Optimization of temperature distributions for regional hyperthermia based on a nonlinear heat transfer model

Pulsing Addition to Modulated Electro-Hyperthermia

Numerous preclinical results have been verified, and clinical results have validated the advantages of modulated electro-hyperthermia (mEHT). This method uses the nonthermal effects of the electric field in addition to thermal energy absorption. Modulation helps with precisely targeting and immunogenically destroying malignant cells, which could have a vaccination-like abscopal effect. A new additional modulation (high-power pulsing) further develops the abilities of the mEHT. My objective is to present the advantages of pulsed treatment and how it fits into the mEHT therapy. Pulsed treatment increases the efficacy of destroying the selected tumor cells; it is active deeper in the body, at least tripling the penetration of the energy delivery. Due to the constant pulse amplitude, the dosing of the absorbed energy is more controllable. The induced blood flow for reoxygenation and drug delivery is high enough but not as high as increasing the risk of the dissemination of malignant cells. The short pulses have reduced surface absorption, making the treatment safer, and the increased power in the pulses allows the reduction of the treatment time needed to provide the necessary dose.

Review of Thermal and Physiological Properties of Human Breast Tissue

Electromagnetic thermal therapies for cancer treatment, such as microwave hyperthermia, aim to heat up a targeted tumour site to temperatures within 40 and 44 °C. Computational simulations used to investigate such heating systems employ the Pennes’ bioheat equation to model the heat exchange within the tissue, which accounts for several tissue properties: density, specific heat capacity, thermal conductivity, metabolic heat generation rate, and blood perfusion rate. We present a review of these thermal and physiological properties relevant for hyperthermia treatments of breast including fibroglandular breast, fatty breast, and breast tumours. The data included in this review were obtained from both experimental measurement studies and estimated properties of human breast tissues. The latter were used in computational studies of breast thermal treatments. The measurement methods, where available, are discussed together with the estimations and approximations considered for values where measurements were unavailable. The review concludes that measurement data for the thermal and physiological properties of breast and tumour tissue are limited. Fibroglandular and fatty breast tissue properties are often approximated from those of generic muscle or fat tissue. Tumour tissue properties are mostly obtained from approximating equations or assumed to be the same as those of glandular tissue. We also present a set of reliable data, which can be used for more accurate modelling and simulation studies to better treat breast cancer using thermal therapies.

Fast Adaptive Temperature-Based Re-Optimization Strategies for On-Line Hot Spot Suppression during Locoregional Hyperthermia

Simple Summary

When treatment limiting hot spots occur during locoregional hyperthermia (i.e., heating tumors to 40–44 °C for ~1 h), system settings are adjusted based on experience. In this study, we developed and evaluated treatment planning with temperature-based re-optimization and compared the predicted effectiveness to clinically applied protocol/experience-based steering. Re-optimization times were typically ~10 s; sufficiently fast for on-line use. Effective hot spot suppression was predicted, while maintaining adequate tumor heating. Inducing new hot spots was avoided. Temperature-based re-optimization to suppress treatment limiting hot spots seemed feasible to match the effectiveness of long-term clinical experience and will be further evaluated in a clinical setting. When numerical algorithms are proven to match long-term experience, the overall treatment quality within hyperthermia centers can significantly improve. Implementing these strategies would then imply that treatments become less dependent on the experience of the center/operator.

Abstract

Background: Experience-based adjustments in phase-amplitude settings are applied to suppress treatment limiting hot spots that occur during locoregional hyperthermia for pelvic tumors. Treatment planning could help to further optimize treatments. The aim of this research was to develop temperature-based re-optimization strategies and compare the predicted effectiveness with clinically applied protocol/experience-based steering. Methods: This study evaluated 22 hot spot suppressions in 16 cervical cancer patients (mean age 67 ± 13 year). As a first step, all potential hot spot locations were represented by a spherical region, with a user-specified diameter. For fast and robust calculations, the hot spot temperature was represented by a user-specified percentage of the voxels with the largest heating potential (HPP). Re-optimization maximized tumor T90, with constraints to suppress the hot spot and avoid any significant increase in other regions. Potential hot spot region diameter and HPP were varied and objective functions with and without penalty terms to prevent and minimize temperature increase at other potential hot spot locations were evaluated. Predicted effectiveness was compared with clinically applied steering results. Results: All strategies showed effective hot spot suppression, without affecting tumor temperatures, similar to clinical steering. To avoid the risk of inducing new hot spots, HPP should not exceed 10%. Adding a penalty term to the objective function to minimize the temperature increase at other potential hot spot locations was most effective. Re-optimization times were typically ~10 s. Conclusion: Fast on-line re-optimization to suppress treatment limiting hot spots seems feasible to match effectiveness of ~30 years clinical experience and will be further evaluated in a clinical setting.

