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.     

A self-heated thermistor technique to measure effective thermal properties from the tissue surface

A microcomputer based instrument to measure effective thermal conductivity and diffusivity at the surface of a tissue has been developed. Self-heated spherical thermistors, partially embedded in an insulator, are used to simultaneously heat tissue and measure the resulting temperature rise. The temperature increase of the thermistor for a given applied power is a function of the combined thermal properties of the insulator, the thermistor, and the tissue. Once the probe is calibrated, the instrument accurately measures the thermal properties of tissue. Conductivity measurements are accurate to 2 percent and diffusivity measurements are accurate to 4 percent. A simplified bioheat equation is used which assumes the effective tissue thermal conductivity is a linear function of perfusion. Since tissue blood flow strongly affects heat transfer, the surface thermistor probe is quite sensitive to perfusion.     

Thermal property measurements on biological materials at subzero temperatures.

The self-heated thermistor technique was used to measure the thermal conductivity and thermal diffusivity of biomaterials at low temperatures. Thermal standards were selected to calibrate the system at temperatures from -10 degrees C to -70 degrees C. The thermal probes were constructed with a convection barrier which eliminates convection inside liquid samples of low viscosity, without affecting the conductivity and diffusivity results. Using this technique, the thermal conductivity and diffusivity of two organ perfusates (HP5 and HP5 + 2M glycerol), one kidney phantom (a low ionic strength gel), as well as rabbit kidney cortex have been measured from -10 degrees C to -70 degrees C.     

Effect of cell arrangement and interstitial volume fraction on the diffusivity of monoclonal antibodies in tissue.

We present theoretical calculations relating the effective diffusivity of monoclonal antibodies in tissue (Deff) to the actual diffusivity in the interstitium (Dint) and the interstitial volume fraction phi. Measured diffusivity values are effective values, deduced from concentration profiles with the tissue treated as a continuum. By using homogenization theory, the ratio Deff/Dint is calculated for a range of interstitial volume fractions from 10 to 65%. It is assumed that only diffusion in the interstitial spaces between cells contributes to the effective diffusivity. The geometries considered have cuboidal cells arranged periodically, with uniform gaps between cells. Deff/Dint is found to generally be between (2/3) phi and phi for these geometries. In general, the pathways for diffusion between cells are not straight. The effect of winding pathways on Deff/Dint is examined by varying the arrangement of the cells, and found to be slight. Also, the estimates of Deff/Dint are shown to be insensitive to typical nonuniformities in the widths of gaps between cells. From our calculations and from published experimental measurements of the effective diffusivity of an IgG polyclonal antibody both in water and in tumor tissue, we deduce that the diffusivity of this molecule in the interstitium is one-tenth to one-twentieth its diffusivity in water. We also conclude that exclusion of molecules from cells (an effect independent of molecular weight) contributes as much as interstitial hindrance to the reduction of effective diffusivity, for small interstitial volume fractions (around 20%). This suggests that the increase in the rate of delivery to tissues resulting from the use of smaller molecular-weight molecules (such as antibody fragments or bifunctional antibodies) may be less than expected.     

Site-specific effects of compression on macromolecular diffusion in articular cartilage

Articular cartilage is the connective tissue that lines joints and provides a smooth surface for joint motion. Because cartilage is avascular, molecular transport occurs primarily via diffusion or convection, and cartilage matrix structure and composition may affect diffusive transport. Because of the inhomogeneous compressive properties of articular cartilage, we hypothesized that compression would decrease macromolecular diffusivity and increase diffusional anisotropy in a site-specific manner that depends on local tissue strain. We used two fluorescence photobleaching methods, scanning microphotolysis and fluorescence imaging of continuous point photobleaching, to measure diffusion coefficients and diffusional anisotropy of 70 kDa dextran in cartilage during compression, and measured local tissue strain using texture correlation. For every 10% increase in normal strain, the fractional change in diffusivity decreased by 0.16 in all zones, and diffusional anisotropy increased 1.1-fold in the surface zone and 1.04-fold in the middle zone, and did not change in the deep zone. These results indicate that inhomogeneity in matrix structure and composition may significantly affect local diffusive transport in cartilage, particularly in response to mechanical loading. Our findings suggest that high strains in the surface zone significantly decrease diffusivity and increase anisotropy, which may decrease transport between cartilage and synovial fluid during compression.     

