A new fundamental bioheat equation for muscle tissue--part II: Temperature of SAV vessels

ESHO benchmarks for computational modeling and optimization in hyperthermia therapy

BACKGROUND

The success of cancer hyperthermia (HT) treatments is strongly dependent on the temperatures achieved in the tumor and healthy tissues as it correlates with treatment efficacy and safety, respectively. Hyperthermia treatment planning (HTP) simulations have become pivotal for treatment optimization due to the possibility for pretreatment planning, optimization and decision making, as well as real-time treatment guidance.

MATERIALS AND METHODS

The same computational methods deployed in HTP are also used for in silico studies. These are of great relevance for the development of new HT devices and treatment approaches. To aid this work, 3 D patient models have been recently developed and made available for the HT community. Unfortunately, there is no consensus regarding tissue properties, simulation settings, and benchmark applicators, which significantly influence the clinical relevance of computational outcomes.

RESULTS AND DISCUSSION

Herein, we propose a comprehensive set of applicator benchmarks, efficacy and safety optimization algorithms, simulation settings and clinical parameters, to establish benchmarks for method comparison and code verification, to provide guidance, and in view of the 2021 ESHO Grand Challenge (Details on the ESHO grand challenge on HTP will be provided at https://www.esho.info/).

CONCLUSION

We aim to establish guidelines to promote standardization within the hyperthermia community such that novel approaches can quickly prove their benefit as quickly as possible in clinically relevant simulation scenarios. This paper is primarily focused on radiofrequency and microwave hyperthermia but, since 3 D simulation studies on heating with ultrasound are now a reality, guidance as well as a benchmark for ultrasound-based hyperthermia are also included.

Journal of Biomechanical Engineering Legacy Paper 2018

The Journal of Biomechanical Engineering has contributed to biomechanical engineering field since 1977. To honor papers published at least 30 years that have had a long-lasting impact on the field, the Editors now recognize "Legacy Papers." The journal is pleased to present the following paper as this year's Legacy Paper: "A New Simplified Bioheat Equation for the Effect of Blood Flow on Local Average Tissue Temperature" by S. Weinbaum and L. Jiji, ASME Journal of Biomechanical Engineering 107: 131-139, 1985.

Mathematical and numerical analysis of thermal distribution in cancerous tissues under the local heat therapy

The main purpose of this study is to investigate the thermal behavior of living tissues in the presence of spatial external heat source. An effort has been made to formulate the mathematical model to study the temperature distribution in in vivo tissues of the human body. The mathematical formulation is governed by bio-heat equation together with appropriate initial, boundary and interface conditions. The solution of the model was carried out using variational finite element method and computational simulations. The model describes the exchange of heat between the internal biological tissues and other surrounding media. The effect of external heat source under different conditions of atmospheric temperature and as a local hyperthermic method provides an important information to the temperature regulation in biological tissues under normal and malignant conditions. Thermal fluctuations at the targeted regions were obtained with respect to various time-dependent heating sources and scattering coefficients. The results obtained may be helpful for clinical purposes especially in the treatment of cancerous tumors through radiotherapy and other local hyperthermic approaches.

Thermal modelling using discrete vasculature for thermal therapy: A review

Reliable temperature information during clinical hyperthermia and thermal ablation is essential for adequate treatment control, but conventional temperature measurements do not provide 3D temperature information. Treatment planning is a very useful tool to improve treatment quality, and substantial progress has been made over the last decade. Thermal modelling is a very important and challenging aspect of hyperthermia treatment planning. Various thermal models have been developed for this purpose, with varying complexity. Since blood perfusion is such an important factor in thermal redistribution of energy in in vivo tissue, thermal simulations are most accurately performed by modelling discrete vasculature. This review describes the progress in thermal modelling with discrete vasculature for the purpose of hyperthermia treatment planning and thermal ablation. There has been significant progress in thermal modelling with discrete vasculature. Recent developments have made real-time simulations possible, which can provide feedback during treatment for improved therapy. Future clinical application of thermal modelling with discrete vasculature in hyperthermia treatment planning is expected to further improve treatment quality.

Thermal interaction of short-pulsed laser focused beams with skin tissues

Time-dependent thermal interaction is developed in a skin tissue cylinder subjected to the irradiation of a train of short laser pulses. The skin embedded with a small tumor is stratified as three layers: epidermis, dermis and subcutaneous fat with different optical, thermal and physiological properties. The laser beam is focused to the tumor site by an objective lens for thermal therapy. The ultrafast radiation heat transfer of the focused beam is simulated by the transient discrete ordinates method. The transient Pennes bio-heat equation is solved numerically by the finite volume method with alternating direction implicit scheme. Emphasis is placed on the characterization of the focused beam propagation and absorption and the temperature rise in the focal spot. The effects of the focal spot size and location, the laser power, and the bio-heat equation are investigated. Comparisons with collimated irradiation are conducted. The focused beam can penetrate a greater depth and produce higher temperature rise at the target area, and thus reduce the possibility of thermal damage to the surrounding healthy tissue. It is ideal for killing cancerous cells and small tumors.

A two-equation coupled system model for determination of liver tissue temperature during radio frequency ablation

A model is presented that is an alternative approach to the bio-heat equation for use in radio frequency heating of the liver. The model comprises both a tissue subvolume and a blood subvolume. Separate bio-heat equations are determined for each subvolume, but with an additional term exchanging heat between them, thus creating a coupled system. The derivation for the two coupled differential equations is outlined and sample simulations are presented to demonstrate the importance of considering the two subvolumes separately, even when the blood subvolume is a small fraction of the tissue subvolume.