Noninvasive intratumoral thermal dose determination during in vivo magnetic nanoparticle hyperthermia: combining surface temperature measurements and computer simulations

PURPOSE

Noninvasive thermometry during magnetic nanoparticle hyperthermia (MNH) remains a challenge. Our pilot study proposes a methodology to determine the noninvasive intratumoral thermal dose during MNH in the subcutaneous tumor model.

METHODS

Two groups of Ehrlich bearing-mice with solid and subcutaneous carcinoma, a control group (n = 6), and a MNH treated group (n = 4) were investigated. Histopathology was used to evaluate the percentage of non-viable lesions in the tumor. MNH was performed at 301 kHz and 17.5 kA.m^-1, using a multifunctional nanocarrier. Surface temperature measurements were obtained using an infrared camera, where an ROI with 750 pixels was used for comparison with computer simulations. Realistic simulations of the bioheat equation were obtained by combining histopathology intratumoral lesion information and surface temperature agreement of at least 50% of the pixel's temperature data calculated and measured at the surface.

RESULTS

One animal of the MNH group showed tumor recurrence, while two others showed complete tumor remission (monitored for 585 days). Sensitivity analysis of the simulation parameters indicated low tumor blood perfusion. Numerical simulations indicated, for the animals with complete remission, an irreversible tissue injury of 91 ± 5% and 100%, while the one with recurrence had a lower value, 56 ± 7%. The computer simulations also revealed the in vivo heat efficiency of the nanocarrier.

CONCLUSION

A new methodology for determining noninvasively the three-dimensional intratumoral thermal dose during MNH was developed. The method demonstrates the potential for predicting the long-term preclinical outcome of animals treated with MNH.

Quo Vadis Oncological Hyperthermia (2020)?

Heating as a medical intervention in cancer treatment is an ancient approach, but effective deep heating techniques are lacking in modern practice. The use of electromagnetic interactions has enabled the development of more reliable local-regional hyperthermia (LRHT) techniques whole-body hyperthermia (WBH) techniques. Contrary to the relatively simple physical-physiological concepts behind hyperthermia, its development was not steady, and it has gone through periods of failures and renewals with mixed views on the benefits of heating seen in the medical community over the decades. In this review we study in detail the various techniques currently available and describe challenges and trends of oncological hyperthermia from a new perspective. Our aim is to describe what we believe to be a new and effective approach to oncologic hyperthermia, and a change in the paradigm of dosing. Physiological limits restrict the application of WBH which has moved toward the mild temperature range, targeting immune support. LRHT does not have a temperature limit in the tumor (which can be burned out in extreme conditions) but a trend has started toward milder temperatures with immune-oriented goals, developing toward immune modulation, and especially toward tumor-specific immune reactions by which LRHT seeks to target the malignancy systemically. The emerging research of bystander and abscopal effects, in both laboratory investigations and clinical applications, has been intensified. Our present review summarizes the methods and results, and discusses the trends of hyperthermia in oncology.

Regional deep hyperthermia: quantitative evaluation of predicted and direct measured temperature distributions in patients with high-risk extremity soft-tissue sarcoma

BACKGROUND

Temperature distributions resulting from hyperthermia treatment of patients with high-risk soft-tissue sarcoma (STS) were quantitatively evaluated and globally compared with thermal simulations performed by a treatment planning system. The aim was to test whether the treatment planning system was able to predict correct temperature distributions.

METHODS

Five patients underwent computed tomography (CT) fluoroscopy-guided placement of tumor catheters used for the interstitial temperature measurements. For the simulations, five 3 D patient models were reconstructed by segmenting the patient CT datasets into different tissues. The measured and simulated data were evaluated by calculating the temperature change ( ΔT ), T90, T50, T20, T_mean, T_min and T_max, as well as the 90th percentile thermal dose (CEM43T90). In order to measure the agreement between both methods quantitatively, the Bland-Altman analysis was applied.

RESULTS

The absolute difference between measured and simulated temperatures were found to be 2°, 6°, 1°, 4°, 5° and 4 °C on average for T_min, T_max, T90, T50, T20 and T_mean, respectively. Furthermore, the thermal simulations exhibited relatively higher thermal dose compared to those that were measured. Finally, the results of the Bland-Altman analysis showed that the mean difference between both methods was above 2 °C which is considered to be clinically unacceptable.

