The mathematical model for tumour spheroid growth is parameterised by multicellular tumour spheroid (MCTS) data.

Blackboard to Bedside: A Mathematical Modeling Bottom-Up Approach Toward Personalized Cancer Treatments

Cancers present with high variability across patients and tumors; thus, cancer care, in terms of disease prevention, detection, and control, can highly benefit from a personalized approach. For a comprehensive personalized oncology practice, this personalization should ideally consider data gathered from various information levels, which range from the macroscale population level down to the microscale tumor level, without omission of the central patient level. Appropriate data mined from each of these levels can significantly contribute in devising personalized treatment plans tailored to the individual patient and tumor. Mathematical models of solid tumors, combined with patient-specific tumor profiles, present a unique opportunity to personalize cancer treatments after detection using a bottom-up approach. Here, we discuss how information harvested from mathematical models and from corresponding in silico experiments can be implemented in preclinical and clinical applications. To conceptually illustrate the power of these models, one such model is presented, and various pertinent tumor and treatment scenarios are demonstrated in silico. The presented model, specifically a multiscale, hybrid cellular automaton, has been fully validated in vitro using multiple cell-line-specific data. We discuss various insights provided by this model and other models like it and their role in designing predictive tools that are both patient, and tumor specific. After refinement and parametrization with appropriate data, such in silico tools have the potential to be used in a clinical setting to aid in treatment protocols and decision making.

Forecasting tumor and vasculature response dynamics to radiation therapy via image based mathematical modeling

Background

Intra-and inter-tumoral heterogeneity in growth dynamics and vascularity influence tumor response to radiation therapy. Quantitative imaging techniques capture these dynamics non-invasively, and these data can initialize and constrain predictive models of response on an individual basis.

Methods

We have developed a family of 10 biologically-based mathematical models describing the spatiotemporal dynamics of tumor volume fraction, blood volume fraction, and response to radiation therapy. To evaluate this family of models, rats (n = 13) with C6 gliomas were imaged with magnetic resonance imaging (MRI) three times before, and four times following a single fraction of 20 Gy or 40 Gy whole brain irradiation. The first five 3D time series data of tumor volume fraction, estimated from diffusion-weighted (DW-) MRI, and blood volume fraction, estimated from dynamic contrast-enhanced (DCE-) MRI, were used to calibrate tumor-specific model parameters. The most parsimonious and well calibrated of the 10 models, selected using the Akaike information criterion, was then utilized to predict future growth and response at the final two imaging time points. Model predictions were compared at the global level (percent error in tumor volume, and Dice coefficient) as well as at the local or voxel level (concordance correlation coefficient).

Result

The selected model resulted in < 12% error in tumor volume predictions, strong spatial agreement between predicted and observed tumor volumes (Dice coefficient > 0.74), and high level of agreement at the voxel level between the predicted and observed tumor volume fraction and blood volume fraction (concordance correlation coefficient > 0.77 and > 0.65, respectively).

Conclusions

This study demonstrates that serial quantitative MRI data collected before and following radiation therapy can be used to accurately predict tumor and vasculature response with a biologically-based mathematical model that is calibrated on an individual basis. To the best of our knowledge, this is the first effort to characterize the tumor and vasculature response to radiation therapy temporally and spatially using imaging-driven mathematical models.

A cellular automaton model for spheroid response to radiation and hyperthermia treatments

Thermo-radiosensitisation is a promising approach for treatment of radio-resistant tumours such as those containing hypoxic subregions. Response prediction and treatment planning should account for tumour response heterogeneity, e.g. due to microenvironmental factors, and quantification of the biological effects induced. 3D tumour spheroids provide a physiological in vitro model of tumour response and a systems oncology framework for simulating spheroid response to radiation and hyperthermia is presented. Using a cellular automaton model, 3D oxygen diffusion, delivery of radiation and/or hyperthermia were simulated for many ([Formula: see text]) individual cells forming a spheroid. The iterative oxygen diffusion model was compared to an analytical oxygenation model and simulations were calibrated and validated against experimental data for irradiated (0-10 Gy) and/or heated (0-240 CEM43) HCT116 spheroids. Despite comparable clonogenic survival, spheroid growth differed significantly following radiation or hyperthermia. This dynamic response was described well by the simulation ([Formula: see text] > 0.85). Heat-induced cell death was implemented as a fast, proliferation-independent process, allowing reoxygenation and repopulation, whereas radiation was modelled as proliferation-dependent mitotic catastrophe. This framework stands out both through its experimental validation and its novel ability to predict spheroid response to multimodality treatment. It provides a good description of response where biological dose-weighting based on clonogenic survival alone was insufficient.

Biomedical Applications of Hyaluronic Acid-Based Nanomaterials in Hyperthermic Cancer Therapy

Hyaluronic acid (HA) is a non-sulfated polysaccharide polymer with the properties of biodegradability, biocompatibility, and non-toxicity. Additionally, HA specifically binds to certain receptors that are over-expressed in cancer cells. To maximize the effect of drug delivery and cancer treatment, diverse types of nanomaterials have been developed. HA-based nanomaterials, including micelles, polymersomes, hydrogels, and nanoparticles, play a critical role in efficient drug delivery and cancer treatment. Hyperthermic cancer treatment using HA-based nanomaterials has attracted attention as an efficient cancer treatment approach. In this paper, the biomedical applications of HA-based nanomaterials in hyperthermic cancer treatment and combined therapies are summarized. HA-based nanomaterials may become a representative platform in hyperthermic cancer treatment.