Optimization and real-time control for laser treatment of heterogeneous soft tissues

Predicting the outcome of thermotherapies in cancer treatment requires an accurate characterization of the bioheat transfer processes in soft tissues. Due to the biological and structural complexity of tumor (soft tissue) composition and vasculature, it is often very difficult to obtain reliable tissue properties that is one of the key factors for the accurate treatment outcome prediction. Efficient algorithms employing in vivo thermal measurements to determine heterogeneous thermal tissues properties in conjunction with a detailed sensitivity analysis can produce essential information for model development and optimal control. The goals of this paper are to present a general formulation of the bioheat transfer equation for heterogeneous soft tissues, review models and algorithms developed for cell damage, heat shock proteins, and soft tissues with nanoparticle inclusion, and demonstrate an overall computational strategy for developing a laser treatment framework with the ability to perform real-time robust calibrations and optimal control. This computational strategy can be applied to other thermotherapies using the heat source such as radio frequency or high intensity focused ultrasound.

Effect of variable heat transfer coefficient on tissue temperature next to a large vessel during radiofrequency tumor ablation

Background

One of the current shortcomings of radiofrequency (RF) tumor ablation is its limited performance in regions close to large blood vessels, resulting in high recurrence rates at these locations. Computer models have been used to determine tissue temperatures during tumor ablation procedures. To simulate large vessels, either constant wall temperature or constant convective heat transfer coefficient (h) have been assumed at the vessel surface to simulate convection. However, the actual distribution of the temperature on the vessel wall is non-uniform and time-varying, and this feature makes the convective coefficient variable.

Methods

This paper presents a realistic time-varying model in which h is a function of the temperature distribution at the vessel wall. The finite-element method (FEM) was employed in order to model RF hepatic ablation. Two geometrical configurations were investigated. The RF electrode was placed at distances of 1 and 5 mm from a large vessel (10 mm diameter).

Results

When the ablation procedure takes longer than 1–2 min, the attained coagulation zone obtained with both time-varying h and constant h does not differ significantly. However, for short duration ablation (5–10 s) and when the electrode is 1 mm away from the vessel, the use of constant h can lead to errors as high as 20% in the estimation of the coagulation zone.

Conclusion

For tumor ablation procedures typically lasting at least 5 min, this study shows that modeling the heat sink effect of large vessels by applying constant h as a boundary condition will yield precise results while reducing computational complexity. However, for other thermal therapies with shorter treatment using a time-varying h may be necessary.

An analytical study of ‘Poisson conduction shape factors’ for two thermally significant vessels in a finite, heated tissue

To conveniently and properly account for the vessel to vessel and vessel to tissue heat transfer rates to predict in vivo tissue temperature distributions, this paper analyses two different types of Poisson conduction shape factors (PCSFs) for unheated and/or uniformly heated, non-insulated, finite tissue domains. One is related to the heat transfer rate from one vessel to another (vessel-vessel PCSF (VVPCSF)) and the other is related to the vessel to tissue heat transfer rates (vessel-tissue PCSF (VTPCSF)). Two alternative formulations for the VTPCSFs are studied; one is based on the difference between the vessel wall and tissue boundary temperatures, and the other on the difference between the vessel wall and the average tissue temperatures. The effects of a uniform source term and of the diameters and locations of the two vessels on the PCSFs are studied for two different cases: one, when the vessel wall temperatures are lower than the tissue boundary temperature, i.e., the vessels cool the tissue, and vice versa. Results show that, first, the VVPCSFs are only geometry dependent and they do not depend on the applied source term and the vessel wall and tissue boundary temperatures. Conversely, the VTPCSFs are strong functions of the source term and of the temperatures of the vessel walls and tissue boundary. These results suggest that to account for the vessel to vessel heat transfer rates, the VVPCSFs can be evaluated solely based on the vessel network geometry. However, to account for the vessel to tissue heat transfer rates, the VTPCSFs should be used iteratively while solving for the tissue temperature distributions. Second, unlike the tissue boundary temperature-based VTPCSFs which may become singular only in heated tissues, the average tissue temperature-based VTPCSFs have the potential to become singular in both unheated and heated tissues. These results suggest that caution should be exercised in the use of the VTPCSFs since they may approach singularity by virtue of their definition and thus may introduce large errors in the evaluation of tissue temperature distribution. Presented results are new and complementary to the previous shape factor results since these include the effect of (1) source term and (2) unequal vessel-tissue heat transfer rates from the two vessels to the tissue.

Experimental measurements of the temperature variation along artery-vein pairs from 200 to 1000 microns diameter in rat hind limb

Theoretical studies have indicated that a significant fraction of all blood-tissue heat transfer occurs in artery-vein pairs whose arterial diameter varies between 200 and 1000 microns. In this study, we have developed a new in vivo technique in which it is possible to make the first direct measurements of the countercurrent thermal equilibration that occurs along thermally significant vessels of this size. Fine wire thermocouples were attached by superglue to the femoral arteries and veins and their subsequent branches in rats and the axial temperature variation in each vessel was measured under different physiological conditions. Unlike the blood vessels < 200 microns in diameter, where the blood rapidly equilibrates with the surrounding tissue, we found that the thermal equilibration length of blood vessels between 200 microns and 1000 microns in diameter is longer than or at least equivalent to the vessel length. It is shown that the axial arterial temperature decays from 44% to 76% of the total core-skin temperature difference along blood vessels of this size, and this decay depends strongly on the local blood perfusion rate and the vascular geometry. Our experimental measurements also showed that the SAV venous blood recaptured up to 41% of the total heat released from its countercurrent artery under normal conditions. The contribution of countercurrent heat exchange is significantly reduced in these larger thermally significant vessels for hyperemic conditions as predicted by previous theoretical analyses. Results from this study, when combined with previous analyses of vessel pairs less than 200 microns diameter, enable one estimate the arterial supply temperature and the correction coefficient in the modified perfusion source term developed by the authors.