Fast FFT-based bioheat transfer equation computation

Theoretical estimation of the thermal damages of living tissues caused by laser irradiation in tumor thermal therapy

This article aims to provide theoretical predictions for the thermal reactions of human tissues during tumor thermotherapy when exposed to laser irradiation and an external heat source. For the construction of a theoretical study of bioheat transfer, the selection of a suitable thermal model capable of accurately predicting the required thermal responses is essential. The effect of heat production by heat treatment on a spherical multilayer tumor tissue is evaluated using this approach. Analytical solution for the non-homogenous differential equations is derived in the Laplace domain. The study examines the impact of thermal relaxation time on tissue temperature and the subsequent thermal damage. The numerical findings of thermal damage and temperatures are depicted in a graphical representation. This model explains laser treatment, physical events, metabolic support, and blood perfusion. The numerical outcomes of the recommended model are validated by comparing them to the literatures.

Influence of thermal relaxation time on thermomechanical interactions in biological tissue during hyperthermia treatment

This study presents an analytical analysis of thermo-mechanical interactions within living tissues using a generalized biothermoelastic model with one thermal relaxation time. Utilizing Laplace transforms and associated techniques, we investigate the response of living tissue to a pulse boundary heat flux that decays exponentially on a traction-free surface. Through detailed graphical illustrations, we elucidate the influence of key parameters such as thermal relaxation time, blood perfusion rate, and the characteristic time of the pulsing heat flux on temperature distribution, displacement, and thermal strain. Our results are presented through comprehensive graphical representations. Furthermore, a parametric analysis is conducted to guide the selection of optimal design factors, enhancing the accuracy of hyperthermia treatments.

Large-Volume Focused-Ultrasound Mild Hyperthermia for Improving Blood-Brain Tumor Barrier Permeability Application

Mild hyperthermia can locally enhance permeability of the blood-tumor barrier in brain tumors, improving delivery of antitumor nanodrugs. However, a clinical transcranial focused ultrasound (FUS) system does not provide this modality yet. The study aimed at the development of the transcranial FUS technique dedicated for large-volume mild hyperthermia in the brain. Acoustic pressure, multiple-foci, temperature and thermal dose induced by FUS were simulated in the brain through the skull. A 1-MHz, 114-element, spherical helmet transducer was fabricated to verify large-volume hyperthermia in the phantom. The simulated results showed that two foci were simultaneously formed at (2, 0, 0) and (−2, 0, 0) and at (0, 2, 0) and (0, −2, 0), using the phases of focusing pattern 1 and the phases of focusing pattern 2, respectively. Switching two focusing patterns at 5 Hz produced a hyperthermic zone with an ellipsoid of 7 mm × 6 mm × 11 mm in the brain and the temperature was 41–45 °C in the ellipsoid as the maximum intensity was 150 W/cm² and sonication time was 3 min. The phased array driven by switching two mode phases generated a 41 °C-contour region of 10 ± 1 mm × 8 ± 2 mm × 13 ± 2 mm in the phantom after 3-min sonication. Therefore, we have demonstrated our developed FUS technique for large-volume mild hyperthermia.

Finite Element Analysis of Nonlinear Bioheat Model in Skin Tissue Due to External Thermal Sources

In this work, numerical estimations of a nonlinear hyperbolic bioheat equation under various boundary conditions for medicinal treatments of tumor cells are constructed. The heating source components in a nonlinear hyperbolic bioheat transfer model, such as the rate of blood perfusions and the metabolic heating generations, are considered experimentally temperature-dependent functions. Due to the nonlinearity of the governing relations, the finite element method is adopted to solve such a problem. The results for temperature are presented graphically. Parametric analysis is then performed to identify an appropriate procedure to select significant design variables in order to yield further accuracy to achieve efficient thermal power in hyperthermia treatments.

Quantitative prediction of the extent of pelvic tumour ablation by magnetic resonance-guided high intensity focused ultrasound

BACKGROUND

Patient suitability for magnetic resonance-guided high intensity focused ultrasound (MRgHIFU) therapy of pelvic tumors is currently assessed by visual estimation of the proportion of tumor that can be reached by the device's focus (coverage). Since it is important to assess whether enough energy reaches the tumor to achieve ablation, a methodology for estimating the proportion of the tumor that can be ablated (treatability) was developed. Predicted treatability was compared against clinically achieved thermal ablation.