CONCLUSION

Given the current practical limitations on resolution of calculation grid, tissue properties, and perfusion information, the software SigmaHyperPlan™ is incapable to produce thermal simulations with sufficient correlation to typically heterogeneous tissue temperatures to be useful for clinical treatment planning.

Oncological hyperthermia: The correct dosing in clinical applications

The problem with the application of conventional hyperthermia in oncology is firmly connected to the dose definition, which conventionally uses the concept of the homogeneous (isothermal) temperature of the target. Its imprecise control and complex evaluation is the primary barrier to the extensive clinical applications. The aim of this study was to show the basis of the problems of the misleading dose concept. A clear clarification of the proper dose concept must begin with the description of the limitations of the present doses in conventional hyperthermia applications. The surmounting of the limits the dose of oncologic hyperthermia has to be based on the applicability of the Eyring transition state theory on thermal effects. In order to avoid the countereffects of thermal homeostasis, the use of precise heating on the nanoscale with highly efficient energy delivery is recommended. The nano‑scale heating allows for an energy‑based dose to control the process. The main aspects of the method are the following: i) It is not isothermal (no homogeneous heating); ii) malignant cells are heated selectively; and iii) it employs high heating efficacy, with less energy loss. The applied rigorous thermodynamical considerations show the proper terminology and dose concept of hyperthermia, which is based on the energy‑absorption (such as in the case of ionizing radiation) instead of the temperature‑based ideas. On the whole, according to the present study, the appropriate dose in oncological hyperthermia must use an energy‑based concept, as it is well‑known in all the ionizing radiation therapies. We propose the use of Gy (J/kg) in cases of non‑ionizing radiation (hyperthermia) as well.

Locoregional hyperthermia of deep-seated tumours applied with capacitive and radiative systems: a simulation study

BACKGROUND

Locoregional hyperthermia is applied to deep-seated tumours in the pelvic region. Two very different heating techniques are often applied: capacitive and radiative heating. In this paper, numerical simulations are applied to compare the performance of both techniques in heating of deep-seated tumours.

METHODS

Phantom simulations were performed for small (30 × 20 × 50 cm³) and large (45 × 30 × 50 cm³), homogeneous fatless and inhomogeneous fat-muscle, tissue-equivalent phantoms with a central or eccentric target region. Radiative heating was simulated with the 70 MHz AMC-4 system and capacitive heating was simulated at 13.56 MHz. Simulations were performed for small fatless, small (i.e. fat layer typically <2 cm) and large (i.e. fat layer typically >3 cm) patients with cervix, prostate, bladder and rectum cancer. Temperature distributions were simulated using constant hyperthermic-level perfusion values with tissue constraints of 44 °C and compared for both heating techniques.

RESULTS

For the small homogeneous phantom, similar target heating was predicted with radiative and capacitive heating. For the large homogeneous phantom, most effective target heating was predicted with capacitive heating. For inhomogeneous phantoms, hot spots in the fat layer limit adequate capacitive heating, and simulated target temperatures with radiative heating were 2-4 °C higher. Patient simulations predicted therapeutic target temperatures with capacitive heating for fatless patients, but radiative heating was more robust for all tumour sites and patient sizes, yielding target temperatures 1-3 °C higher than those predicted for capacitive heating.

CONCLUSION

Generally, radiative locoregional heating yields more favourable simulated temperature distributions for deep-seated pelvic tumours, compared with capacitive heating. Therapeutic temperatures are predicted for capacitive heating in patients with (almost) no fat.

Regional deep hyperthermia: impact of observer variability in CT-based manual tissue segmentation on simulated temperature distribution

