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

A translational review of hyperthermia biology

This review was written to be included in the Special Collection 'Therapy Ultrasound: Medicine's Swiss Army Knife?' The purpose of this review is to provide basic presentation and interpretation of the fundamentals of hyperthermia biology, as it pertains to uses of therapeutic ultrasound. The fundamentals are presented but in the setting of a translational interpretation and a view toward the future. Subjects that require future research and development are highlighted. The effects of hyperthermia are time and temperature dependent. Because intra-tumoral temperatures are non-uniform in tumors, one has to account for differential biologic effects in different parts of a tumor that occur simultaneously during and after hyperthermia.

Generalized, sublethal damage-based mathematical approach for improved modeling of clonogenic survival curve flattening upon hyperthermia, radiotherapy, and beyond

Objective. Mathematical modeling can offer valuable insights into the behavior of biological systems upon treatment. Different mathematical models (empirical, semi-empirical, and mechanistic) have been designed to predict the efficacy of either hyperthermia (HT), radiotherapy (RT), or their combination. However, mathematical approaches capable of modeling cell survival from shared general principles for both mono-treatments alone and their co-application are rare. Moreover, some cell cultures show dose-dependent saturation in response to HT or RT, manifesting in survival curve flattenings. An advanced survival model must, therefore, appropriately reflect such behavior.Approach. We propose a mathematical approach to model the effect of both treatments based on the general principle of sublethal damage (SLD) accumulation for the induction of cell death and irreversible proliferation arrest. Our approach extends Jung's model on heat-induced cellular inactivation by incorporating dose-dependent recovery rates that delineate changes in SLD restoration.Main results. The resulting unified model (Umodel) accurately describes HT and RT survival outcomes, applies to simultaneous thermoradiotherapy modeling, and is particularly suited to reproduce survival curve flattening phenomena. We demonstrate the Umodel's robust performance (R2 0.95) based on numerous clonogenic cell survival data sets from the literature and our experimental studies.Significance. The proposed Umodel allows using a single unified mathematical function based on generalized principles of accumulation of SLD with implemented radiosensitization, regardless of the type of energy deposited and the mechanism of action. It can reproduce various patterns of clonogenic survival curves, including any flattening, thus encompassing the variability of cell reactions to therapy, thereby potentially better reflecting overall tumor responses. Our approach opens a range of options for further model developments and strategic therapy outcome predictions of sequential treatments applied in different orders and varying recovery intervals between them.

Theoretical evaluation of the impact of diverse treatment conditions by calculation of the tumor control probability (TCP) of simulated cervical cancer Hyperthermia-Radiotherapy (HT-RT) treatments in-silico

INTRODUCTION

Hyperthermia (HT) induces various cellular biological processes, such as repair impairment and direct HT cell killing. In this context, in-silico biophysical models that translate deviations in the treatment conditions into clinical outcome variations may be used to study the extent of such processes and their influence on combined hyperthermia plus radiotherapy (HT + RT) treatments under varying conditions.

METHODS

An extended linear-quadratic model calibrated for SiHa and HeLa cell lines (cervical cancer) was used to theoretically study the impact of varying HT treatment conditions on radiosensitization and direct HT cell killing effect. Simulated patients were generated to compute the Tumor Control Probability (TCP) under different HT conditions (number of HT sessions, temperature and time interval), which were randomly selected within margins based on reported patient data.

RESULTS

Under the studied conditions, model-based simulations suggested a treatment improvement with a total CEM43 thermal dose of approximately 10 min. Additionally, for a given thermal dose, TCP increased with the number of HT sessions. Furthermore, in the simulations, we showed that the TCP dependence on the temperature/time interval is more correlated with the mean value than with the minimum/maximum value and that comparing the treatment outcome with the mean temperature can be an excellent strategy for studying the time interval effect.

CONCLUSION

The use of thermoradiobiological models allows us to theoretically study the impact of varying thermal conditions on HT + RT treatment outcomes. This approach can be used to optimize HT treatments, design clinical trials, and interpret patient data.

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.

Optimization of hyperthermia process applied to cancer treatment using multi-objective optimization differential evolution

Due to the number of cancer cases diagnosed each year and the fatality rate resulting from some more severe types, the improvement of less invasive and more efficient treatment techniques is of great importance. In this context, hyperthermia is a medical procedure in which the tumor region is heated by using an applicator for a certain period, aiming to destroy pathological cells. Computational models can be used to simulate the heating effect of tumors and adjacent cells. In general, the solution to an optimization problem considering factors such as heating temperature, applicator position, and the time in which the region will be subjected to heating can provide important information about the procedure. Traditionally, this type of problem has been addressed in a single objective context, focusing on minimizing the destruction of adjacent healthy tissue considering the area of the applicator constant. Our fundamental objective is to propose a multi-objective design problem considering the minimization of the area subject to the procedure and the time required for the process of hyperthermia in a breast cancer treatment. The problem is constrained by the degree of tissue destruction and by a partial differential equation that describes the phenomenon of heat transfer in both healthy and tumor tissues. The results obtained demonstrate that a point with a good compromise between the objectives can be chosen in such a way that a particular strategy can be defined for each patient.