METHODS

MR Dixon sequence images of five patients with recurrent gynecological tumors were acquired during their treatment. Acousto-thermal simulations were performed using k-Wave for three exposure points (the deepest and shallowest reachable focal points within the tumor, identified from tumor coverage analysis, and a point halfway in-between) per patient. Interpolation between the resulting simulated ablated tissue volumes was used to estimate the maximum treatable depth and hence, tumor treatability. Predicted treatability was compared both to predicted tumor coverage and to the clinically treated tumor volume. The intended and simulated volumes and positions of ablated tissues were compared.

RESULTS

Predicted treatability was less than coverage by 52% (range: 31-78%) of the tumor volume. Predicted and clinical treatability differed by 9% (range: 1-25%) of tumor volume. Ablated tissue volume and position varied with beam path length through tissue.

CONCLUSION

Tumor coverage overestimated patient suitability for MRgHIFU therapy. Employing patient-specific simulations improved treatability assessment. Patient treatability assessment using simulations is feasible.

Synchronous temperature variation monitoring during ultrasound imaging and/or treatment pulse application: a phantom study

Ultrasound attenuation through soft tissues can produce an acoustic radiation force (ARF) and heating. The ARF-induced displacements and temperature evaluations can reveal tissue properties and provide insights into focused ultrasound (FUS) bio-effects. In this study, we describe an interleaving pulse sequence tested in a tissue-mimicking phantom that alternates FUS and plane-wave imaging pulses at a 1 kHz frame rate. The FUS is amplitude modulated, enabling the simultaneous evaluation of tissue-mimicking phantom displacement using harmonic motion imaging (HMI) and temperature rise using thermal strain imaging (TSI). The parameters were varied with a spatial peak temporal average acoustic intensity (I _spta ) ranging from 1.5 to 311 W.cm^-2, mechanical index (MI) from 0.43 to 4.0, and total energy (E) from 0.24 to 83 J.cm^-2. The HMI and TSI processing could estimate displacement and temperature independently for temperatures below 1.80°C and displacements up to ~117 μm (I _spta <311 W.cm^-2, MI<4.0, and E<83 J.cm^-2) indicated by a steady-state tissue-mimicking phantom displacement throughout the sonication and a comparable temperature estimation with simulations in the absence of tissue-mimicking phantom motion. The TSI estimations presented a mean error of ±0.03°C versus thermocouple estimations with a mean error of ±0.24°C. The results presented herein indicate that HMI can operate at diagnostic-temperature levels (i.e., <1°C) even when exceeding diagnostic acoustic intensity levels (720 mW.cm^-2 < I _spta < 207 W.cm^-2). In addition, the combined HMI and TSI can potentially be used for simultaneous evaluation of safety during tissue elasticity imaging as well as FUS mechanism involved in novel ultrasound applications such as ultrasound neuromodulation and tumor ablation.

Fast Simulation of Laser Heating Processes on Thin Metal Plates with FFT Using CPU/GPU Hardware

In flexible manufacturing systems, fast feedback from simulation solutions is required for effective tool path planning and parameter optimization. In the particular sub-domain of laser heating/cutting of thin rectangular plates, current state-of-the-art methods include frequency-domain (spectral) analytic solutions that greatly reduce the required computational time in comparison to industry standard finite element based approaches. However, these spectral solutions have not been presented previously in terms of Fourier methods and Fast Fourier Transform (FFT) implementations. This manuscript presents four different schemes that translate the problem of laser heating of rectangular plates into equivalent FFT problems. The presented schemes make use of the FFT algorithm to reduce the computational time complexity of the problem from O ( M 2 N 2 ) to O ( M N log ( M N ) ) (with M × N being the discretization size of the plate). The test results show that the implemented schemes outperform previous non-FFT approaches both in CPU and GPU hardware, resulting in 100 × faster runs. Future work addresses thermal/stress analysis, non-rectangular geometries and non-linear interactions (such as material melting/ablation, convection and radiation heat transfer).

The Effect of Fractional Time Derivative of Bioheat Model in Skin Tissue Induced to Laser Irradiation

This work uses the “fractional order bio-heat model” (Fob) model of heat conduction to offer a new interpretation to study the thermal damages in a skin tissue caused by laser irradiation. The influences of fractional order and the thermal relaxation time parameters on the temperature of skin tissue and the resulting thermal damage are studied. In the Laplace domain, the analytical solutions of temperature are obtained. Using the equation of Arrhenius, the resulting thermal injury to the tissues is assessed by the denatured protein ranges. The numerical results of the thermal damages and temperature are presented graphically. A parametric analysis is dedicated to the identifications of suitable procedures for the selection of significant design variables to achieve an effective thermal in the therapy of hyperthermia.

