Thermomechanical analysis of soft-tissue thermotherapy

Soft-tissue thermotherapy based on sub-ablative heating of collagenous tissues finds wide-spread application in medicine such as tissue welding, thermokeratoplasty, skin resurfacing, elimination of discogenic pain in the spine and treatment of joint instability. In this paper, heat-induced thermomechanical response characteristics of collagenous tissues are quantified by means of in vitro experimentation with a representative model tissue (New Zealand white rabbit patellar tendon). Three distinct heat-induced thermomechanical response regimes (defined by the rate of deformation and the variation of material properties) are identified. Arrhenius damage integral representation of collagenous tissue thermal history is shown to be adequate in establishing the master response curves for quantification of thermomechanical response for modeling purposes. The trade-off between the improved kinematical stability and compromised mechanical stability of the heated collagenous tissue is shown to be the major challenge hindering the success of subablative thermotherapies.     

Electrical injury mechanisms: dynamics of the thermal response

The thermal response of the human upper extremity to large electric currents was examined using an axisymmetric unidimensional model containing bone, skeletal muscle, fat, and skin in coaxial cylindrical geometry. Appropriate thermal and electrical properties were assigned to each tissue, and the tissue response to joule heating was determined by a finite-element numerical technique. We found that when the tissues are electrically in parallel, skeletal muscle sustained the largest temperature rise and then heated adjacent tissues. Thus, when bone is not in series with other tissues, joule heating of bone is unlikely to be responsible for thermal damage to adjacent tissue. In addition, the effect of tissue perfusion on the thermal response was found to be essential for rapid cooling of the centrally located tissues.     

Altered mechanical behavior of epicardium under isothermal biaxial loading

Most soft tissues that are treated clinically via heating experience multiaxial states of stress and strain in vivo and are subject to complex constraints during treatment. Remarkably, however, there are no prior data on changes in the multiaxial mechanical behavior of a collagenous tissue subjected to isometric constraints during heating. This paper presents the first biaxial stress-stretch data on a collagenous membrane (epicardium) before and after heating while subjected to various biaxial isometric constraints. It was found that isometric heating does not allow the increase in stiffness at low strains that occurs following isotonic heating. Moreover increasing the degree of stretch prior to heating increased the thermal stability of the tissue consistent with the concept that mechanical loading primarily affects the activation entropy, not the activation energy.     

Histological evidence for the role of mechanical stress in modulating thermal denaturation of collagen

The hyperthermia and thermal denaturation literatures reveal a time-temperature equivalency when heating cells or connective tissues: thermal damage increases with increasing temperature (for the same duration) and increases with increasing duration (for the same temperature). Recent findings conversely suggest that increasing the mechanical loading on a tissue during heating decreases the thermal damage (for a given temperature and duration of heating). Surprisingly, however, there are few histological correlates of such damage. In this paper, we show that progressive light microscopic changes – swelling of collagen bands, thickening of collagen-rich layers, hyalinization, and loss of birefringence~– correlate very well with both increased heating times and decreased mechanical loading. Increased mechanical stress is thus thermally protective and should be considered in the design of clinical procedures that use heating to treat diseases or injuries. P. B. Wells and S. Thomsen contributed equally to this work.     

Heat-induced changes in the finite strain viscoelastic behavioir of a collaagenous tissue

Supra-physiological temperatures are increasingly being used to treat many different soft need for injuries. To identify improved clinical treatments, however, there is a need for better information on the effect of the mechanics on the thermal damage process as well as the effect of the incurred damage on the subsequent mechanical properties. In this paper we report the first biaxial data on the stress relaxation behavior of a collagenous tissue before and after thermal damage. Based on a two-dimensional finite strain viscoelastic model, which incorporates an exponential elastic response, it is shown that the thermal damage can significantly decrease the characteristic time for stress relaxation and the stress residual.     