The aim of this study was to systematically investigate the influence of the inter- and intra-observer segmentation variation of tumors and organs at risk on the simulated temperature coverage of the target. CT scans of six patients with tumors in the pelvic region acquired for radiotherapy treatment planning were used for hyperthermia treatment planning. To study the effect of inter-observer variation, three observers manually segmented in the CT images of each patient the following structures: fat, muscle, bone and the bladder. The gross tumor volumes (GTV) were contoured by three radiation oncology residents and used as the hyperthermia target volumes. For intra-observer variation, one of the observers of each group contoured the structures of each patient three times with a time span of one week between the segmentations. Moreover, the impact of segmentation variations in organs at risk (OARs) between the three inter-observers was investigated on simulated temperature distributions using only one GTV. The spatial overlap between individual segmentations was assessed by the Dice similarity coefficient (DSC) and the mean surface distance (MSD). Additionally, the temperatures T90/T10 delivered to 90%/10% of the GTV, respectively, were assessed for each observer combination. The results of the segmentation similarity evaluation showed that the DSC of the inter-observer variation of fat, muscle, the bladder, bone and the target was 0.68  ±  0.12, 0.88  ±  0.05, 0.73  ±  0.14, 0.91  ±  0.04 and 0.64  ±  0.11, respectively. Similar results were found for the intra-observer variation. The MSD results were similar to the DSCs for both observer variations. A statistically significant difference (p  <  0.05) was found for T90 and T10 in the predicted target temperature due to the observer variability. The conclusion is that intra- and inter-observer variations have a significant impact on the temperature coverage of the target. Furthermore, OARs, such as bone and the bladder, may essentially influence the homogeneity of the simulated target temperature distribution.

Determination of time of death in forensic science via a 3-D whole body heat transfer model

This study is focused on developing a whole body heat transfer model to accurately simulate temperature decay in a body postmortem. The initial steady state temperature field is simulated first and the calculated weighted average body temperature is used to determine the overall heat transfer coefficient at the skin surface, based on thermal equilibrium before death. The transient temperature field postmortem is then simulated using the same boundary condition and the temperature decay curves at several body locations are generated for a time frame of 24h. For practical purposes, curve fitting techniques are used to replace the simulations with a proposed exponential formula with an initial time delay. It is shown that the obtained temperature field in the human body agrees very well with that in the literature. The proposed exponential formula provides an excellent fit with an R² value larger than 0.998. For the brain and internal organ sites, the initial time delay varies from 1.6 to 2.9h, when the temperature at the measuring site does not change significantly from its original value. The curve-fitted time constant provides the measurement window after death to be between 8h and 31h if the brain site is used, while it increases 60-95% at the internal organ site. The time constant is larger when the body is exposed to colder air, since a person usually wears more clothing when it is cold outside to keep the body warm and comfortable. We conclude that a one-size-fits-all approach would lead to incorrect estimation of time of death and it is crucial to generate a database of cooling curves taking into consideration all the important factors such as body size and shape, environmental conditions, etc., therefore, leading to accurate determination of time of death.

Bioheat transfer problem for one-dimensional spherical biological tissues

Based on the Pennes bioheat transfer equation with constant blood perfusion, we set up a simplified one-dimensional bioheat transfer model of the spherical living biological tissues for application in bioheat transfer problems. Using the method of separation of variables, we present in a simple way the analytical solution of the problem. The obtained exact solution is used to investigate the effects of tissue properties, the cooling medium temperature, and the point-heating on the temperature distribution in living bodies. The obtained analytical solution can be useful for investigating thermal behavior research of biological system, thermal parameter measurements, temperature field reconstruction and clinical treatment.

Oncothermia: a new paradigm and promising method in cancer therapies

In "hypethermia", the procedure of raising the temperature of a part, or the whole body, up to 42 degrees C to kill cancer cells for a defined period of time is applied alone or as an adjunctive with various established cancer treatment modalities such as radiotherapy and chemotherapy. However, "hyperthermia" is not generally accepted as conventional therapy due to the complications of deep heating and lack of focusing of the heat effect only for malignant tissues. The idea of oncothermia solves the selective deep action on malignant tissue on nearly cellular level. Oncothermia is highly improved, safe and effective "hyperthermia" in clinical cancer therapy supported by in vivo, in vitro, and human research as shown in this article. Advantage of oncothermia: while the classical insufficiently, focused "hyperthermia" has to heat up in case of the multiple lesions overlapping all the volume, which contains both normal tissues and malignant tissues; while oncothermia automatically focuses on the malignant tissues in its multiple places, without treating the healthy tissue in between. The modulated radiofrequency current (RF) flows through the malignancies only. The radiofrequency modulated current with 13,56 MHz (fractal modulated) between 2 electrodes automatically focuses through malignant tissues with lower impedance and will flow mainly in the extracellular electrolyte because the normal cells are electronically isolated by their membrane by more than one-million V/m electrical field strength. Oncothermia today has the ability to be a candidate to a widely accepted modality of the standard cancer treatment.