Fast computation of soft tissue thermal response under deformation based on fast explicit dynamics finite element algorithm for surgical simulation

BACKGROUND AND OBJECTIVES

During thermal heating surgical procedures such as electrosurgery, thermal ablative treatment and hyperthermia, soft tissue deformation due to surgical tool-tissue interaction and patient movement can affect the distribution of thermal energy induced. Soft tissue temperature must be obtained from the deformed tissue for precise delivery of thermal energy. However, the classical Pennes bio-heat transfer model can handle only the static non-moving state of tissue. In addition, in order to enable a surgeon to visualise the simulated results immediately, the solution procedure must be suitable for real-time thermal applications.

METHODS

This paper presents a formulation of bio-heat transfer under the effect of soft tissue deformation for fast or near real-time tissue temperature prediction, based on fast explicit dynamics finite element algorithm (FED-FEM) for transient heat transfer. The proposed thermal analysis under deformation is achieved by transformation of the unknown deformed tissue state to the known initial static state via a mapping function. The appropriateness and effectiveness of the proposed formulation are evaluated on a realistic virtual human liver model with blood vessels to demonstrate a clinically relevant scenario of thermal ablation of hepatic cancer.

RESULTS

For numerical accuracy, the proposed formulation can achieve a typical 10^-3 level of normalised relative error at nodes and between 10^-4 and 10^-5 level of total errors for the simulation, by comparing solutions against the commercial finite element analysis package. For computation time, the proposed formulation under tissue deformation with anisotropic temperature-dependent properties consumes 2.518 × 10^-4 ms for one element thermal loads computation, compared to 2.237 × 10^-4 ms for the formulation without deformation which is 0.89 times of the former. Comparisons with three other formulations for isotropic and temperature-independent properties are also presented.

CONCLUSIONS

Compared to conventional methods focusing on numerical accuracy, convergence and stability, the proposed formulation focuses on computational performance for fast tissue thermal analysis. Compared to the classical Pennes model that handles only the static state of tissue, the proposed formulation can achieve fast thermal analysis on deformed states of tissue and can be applied in addition to tissue deformable models for non-linear heating analysis at even large deformation of soft tissue, leading to great translational potential in dynamic tissue temperature analysis and thermal dosimetry computation for computer-integrated medical education and personalised treatment.

Iterative Curve Fitting of the Bioheat Transfer Equation for Thermocouple-Based Temperature Estimation In Vitro and In Vivo

Temperature measurements with thin thermocouples embedded in ultrasound fields are strongly subjected to a viscous heating artifact (VHA). The artifact contribution decays over time; therefore, it can be minimized at late temperature readings. However, previous studies have failed to demonstrate a rigorous method for determining the optimal time point at which the artifact contribution is negligible. In this study, we present an iterative processing method based on successive curve fittings using an artifact-independent model. The fitting starting point moves at each iteration until the maximum R² indicates where the viscous heating is minimum. A solution of the bioheat transfer equation is used to account for blood perfusion, thus enabling in vivo measurements. Three T-type thermocouples with different diameters and sensitivities were assessed in an excised canine liver and in the mouse brain in vivo. We found that the artifact constitutes up to 81% ± 5% of wire thermocouple readings. The best-fit time varied in the liver samples ( n = 3 ) from 0 to 3.335 ± 0.979 s and in the mouse brain ( n = 5 ) from 0 to 0.498 ± 0.457 s at variable experimental conditions, which clearly demonstrates the need of the method for finding the appropriate starting time point of the fit. This study introduces a statistical method to determine the best time to fit a curve that can back-estimate temperature in tissues under ultrasound exposure using thermocouples. This method allows temperature evaluation in vivo and in vitro during a validation and safety assessment of a wide range of therapeutic and diagnostic ultrasound modalities.