Effect of thermal damage and biaxial loading on the optical properties of a collagenous tissue

Thermal denaturation can induce marked changes in the optical and mechanical properties of collagenous tissues. The optical properties are important in both therapeutic and diagnostic applications of lasers in medicine. Although mechanical stress can be caused by collagen shrinkage in laser-based therapies, how the mechanical loading state affects the optical properties is not well understood. We used a new computer-controlled biaxial testing system to subject bovine epicardium to various loading conditions both before and after multiple levels of thermal damage. An integrating sphere technique was used to measure transmittance and diffuse reflectance, from which absorption and scattering coefficients were calculated using a Monte Carlo method. Results showed that the scattering coefficient increased with increasing mechanical load but decreased as the degree of thermal damage increased. There was no significant change in the absorption coefficient due to thermal damage over the ranges studied.     

A new model of thermal inactivation and its application to clonogenic survival data for WiDr human colonic adenocarcinoma cells

Based on the analysis of clonogenic survival data for human colonic adenocarcinoma cells (WiDr) after a single heating, a new model is proposed to describe cell survival after hyperthermia quantitatively. The effects of heat are explained as heat-induced cell damage assuming a first-order (single-hit) and a second-order (cumulative damage) process. Thus cell survival at a specified temperature can be described by the linear-quadratic (LQ) model. The proposed model is based on an alternative definition of the (single) thermal dose, given as the (normalized) product of heating time and a specified nonlinear function of the increase in temperature (relative to a threshold temperature) to be interpreted as the thermal dose rate. In further analogy to the modeling of the effects of low-dose-rate radiation, an inherent capacity of the cells to repair sublethal damage is assumed, and these effects are quantified by the usual g factor measuring incomplete repair effects. The model defines thermal dose-response and isoeffect dose relationships, enabling a direct (i. e. single-step) analysis of the available thermal response data. Additionally, the analysis of our data based on heating times in the range from 0 to 360 min and temperatures from 41 to 46 degrees C and covering a broad spectrum of different densities of cells seeded for colony formation did not yield any evidence of the existence of a breaking point usually derived from Arrhenius plots based on the single-hit, multitarget model and the Arrhenius equation. The model includes no specific assumptions describing the development of thermotolerance, which can be assumed to be negligible under our experimental conditions. The proposed thermal dose-response model correlates satisfactorily with the in vitro survival data for WiDr adenocarcinoma cells.     

Thermal injury kinetics in electrical trauma.

The distribution of electrical current and the resultant Joule heating in tissues of the human upper extremity for a worst-case hand-to-hand high-voltage electrical shock was modelled by solving the Bioheat equation using the finite element method. The model of the upper extremity included skin, fat, skeletal muscle, and bone. The parameter sets for these tissues included specific thermal and electrical properties and their respective tissue blood flow rates. The extent of heat mediated cellular injury was estimated by using a damage rate equation based on a single energy barrier chemical reaction model. No cellular injury was assumed to occur for temperatures less than 42 degrees C. This model was solved for the duration of Joule heating required to produce membrane damage in cells, termed the lethal time (of contact) for injury. LT's were determined for contact voltages ranging from 5 to 20 kV. For a 10,000 volt electrical shock LT's for skeletal muscle are predicted to be: 0.5 second in the distal forearm, 1.1 second in the mid-forearm, 1.2 second in the proximal elbow, and 2.0 seconds in the mid-arm. This analysis of the electrical shock provides useful insight into the mechanisms of resultant tissue damage and provides important performance guidelines for the development of safety devices.     

Stress and strain localization in stretched collagenous tissues via a multiscale modelling approach

Mechanobiology of cells in soft collagenous tissues is highly affected by both tissue response at the macroscale and stress/strain localization mechanisms due to features at lower scales. In this paper, the macroscale mechanical behaviour of soft collagenous tissues is modelled by a three-level multiscale approach, based on a multi-step homogenisation technique from nanoscale up to the macroscale. Nanoscale effects, related to both intermolecular cross-links and collagen mechanics, are accounted for, together with geometric nonlinearities at the microscale. Moreover, an effective submodelling procedure is conceived in order to evaluate the local stress and strain fields at the microscale, which is around and within cells. Numerical results, obtained by using an incremental finite element formulation and addressing stretched tendinous tissues, prove consistency and accuracy of the model at both macroscale and microscale, confirming also the effectiveness of the multiscale modelling concept for successfully analysing physiopathological processes in biological tissues.     