Effect of volumetric water content on thermal properties of dairy cattle feces mixed with sawdust

This paper describes the thermal properties (effective thermal conductivity and thermal diffusivity) of an organic waste used to model the composting process in relation to volumetric water content at 20°C. The organic waste was a mixture of fresh dairy cattle feces and sawdust with a ratio of one-to-one on a dry weight basis. The thermal probe method was used to determine the effective thermal conductivity and diffusivity. The effective thermal conductivities were found to increase with volumetric water content, and ranged from 0.0500 to 0.202 W m⁻¹ K⁻¹ at volumetric water contents of 0% and 44.2%, respectively. The thermal diffusivity was not affected by the volumetric water content, and was found to have a mean value of 1.08 × 10⁻⁷ m² s⁻¹.     

Review of biomaterial thermal property measurements in the cryogenic regime and their use for prediction of equilibrium and non-equilibrium freezing applications in cryobiology

It is well accepted in cryobiology that the temperature history and cooling rates experienced in biomaterials during freezing procedures correlate strongly with biological outcome. Therefore, heat transfer measurement and prediction in the cryogenic regime is central to the field. Although direct measurement of temperature history (i.e. heat transfer) can be performed, accuracy is usually achieved only for local measurements within a given system and cannot be readily generalized to another system without the aid of predictive models. The accuracy of these models rely upon thermal properties which are known to be highly dependent on temperature, and in the case of significant cryoprotectant loading, also on crystallized fraction. In this work, we review the available thermal properties of biomaterials in the cryogenic regime. The review shows a lack of properties for many biomaterials in the subzero temperature domain, and especially for systems with cryoprotective agents. Unfortunately, use of values from the limited data available (usually only down to −40 °C) lead to an underestimation of thermal property change (i.e. conductivity rise and specific heat drop due to ice crystallization) with lower temperatures. Conversely, use of surrogate values based solely on ice thermal properties lead to an overestimation of thermal property change for most biomaterials. Additionally, recent work extending the range of available thermal properties to −150 °C has shown that the thermal conductivity will drop in both PBS and tissue (liver) due to amorphous/glassy phases (versus crystalline) of biomaterials with the addition of cryoprotective additives such as glycerol. Thus, we investigated the implications of using approximated or constant property values versus measured temperature-dependent values for predicting temperature history during freezing in PBS (phosphate-buffered saline) and porcine liver with and without cryoprotectants (glycerol). Using measured property values (thermal conductivity, specific heat, and latent heat of phase change) of porcine liver, a standard was created which showed that values based on surrogate ice properties under-predicted cooling times, while constant properties (i.e. based on limited data reported near the freezing point) over-predicted cooling times. Additionally, a new iterative numerical method that accommodates non-equilibrium cooling effects as a function of time and position (i.e. crystallization versus amorphous phase) was used to predict temperature history during freezing in glycerol loaded systems. Results indicate that in addition to the increase in cooling times due to the lowering of thermal diffusivity with more glycerol, non-equilibrium effects such as the prevention of maximal crystallization (i.e. amorphous phases) will further increase required cooling times. It was also found that the amplified effect of non-equilibrium cooling and crystallization with system size prevents the thermal history to be described with non-dimensional lengths, such as was possible under equilibrium cooling. These results affirm the need to use accurate thermal properties that incorporate temperature dependence and crystallized fraction. Further studies are needed to extract thermal properties of other important biomaterials in the subzero temperature domain and to develop accurate numerical methods which take into account non-equilibrium cooling events encountered in cryobiology when partial or total vitrification occurs.     