Thermal analysis of ultrasound-powered miniaturized implants: A tissue-phantom study

Neurological implants that harvest ultrasound power have the potential to provide long-term stimulation without complications associated with battery power. An important safety question associated with long-term operation of the implant involves the heat generated by the interaction of the device with the ultrasound field. A study was performed in which the temperature rise generated by this interaction was measured. Informed by temperature data from thermocouples outside the ultrasound beam, a mathematical inverse method was used to determine the volume heat source generated by ultrasound absorption within the implant as well as the surface heat source generated within the viscous boundary layer on the surface of the implant. For the test implant used, it was determined that most of the heat was generated in the boundary layer, giving a maximum temperature rise ∼5 times that for absorption in an equivalent volume of soft tissue. This result illustrates that thermal safety guidelines based solely on ultrasound absorption of tissue alone are not sufficient. The method presented represents an alternative approach for quantifying ultrasound thermal effects in the presence of implants. The analysis shows a steady temperature rise of about 0.2 °C for every 100 mW/cm² for the presented test implant.

EXACT ANALYTICAL SOLUTION OF BIOHEAT EQUATION SUBJECTED TO INTENSIVE MOVING HEAT SOURCE

Presented is the analytical solution of Pennes bio-heat equation, under localized moving heat source. The thermal behavior of one-dimensional (1D) nonhomogeneous layer of biological tissue is considered with blood perfusion term and modeled under the effect of concentric moving line heat source. The procedure of the solution is Eigen function expansion. The temperature profiles are calculated for three tissues of liver, kidney, and skin. Behavior of temperature profiles are studied parametrically due to the different moving speeds. The analytical solution can be used as a verification branch for studying the practical operations such as scanning laser treatment and other numerical solutions.

A neural controller for online laser power adjustment during the heat therapy process in the presence of nanoparticles

The present research evaluated the efficiency of a control approach to control the temperature of a breast tumor mass in the presence of nanoparticles exposed to laser radiation. However, if the radiation is carried out in open loop manner it may result in excessive temperature rise healthy cells that exist in the vicinity of tumor's cells. This may lead to the death of healthy cells. So, using closed loop control methods is necessary to guarantee the preservation of healthy cells during the period of radiation. Therefore, in this study, an artificial neural network was trained as a controller. In other words, the trained neural network adjusted the laser power over a period of time in such a way that the temperature in the center of the tumor reached the desired level with an appropriate temporal behavior. The difference between the real temperature of the tumor and the desired temperature of it is the controller input, while the controller output determined the amount of laser power. The simulation studies were carried out using an appropriate physiological model in the presence of nanoparticles. First, Schrödinger equations were solved followed by the effective mass equation. Afterward the optimum number of nanoparticles to be used in the IR field was calculated. Next, the important electro-optical features related to the nanostructure, such as the absorption continuum and reflection continuum had been calculated. The neural network proposed controller was then evaluated through other simulation studies in the tumor mass model. The results showed a promising performance by the trained artificial neural network in adjusting radiated laser power for the desired temperature increase in the center of a tumor mass.

A Tikhonov Regularization Scheme for Focus Rotations With Focused Ultrasound-Phased Arrays

Phased arrays have a wide range of applications in focused ultrasound therapy. By using an array of individually driven transducer elements, it is possible to steer a focus through space electronically and compensate for acoustically heterogeneous media with phase delays. In this paper, the concept of focusing an ultrasound-phased array is expanded to include a method to control the orientation of the focus using a Tikhonov regularization scheme. It is then shown that the Tikhonov regularization parameter used to solve the ill-posed focus rotation problem plays an important role in the balance between quality focusing and array efficiency. Finally, the technique is applied to the synthesis of multiple foci, showing that this method allows for multiple independent spatial rotations.

Monitoring local heating around an interventional MRI antenna with RF radiometry

PURPOSE

Radiofrequency (RF) radiometry uses thermal noise detected by an antenna to measure the temperature of objects independent of medical imaging technologies such as magnetic resonance imaging (MRI). Here, an active interventional MRI antenna can be deployed as a RF radiometer to measure local heating, as a possible new method of monitoring device safety and thermal therapy.

METHODS

A 128 MHz radiometer receiver was fabricated to measure the RF noise voltage from an interventional 3 T MRI loopless antenna and calibrated for temperature in a uniformly heated bioanalogous gel phantom. Local heating (ΔT) was induced using the antenna for RF transmission and measured by RF radiometry, fiber-optic thermal sensors, and MRI thermometry. The spatial thermal sensitivity of the antenna radiometer was numerically computed using a method-of-moment electric field analyses. The gel's thermal conductivity was measured by MRI thermometry, and the localized time-dependent ΔT distribution computed from the bioheat transfer equation and compared with radiometry measurements. A "H-factor" relating the 1 g-averaged ΔT to the radiometric temperature was introduced to estimate peak temperature rise in the antenna's sensitive region.