Effects of heat-induced damage on the radial component of thermal diffusivity of bovine aorta

The extent of the change in thermal diffusivity of soft tissues due to heat-induced damage is not well known. Reported here are the results of using the flash method to measure the through-the-wall component of thermal diffusivity of bovine aorta before and after the tissue has undergone two hours of heating at 75 degrees C. The measurements indicate a 10.1 percent increase in the thermal diffusivity of the tissue post-heating. While this change may not result in a significant change in the tissue temperature profile, further study is needed to quantify the thermal diffusivity in other coordinate directions, as well as the mechanisms by which this change in properties occurs.     

MicroCT image based simulation to design heating protocols in magnetic nanoparticle hyperthermia for cancer treatment

ObjectivesThe objective is to design heating protocols to completely damage PC3 tumors after a single magnetic nanoparticle hyperthermia session with minimal collateral thermal damage, based on microCT image generated tumor and mouse models.MethodsTumor geometries and volumetric heat generation rate distributions that are generated from microCT scans in our previous study are imported into COMSOL 4.3® multiphysics for heat transfer simulations and heating protocol design using the Arrhenius damage model. Then, parametric studies are performed to evaluate how significantly the infusion rate affects the protocol design and its resulted collateral thermal damage.ResultsThe simulated temperature field in the generated tumor geometry and volumetric heat generation rate distribution are reasonable and correlates well with the amount of the total thermal energy deposited into the tumors. The time needed for complete thermal damage is determined to be approximately 12 min or 25 min if one uses the Arrhenius integral Ω equal to 1 or 4 as the damage threshold, when the infusion rate is 3 μL/min. The heating time increases 26% or 91% in the higher infusion rate groups of 4 or 5 μL/min, respectively. Collateral thermal damage to the surrounding tissue is also assessed. Although the two larger infusion rate groups can still cause thermal damage to the entire tumor, the collateral thermal damage would have exceeded the design criterion of 5%, while the assessment criterion is acceptable only in the infusion rate group of 3 μL/min. Based on the results of this study, we identify an injection strategy and heating protocols to be implemented in future animal experiments to evaluate treatment efficacy for model validation.     

Selective freezing of target biological tissues after injection of solutions with specific thermal properties

Cryosurgery is a minimally invasive surgical technique that employs the destructive effect of freezing to eradicate undesirable tissues. This paper proposes a flexible method to control the size and shape of the iceball by injecting solutions with specific thermal properties into the target tissues, to enhance freezing damage to the diseased tissues while preserving the normal tissues from injury. The cryosurgical procedure was performed using a minimally invasive cryoprobe cooled by liquid nitrogen (LN2) to obtain deep regional freezing. Several needle thermocouples were applied simultaneously to record the transient temperature to detect the freezing effect on the tissues. Simulation experiments on biological tissue (fresh pork) were performed in vitro and four different liquids were injected into the test materials; these were distilled water, an aqueous suspension of aluminum nanoparticles in water, ethanol, and a 10% solution of the cryoprotective agent dimethyl sulfoxide (Me2SO). The experimental results demonstrate that the localized injection of an appropriate solution could enhance the tumor-killing effect without altering the freezing conditions. The study also suggests the potential value of combining cryosurgery with other therapeutic methods, such as electrical, chemical, and thermal treatments, to develop new clinical modalities in the near future.     

The development of structural and mechanical anisotropy in fibroblast populated collagen gels

An in vitro model system was developed to study structure-function relationships and the development of structural and mechanical anisotropy in collagenous tissues. Fibroblast-populated collagen gels were constrained either biaxially or uniaxially. Gel remodeling, biaxial mechanical properties, and collagen orientation were determined after 72 h of culture. Collagen gels contracted spontaneously in the unconstrained direction, uniaxial mechanical constraints produced structural anisotropy, and this structural anisotropy was associated with mechanical anisotropy. Cardiac and tendon fibroblasts were compared to test the hypothesis that tendon fibroblasts should generate greater anisotropy in vitro. However, no differences were seen in either structure or mechanics of collagen gels populated with these two cell types, or between fibroblast populated gels and acellular gels. This study demonstrates our ability to control and measure the development of structural and mechanical anisotropy due to imposed mechanical constraints in a fibroblast-populated collagen gel model system. While imposed constraints were required for the development of anisotropy in this system, active remodeling of the gel by fibroblasts was not. This model system will provide a basis for investigating structure-function relationships in engineered constructs and for studying mechanisms underlying the development of anisotropy in collagenous tissues.     