Sequential activation of a segmented ground pad reduces skin heating during radiofrequency tumor ablation: optimization via computational models

Radiofrequency (RF) ablation has become an accepted treatment modality for unresectable tumors. The need for larger ablation zones has resulted in increased RF generator power. Skin burns due to ground pad heating are increasingly limiting further increases in generator power, and thus, ablation zone size. We investigated a method for reducing ground pad heating in which a commercial ground pad is segmented into multiple ground electrodes, with sequential activation of ground electrode subsets. We created finite-element method computer models of a commercial ground pad (14 x 23 cm) and compared normal operation of a standard pad to sequential activation of a segmented pad (two to five separate ground electrode segments). A constant current of 1 A was applied for 12 min in all simulations. Time periods during sequential activation simulations were adjusted to keep the leading edge temperatures at each ground electrode equal. The maximum temperature using standard activation of the commercial pad was 41.7 degrees C. For sequential activation of a segmented pad, the maximum temperature ranged from 39.3 degrees C (five segments) to 40.9 degrees C (two segments). Sequential activation of a segmented ground pad resulted in lower tissue temperatures. This method may reduce the incidence of ground pad burns and enable the use of higher power generators during RF tumor ablation.

Determination of heterogeneous thermal parameters using ultrasound induced heating and MR thermal mapping

In this paper, a method for the determination of spatially varying thermal conductivity and perfusion coefficients of tissue is proposed. The temperature evolution in tissue is modelled with the Pennes bioheat equation. The main motivation here is a model-based optimal control for ultrasound surgery, in which the tissue properties are needed when the treatment is planned. The overview of the method is as follows. The same ultrasound transducers, which are eventually used for the treatment, are used to inflict small temperature changes in tissue. This temperature evolution is monitored using MR thermal imaging, and the tissue properties are then estimated on the basis of these measurements. Furthermore, an approach to choose transducer excitations for the determination procedure is also considered. The purpose of this paper is to introduce a method and therefore simulations are used to verify the method. Furthermore, computations are accomplished in a 2D spatial domain.

Influence of electrical and thermal properties on RF ablation of breast cancer: is the tumour preferentially heated?

Background

Techniques based on radio frequency (RF) energy have many applications in medicine, in particular tumour ablation. Today, mammography screening detects many breast cancers at an early stage, facilitating treatment by minimally invasive techniques such as radio frequency ablation (RFA). The breast cancer is mostly surrounded by fat, which during RFA-treatment could result in preferential heating of the tumour due to the substantial differences in electrical parameters. The object of this study was to investigate if this preferential heating existed during experimental in vitro protocols and during computer simulations.

Methods

Excised breast material from four patients with morphologically diagnosed breast cancers were treated with our newly developed RFA equipment. Subsequently, two finite element method (FEM) models were developed; one with only fat and one with fat and an incorporated breast cancer of varying size. The FEM models were solved using temperature dependent electrical conductivity versus constant conductivity, and transient versus steady-state analyses.

Results

Our experimental study performed on excised breast tissue showed a preferential heating of the tumour, even if associated with long tumour strands. The fat between these tumour strands was surprisingly unaffected. Furthermore, the computer simulations demonstrated that the difference in electrical and thermal parameters between fat and tumour tissue can cause preferential heating of the tumour. The specific absorption rate (SAR) distribution changed significantly when a tumour was present in fatty tissue. The degree of preferential heating depended on tissue properties, tumour shape, and placement relative to the electrode. Temperature dependent electrical conductivity increased the thermal lesion volume, but did not change the preferential heating. Transient solutions decreased the thermal lesion volume but increased the preferential heating of the tumour.

Conclusion

Both the computer model and the in vitro study confirmed that preferential heating of the tumour during RFA exists in breast tissue. However, the observed preferential heating in the in vitro studies were more pronounced, indicating that additional effects other than the difference in tissue parameters might be involved. The existing septa layers between the cancer tissue and the fatty tissue could have an additional electrical or thermal insulating effect, explaining the discrepancy between the in vitro study and the computer model.

Transport lattice models of heat transport in skin with spatially heterogeneous, temperature-dependent perfusion

BACKGROUND

Investigation of bioheat transfer problems requires the evaluation of temporal and spatial distributions of temperature. This class of problems has been traditionally addressed using the Pennes bioheat equation. Transport of heat by conduction, and by temperature-dependent, spatially heterogeneous blood perfusion is modeled here using a transport lattice approach.