RESULTS

The loopless antenna radiometer linearly tracked temperature inside a thermally equilibrated phantom up to 73 °C to within ±0.3 °C at a 2 Hz sample rate. Computed and MRI thermometric measures of peak ΔT agreed within 13%. The peak 1 g-average temperature was H = 1.36 ± 0.02 times higher than the radiometric temperature for any media with a thermal conductivity of 0.15-0.50 (W/m)/K, indicating that the radiometer can measure peak 1 g-averaged ΔT in physiologically relevant tissue within ±0.4 °C.

CONCLUSIONS

Active internal MRI detectors can serve as RF radiometers at the MRI frequency to provide accurate independent measures of local and peak temperature without the artifacts that can accompany MRI thermometry or the extra space needed to accommodate alternative thermal transducers. A RF radiometer could be integrated in a MRI scanner to permit "self-monitoring" for assuring device safety and/or monitoring delivery of thermal therapy.

Frequency considerations for deep ablation with high-intensity focused ultrasound: A simulation study

PURPOSE

The objective of this study was to explore frequency considerations for large-volume, deep thermal ablations with focused ultrasound. Though focal patterns, focal steering rate, and the size of focal clusters have all been explored in this context, frequency studies have generally explored shallower depths and hyperthermia applications. This study examines both treatment efficiency and near-field heating rate as functions of frequency and depth.

METHODS

Flat, 150 mm transducer arrays were simulated to operate at frequencies of 250, 500, 750, 1000, 1250, and 1500 kHz. Each array had λ2 interelement spacing yielding arrays of 2000-70 000 piston-shaped elements arranged in concentric rings. Depths of 50, 100, and 150 mm were explored, with attenuation (α) values of 2.5-10 (Np/m)/MHz. Ultrasound propagation was simulated with the Rayleigh-Sommerfeld integral over a volume of homogeneous simulated tissue. Absorbed power density was determined from the acoustic pressure which, in turn, was modeled with the Pennes bioheat transfer equation. Using this knowledge of temperature over time, thermal dose function of Sapareto and Dewey was used to model the resulting bioeffect of each simulated sonication. Initially, single foci at each depth, frequency, and α were examined with either fixed peak temperatures or fixed powers. Based on the size of the resulting, single foci lesions, larger compound sonications were designed with foci packed together in multiple layers and rings. For each depth, focal patterns were chosen to produce a similar total ablated volume for each frequency. These compound sonications were performed with a fixed peak temperature at each focus. The resulting energy efficiency (volume ablated per acoustic energy applied), near-field heating rate (temperature increase in the anterior third of the simulation space per unit volume ablated), and near- and far-field margins were assessed.

RESULTS

Lesions of comparable volume were created with different frequencies at different depths. The results reflect the interconnected nature of frequency as it effects focal size (decreasing with frequency), peak pressure (generally increasing with frequency), and attenuation (also increasing with frequency). The ablation efficiency was the highest for α = 5 (Np/m)/MHz at a frequency of 750 kHz at each depth. For α = 10 (Np/m)/MHz, efficiency was the highest at 750 kHz for a depth of 50 mm, and 500 kHz at depths of 100 and 150 mm. At all sonication depths, near-field heating was minimized with lower frequencies of 250 and 500 kHz.

CONCLUSIONS

Large-volume ablations are most efficient at frequencies of 500-750 kHz at depths of 100-150 mm. When one considers that near-field heat accumulation tends to be the rate limiting factor in large-volume ablations like uterine fibroid surgery, the results show that frequencies as low as 500 kHz are favored for their ability to reduce heating in the near-field.