A two-state cell damage model under hyperthermic conditions: theory and in vitro experiments

The ultimate goal of cancer treatment utilizing thermotherapy is to eradicate tumors and minimize damage to surrounding host tissues. To achieve this goal, it is important to develop an accurate cell damage model to characterize the population of cell death under various thermal conditions. The traditional Arrhenius model is often used to characterize the damaged cell population under the assumption that the rate of cell damage is proportional to exp(-EaRT), where Ea is the activation energy, R is the universal gas constant, and T is the absolute temperature. However, this model is unable to capture transition phenomena over the entire hyperthermia and ablation temperature range, particularly during the initial stage of heating. Inspired by classical statistical thermodynamic principles, we propose a general two-state model to characterize the entire cell population with two distinct and measurable subpopulations of cells, in which each cell is in one of the two microstates, viable (live) and damaged (dead), respectively. The resulting cell viability can be expressed as C(tau,T)=exp(-Phi(tau,T)kT)(1+exp(-Phi(tau,T)kT)), where k is a constant. The in vitro cell viability experiments revealed that the function Phi(tau,T) can be defined as a function that is linear in exposure time tau when the temperature T is fixed, and linear as well in terms of the reciprocal of temperature T when the variable tau is held as constant. To determine parameters in the function Phi(tau,T), we use in vitro cell viability data from the experiments conducted with human prostate cancerous (PC3) and normal (RWPE-1) cells exposed to thermotherapeutic protocols to correlate with the proposed cell damage model. Very good agreement between experimental data and the derived damage model is obtained. In addition, the new two-state model has the advantage that is less sensitive and more robust due to its well behaved model parameters.     

Histochemical model studies of enzyme activity after thermal damage

Summary The reliability of histochemical determinations of the enzyme activity after thermal damage has been studied with the aid of two model systems. Polyacrylamide films and erythrocyte ghosts containing either -glucuronidase or alkaline phosphatase, were submitted to heating and the activities retained were assessed both biochemically and histochemically. For the enzymes studied, the results show that tissue alterations induced by heat can influence histochemical reaction procedures, and that with these model systems, factors which are important for the histochemical quantitation of enzyme activities in thermally damaged tissues can be evaluated quantitatively. Potentialities of these model systems in the study of evaluating thermal damage through histochemical enzyme activity determinations, are discussed.To whom offprint requests should be sent     

Multiscale model predicts tissue-level failure from collagen fiber-level damage

Excessive tissue-level forces communicated to the microstructure and extracellular matrix of soft tissues can lead to damage and failure through poorly understood physical processes that are multiscale in nature. In this work, we propose a multiscale mechanical model for the failure of collagenous soft tissues that incorporates spatial heterogeneity in the microstructure and links the failure of discrete collagen fibers to the material response of the tissue. The model, which is based on experimental failure data derived from different collagen gel geometries, was able to predict the mechanical response and failure of type I collagen gels, and it demonstrated that a fiber-based rule (at the micrometer scale) for discrete failure can strongly shape the macroscale failure response of the gel (at the millimeter scale). The model may be a useful tool in predicting the macroscale failure conditions for soft tissues and engineered tissue analogs. In addition, the multiscale model provides a framework for the study of failure in complex fiber-based mechanical systems in general.     

Experimental validation of an inverse heat transfer algorithm for optimizing hyperthermia treatments

Hyperthermia is a cancer treatment modality in which body tissue is exposed to elevated temperatures to destroy cancerous cells. Hyperthermia treatment planning refers to the use of computational models to optimize the heating protocol with the goal of isolating thermal damage to predetermined treatment areas. This paper presents an algorithm to optimize a hyperthermia treatment protocol using the conjugate gradient method with the adjoint problem. The output of the minimization algorithm is a heating protocol that will cause a desired amount of thermal damage. The transient temperature distribution in a cylindrical region is simulated using the bioheat transfer equation. Temperature and time are integrated to calculate the extent of thermal damage in the region via a first-order rate process based on the Arrhenius equation. Several validation experiments are carried out by applying the results of the minimization algorithm to an albumen tissue phantom. Comparisons of metrics describing the damage region (the height and radius of the volume of thermally ablated phantom) show good agreement between the desired extent of damage and the measured extent of damage. The sensitivity of the bioheat transfer model and the Arrhenius damage model to their constituent parameters is calculated to create a tolerable range of error between the desired and measured extent of damage. The measured height and radius of the ablated region fit well within the tolerable range of error found in the sensitivity analysis.     