METHODS

We represent heat transport processes by using a lattice that represents the Pennes bioheat equation in perfused tissues, and diffusion in nonperfused regions. The three layer skin model has a nonperfused viable epidermis, and deeper regions of dermis and subcutaneous tissue with perfusion that is constant or temperature-dependent. Two cases are considered: (1) surface contact heating and (2) spatially distributed heating. The model is relevant to the prediction of the transient and steady state temperature rise for different methods of power deposition within the skin. Accumulated thermal damage is estimated by using an Arrhenius type rate equation at locations where viable tissue temperature exceeds 42 degrees C. Prediction of spatial temperature distributions is also illustrated with a two-dimensional model of skin created from a histological image.

RESULTS

The transport lattice approach was validated by comparison with an analytical solution for a slab with homogeneous thermal properties and spatially distributed uniform sink held at constant temperatures at the ends. For typical transcutaneous blood gas sensing conditions the estimated damage is small, even with prolonged skin contact to a 45 degrees C surface. Spatial heterogeneity in skin thermal properties leads to a non-uniform temperature distribution during a 10 GHz electromagnetic field exposure. A realistic two-dimensional model of the skin shows that tissue heterogeneity does not lead to a significant local temperature increase when heated by a hot wire tip.

CONCLUSIONS

The heat transport system model of the skin was solved by exploiting the mathematical analogy between local thermal models and local electrical (charge transport) models, thereby allowing robust, circuit simulation software to obtain solutions to Kirchhoff's laws for the system model. Transport lattices allow systematic introduction of realistic geometry and spatially heterogeneous heat transport mechanisms. Local representations for both simple, passive functions and more complex local models can be easily and intuitively included into the system model of a tissue.

Theoretical model of internally cooled interstitial ultrasound applicators for thermal therapy

Interstitial ultrasound applicators for high-temperature thermal therapy are currently being developed for treating cancerous and benign disease. Internally cooled, direct-coupled (ICDC) applicators, composed of a segmented array of cylindrical ultrasound transducers, have demonstrated capabilities of producing controllable and conformal heating distributions along the applicator length and angular orientation. In this study, 2D transient acoustic and biothermal models of ICDC applicators were developed using a mixed implicit and explicit finite difference solution with variable node spacing in cylindrical coordinates for enhanced speed, stability and accuracy. The model incorporates dynamic behaviour of acoustic parameters and blood perfusion as a function of temperature and thermal dose. Acoustic intensity distributions were modelled as a composite of measured and theoretical intensity distributions. The shape and time evolution of temperature contours and thermal lesions for 90 degrees, 200 and 360 degrees angularly directional applicators and multi-transducer applicators were modelled for heating durations between 1 and 5 min. Model parameters were selected to match previously reported ex vivo and in vivo studies of 2.2 mm diameter ICDC devices in thigh muscle and liver (15-30 W cm(-2) applied power density, 0.5-5 min treatment times, 2.8-3.6 cm diameter thermal lesions). The temperatures and lethal thermal dose (600 EM43 degrees C) contours calculated using the models were in excellent agreement with temperatures and thermal lesion dimensions (visible coagulation) determined experimentally. The differences between maximum radial depths of coagulation calculated using the r-z and r-theta models were small, less than approximately 2 mm for 10-15 mm lesions. There was a strong correlation between the calculated 50 degrees C contour and the radial, angular and axial lesion dimensions obtained for 3-5 min heating protocols. The models developed in this study have significant application in design studies and potential future use in treatment planning of ICDC interstitial ultrasound thermal therapy.

Estimation of heat transfer and temperature rise in partial-body regions during MR procedures: an analytical approach with respect to safety considerations

In order to assess thermal response to RF exposure during MR procedures at the tissue level, simple analytical solutions to the non-stationary Pennes' bio-heat equation were obtained using the Green's function approach. Two thermal models appropriate for partial-body exposure were analyzed: In the first model, the temperature field at the periphery of an idealized volume RF resonator was modeled. The analytical solution reveals that tissue response to RF heating is characterized by an equilibration time and length. Both parameters are inversely related to tissue perfusion and vary for the soft-tissues considered between 0.27-25 min and 1.5-12 mm, respectively. None of the tissues investigated increase in temperature more than 0.5 degrees C for each W/kg of power dissipated. Secondly, a homogeneous tissue solution was derived that predicts the temperature-time course to an MR examination with time-varying specific absorption rates (SAR). Since SAR limits indicated in current MR safety standards relate to running SAR averages computed over an appropriate period of time, an expression was formulated that gives an upper limit for the temperature rise averaged over the same period of time, as a function of both the upper limit of running SAR averages and the duration of the MR examination. The analysis revealed that the partial-body SAR limits indicated in the IEC standard may not guarantee under all circumstances compliance with the basic restrictions concerning temperature rise.