Numerical simulations of clinical focused ultrasound functional neurosurgery

A computational model utilizing grid and finite difference methods were developed to simulate focused ultrasound functional neurosurgery interventions. The model couples the propagation of ultrasound in fluids (soft tissues) and solids (skull) with acoustic and visco-elastic wave equations. The computational model was applied to simulate clinical focused ultrasound functional neurosurgery treatments performed in patients suffering from therapy resistant chronic neuropathic pain. Datasets of five patients were used to derive the treatment geometry. Eight sonications performed in the treatments were then simulated with the developed model. Computations were performed by driving the simulated phased array ultrasound transducer with the acoustic parameters used in the treatments. Resulting focal temperatures and size of the thermal foci were compared quantitatively, in addition to qualitative inspection of the simulated pressure and temperature fields. This study found that the computational model and the simulation parameters predicted an average of 24 ± 13% lower focal temperature elevations than observed in the treatments. The size of the simulated thermal focus was found to be 40 ± 13% smaller in the anterior-posterior direction and 22 ± 14% smaller in the inferior-superior direction than in the treatments. The location of the simulated thermal focus was off from the prescribed target by 0.3 ± 0.1 mm, while the peak focal temperature elevation observed in the measurements was off by 1.6 ± 0.6 mm. Although the results of the simulations suggest that there could be some inaccuracies in either the tissue parameters used, or in the simulation methods, the simulations were able to predict the focal spot locations and temperature elevations adequately for initial treatment planning performed to assess, for example, the feasibility of sonication. The accuracy of the simulations could be improved if more precise ultrasound tissue properties (especially of the skull bone) could be obtained.

Spectral analysis based on fast Fourier transformation (FFT) of surveillance data: the case of scarlet fever in China

Many infectious diseases exhibit repetitive or regular behaviour over time. Time-domain approaches, such as the seasonal autoregressive integrated moving average model, are often utilized to examine the cyclical behaviour of such diseases. The limitations for time-domain approaches include over-differencing and over-fitting; furthermore, the use of these approaches is inappropriate when the assumption of linearity may not hold. In this study, we implemented a simple and efficient procedure based on the fast Fourier transformation (FFT) approach to evaluate the epidemic dynamic of scarlet fever incidence (2004-2010) in China. This method demonstrated good internal and external validities and overcame some shortcomings of time-domain approaches. The procedure also elucidated the cycling behaviour in terms of environmental factors. We concluded that, under appropriate circumstances of data structure, spectral analysis based on the FFT approach may be applicable for the study of oscillating diseases.

An approach to rapid calculation of temperature change in tissue using spatial filters to approximate effects of thermal conduction

We present an approach to performing rapid calculations of temperature within tissue by interleaving, at regular time intervals, 1) an analytical solution to the Pennes (or other desired) bioheat equation excluding the term for thermal conduction and 2) application of a spatial filter to approximate the effects of thermal conduction. Here, the basic approach is presented with attention to filter design. The method is applied to a few different cases relevant to magnetic resonance imaging, and results are compared to those from a full finite-difference (FD) implementation of the Pennes bioheat equation. It is seen that results of the proposed method are in reasonable agreement with those of the FD approach, with about 15% difference in the calculated maximum temperature increase, but are calculated in a fraction of the time, requiring less than 2% of the calculation time for the FD approach in the cases evaluated.

The ability of different areas of the skin to absorb heat from a locally applied heat source: the impact of diabetes

BACKGROUND

When heat is applied to the skin, heat is conducted away because of the latent heat transfer properties of the skin and an increase in skin circulation, but little attention has been paid to the heat transfer properties of skin in different areas of the body and in people with diabetes. research design: Thirty subjects in the age range of 20-75 years had a thermode (44°C) applied to the skin of their arm, leg, foot, and back for 6 min to assess the heat transfer characteristics of skin in these four areas of the body. Skin blood flow and skin temperature were monitored over the 6-min period.

RESULTS

For the younger subjects, blood flow was not statistically different in response to heat in three areas of the body, starting at less than 200 flux measured by a laser Doppler imager and ending at approximately 1,200 flux after heat exposure. The foot had higher resting blood flow and higher blood flow in response to heat. Temperature and the rate of rise of temperature were also not different in any of the areas. The heat added to raise temperature, however, varied by body region. The arm required the least, whereas the leg and foot required the most. For the older group and subjects with diabetes, the heat required for any region of the body was much less to achieve the same increase in skin temperature, and blood flows were also much less; the subjects with diabetes showed the least blood flow and required the fewest calories to heat the skin. Whereas the foot required the greatest number of calories to heat the tissue in younger and older subjects, in subjects with diabetes, the foot took proportionally fewer calories.

CONCLUSION

Thus, specific areas of the body are damaged more by diabetes than other areas.