A transient heating technique for the measurement of thermal properties of perfused biological tissue

Knowledge of tissue thermal transport properties is imperative for any therapeutic medical tool which employs the localized application of heat to perfused biological tissue. In this study, several techniques are proposed to measure local tissue thermal diffusion by heating with a focused ultrasound field. Transient as well as near steady-state heat inputs are discussed and examined for their suitability as a measurement technique for either tissue thermal diffusivity or perfusion rate. It is shown that steady-state methods are better suited for the measurement of perfusion; however the uncertainty in the perfusion measurement is directly related to knowledge of the tissue's intrinsic thermal diffusivity. Results are presented for a transient thermal pulse technique for the measurement of the thermal diffusivity of perfused and nonperfused tissues, in vitro and in vivo. Measurements conducted in plexiglas, animal muscle, kidney and brain concur with tabulated values and show a scatter from 5-15 percent from the mean; measurements made in perfused muscle and brain compare well with the nonperfused values. An estimate of the error introduced by the effect of perfusion shows that except for highly perfused kidney tissue the effect of perfusion is less than the experimental scatter. This validation of the tissue heat transfer model will allow its eventual extension to the simultaneous measurement of local tissue thermal diffusivity and perfusion.     

Modeling of laser coagulation of tissue with MRI temperature monitoring

Light energy from a laser source that is delivered into body tissue via a fiber-optic probe with minimal invasiveness has been used to ablate solid tumors. This thermal coagulation process can be guided and monitored accurately by continuous magnetic resonance imaging (MRI) since the laser energy delivery system does not interfere with MRI. This report deals with mathematical modeling and analysis of laser coagulation of tissue. This model is intended for "real-time" analysis of magnetic resonance images obtained during the coagulation process to guide clinical treatment. A mathematical model is developed to simulate the thermal response of tissue to a laser light heating source. For fast simulation, an approximate solution of the thermal model is used to predict the dynamics of temperature distribution and tissue damage induced by a laser energy line source. The validity of these simulations is tested by comparison with MRI-based temperature data acquired from in vivo experiments in rabbits. The model-simulated temperature distribution and predicted lesion dynamics correspond closely with MRI-based data. These results demonstrate the potential for using this combination of fast modeling and MRI technologies during laser heating of tissue for online prediction of tumor lesion size during laser heating.     

Interplay of temperature,thermal‐stresses and strains in laser‐assisted modification of collagenous tissues: Speckle‐contrast and OCT‐based studies

Moderate heating of collagenous tissues such as cartilage and cornea by infrared laser irradiation can produce biologically nondestructive structural rearrangements and relaxation of internal stresses resulting in the tissue reshaping. The reshaping results and eventual changes in optical and biological properties of the tissue strongly depend on the laser‐irradiation regime. Here, a speckle‐contrast technique based on monochromatic illumination of the tissue in combination with strain mapping by means of optical coherence elastography (OCE) is applied to reveal the interplay between the temperature and thermal stress fields producing tissue modifications. The speckle‐based technique ensured en face visualization of cross correlation and contrast of speckle images, with evolving proportions between contributions of temperature increase and thermal‐stresses determined by temperature gradients. The speckle‐technique findings are corroborated by quantitative OCE‐based depth‐resolved imaging of irradiation‐induced strain‐evolution. The revealed relationships can be used for real‐time control of the reshaping procedures (e.g., for laser shaping of cartilaginous implants in otolaryngology and maxillofacial surgery) and optimization of the laser‐irradiation regimes to ensure the desired reshaping using lower and biologically safer temperatures. The figure of waterfall OCE‐image demonstrates how the strain‐rate maximum arising in the heating‐beam center gradually splits and drifts towards the zones of maximal thermal stresses located at the temperature‐profile slopes.