Dosimetry Effects Due to the Presence of Fe Nanoparticles for Potential Combination of Hyperthermic Cancer Treatment with MRI-Based Image-Guided Radiotherapy

Nanoparticles have proven to be biocompatible and suitable for many biomedical applications. Currently, hyperthermia cancer treatments based on Fe nanoparticle infusion excited by alternating magnetic fields are commonly used. In addition to this, MRI-based image-guided radiotherapy represents, nowadays, one of the most promising accurate radiotherapy modalities. Hence, assessing the feasibility of combining both techniques requires preliminary characterization of the corresponding dosimetry effects. The present work reports on a theoretical and numerical simulation feasibility study aimed at pointing out preliminary dosimetry issues. Spatial dose distributions incorporating magnetic nanoparticles in MRI-based image-guided radiotherapy have been obtained by Monte Carlo simulation approaches accounting for all relevant radiation interaction properties as well as charged particles coupling with strong external magnetic fields, which are representative of typical MRI-LINAC devices. Two main effects have been evidenced: local dose enhancement (up to 60% at local level) within the infused volume, and non-negligible changes in the dose distribution at the interfaces between different tissues, developing to over 70% for low-density anatomical cavities. Moreover, cellular uptakes up to 10% have been modeled by means of considering different Fe nanoparticle concentrations. A theoretical temperature-dependent model for the thermal enhancement ratio (TER) has been used to account for radiosensitization due to hyperthermia. The outcomes demonstrated the reliability of the Monte Carlo approach in accounting for strong magnetic fields and mass distributions from patient-specific anatomy CT scans to assess dose distributions in MRI-based image-guided radiotherapy combined with magnetic nanoparticles, while the hyperthermic radiosensitization provides further and synergic contributions.

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.

Design and Characterization of an RF Applicator for In Vitro Tests of Electromagnetic Hyperthermia

The evaluation of the biological effects of therapeutic hyperthermia in oncology and the precise quantification of thermal dose, when heating is coupled with radiotherapy or chemotherapy, are active fields of research. The reliable measurement of hyperthermia effects on cells and tissues requires a strong control of the delivered power and of the induced temperature rise. To this aim, we have developed a radiofrequency (RF) electromagnetic applicator operating at 434 MHz, specifically engineered for in vitro tests on 3D cell cultures. The applicator has been designed with the aid of an extensive modelling analysis, which combines electromagnetic and thermal simulations. The heating performance of the built prototype has been validated by means of temperature measurements carried out on tissue-mimicking phantoms and aimed at monitoring both spatial and temporal temperature variations. The experimental results demonstrate the capability of the RF applicator to produce a well-focused heating, with the possibility of modulating the duration of the heating transient and controlling the temperature rise in a specific target region, by simply tuning the effectively supplied power.

Experimental Evaluation of Radiation Response and Thermal Properties of NPs-Loaded Tissues-Mimicking Phantoms

Many efforts have recently concentrated on constructing and developing nanoparticles (NPs) as promising thermal agent for optical hyperthermia and photothermal therapy. However, thermal energy transfer in biological tissue is a complex process involving different mechanisms such as conduction, convection, radiation. Therefore, having information about thermal properties of tissue especially when NPs are embedded in is a necessity for predicting the heat transfer during hyperthermia. In this work, the thermal properties of solid phantom based on agar in the presence of three different nanoparticles (BPSi, tNAs, GNRs) and alone were measured and reported as a function of temperature (ranging from 22 to 62 °C). The thermal response of these NPs to an 808 nm laser beam with three different powers were studied in the water comparatively. Agar and tNAs have almost constant thermal properties in the considered range. Among the three NPs, gold has the highest conductivity and diffusivity. At 62 °C BPSi NPs have the similar amount of increase for the diffusivity. The thermal parameters reported in this paper can be useful for the mathematical modeling. Irradiation of the NPs-loaded water phantom displayed the highest radiosensitivity of gold among the three mentioned NPs. However, for the higher power of irradiation, BPSi and tNAs NPs showed the increased absorption of heat during shorter time and the increased temperature gradient slope for the initial 15 s after the irradiation started. The three NPs showed different thermal and irradiation response behavior; however, this comparison study notes the worth of having information about thermal parameters of NPs-loaded tissue for pre-clinical planning.

A Novel Framework for the Optimization of Simultaneous ThermoBrachyTherapy

In high-dose-rate brachytherapy (HDR-BT) for prostate cancer treatment, interstitial hyperthermia (IHT) is applied to sensitize the tumor to the radiation (RT) dose, aiming at a more efficient treatment. Simultaneous application of HDR-BT and IHT is anticipated to provide maximum radiosensitization of the tumor. With this rationale, the ThermoBrachyTherapy applicators have been designed and developed, enabling simultaneous irradiation and heating. In this research, we present a method to optimize the three-dimensional temperature distribution for simultaneous HDR-BT and IHT based on the resulting equivalent physical dose (EQDphys) of the combined treatment. First, the temperature resulting from each electrode is precomputed. Then, for a given set of electrode settings and a precomputed radiation dose, the EQDphys is calculated based on the temperature-dependent linear-quadratic model. Finally, the optimum set of electrode settings is found through an optimization algorithm. The method is applied on implant geometries and anatomical data of 10 previously irradiated patients, using reported thermoradiobiological parameters and physical doses. We found that an equal equivalent dose coverage of the target can be achieved with a physical RT dose reduction of 20% together with a significantly lower EQDphys to the organs at risk (p-value < 0.001), even in the least favorable scenarios. As a result, simultaneous ThermoBrachyTherapy could lead to a relevant therapeutic benefit for patients with prostate cancer.