A novel three-phase model of brain tissue microstructure

We propose a novel biologically constrained three-phase model of the brain microstructure. Designing a realistic model is tantamount to a packing problem, and for this reason, a number of techniques from the theory of random heterogeneous materials can be brought to bear on this problem. Our analysis strongly suggests that previously developed two-phase models in which cells are packed in the extracellular space are insufficient representations of the brain microstructure. These models either do not preserve realistic geometric and topological features of brain tissue or preserve these properties while overestimating the brain's effective diffusivity, an average measure of the underlying microstructure. In light of the highly connected nature of three-dimensional space, which limits the minimum diffusivity of biologically constrained two-phase models, we explore the previously proposed hypothesis that the extracellular matrix is an important factor that contributes to the diffusivity of brain tissue. Using accurate first-passage-time techniques, we support this hypothesis by showing that the incorporation of the extracellular matrix as the third phase of a biologically constrained model gives the reduction in the diffusion coefficient necessary for the three-phase model to be a valid representation of the brain microstructure.     

Capture of spatially homogeneous chemical reactions in tissue by freezing.

A useful technique in studying the saturation of hemoglobin in erythrocytes or myoglobin in tissue is cryophotometry, in which tissue is frozen for later spectrophotometric analysis. A general question associated with this technique is whether the freezing process alters the chemical state. This paper presents a theoretical analysis of the simplest model relevant to that question. We study the effect of rapid cooling on a spatially homogeneous chemical reaction. The analysis shows that changes during freezing are negligible near the boundary to which the heat sink is applied, but can be significant deeper in the sample. The distance from the boundary at which the changes during freezing become appreciable can be expressed simply in terms of the chemical reaction rates and the thermal diffusivity of the tissue. Detailed results are given for the case of oxygen and myoglobin in skeletal muscle.     

Characterization of Thermal Transport in One-dimensional Solid Materials

The TET (transient electro-thermal) technique is an effective approach developed to measure the thermal diffusivity of solid materials, including conductive, semi-conductive or nonconductive one-dimensional structures. This technique broadens the measurement scope of materials (conductive and nonconductive) and improves the accuracy and stability. If the sample (especially biomaterials, such as human head hair, spider silk, and silkworm silk) is not conductive, it will be coated with a gold layer to make it electronically conductive. The effect of parasitic conduction and radiative losses on the thermal diffusivity can be subtracted during data processing. Then the real thermal conductivity can be calculated with the given value of volume-based specific heat (ρc_p), which can be obtained from calibration, noncontact photo-thermal technique or measuring the density and specific heat separately. In this work, human head hair samples are used to show how to set up the experiment, process the experimental data, and subtract the effect of parasitic conduction and radiative losses.     

Measurement of Gd-DTPA diffusion through PVA hydrogel using a novel magnetic resonance imaging method.

Polyvinyl alcohol-cryogel (PVA-C) is a hydrogel that is an excellent tissue mimic. In order to characterize mass transfer in this material, as well as to demonstrate in principle the ability to noninvasively measure solute diffusion in tissue, we measured the diffusion coefficient of the magnetic resonance (MR) contrast agent gadolinium diethylene triaminopentaacetic acid (Gd-DTPA) through PVA-C using a clinical MR imager. The method involved filling thick-walled rectangular PVA-C "cups" with known concentrations of Gd-DTPA solutions. Then by using a fast inversion recovery spin echo MR imaging protocol, a signal "null" contour was created in the MR image that corresponded to a second, known concentration of Gd-DTPA. By collecting a series of MR images through the PVA-C wall as a function of time, the displacement of this second known isoconcentration contour could be tracked. Application of Fick's second law of diffusion yielded the diffusion coefficient. Seven separate experiments were performed using various combinations of initial concentrations of Gd-DTPA within the PVA-C cups (3.2, 25.6, or 125 mM) and tracked isoconcentrations contours (0.096, 0.182, or 0.435 mM Gd-DTPA). The experimental results and the predictions of Fick's law were in excellent agreement. The diffusivity of Gd-DTPA through 10% PVA hydrogel was found to be (2.6 +/- 0.04) x 10(-10) m(2)/s (mean +/- s.e.m.). Separate permeability studies showed that the diffusion coefficient of Gd-DTPA through this hydrogel did not change with an applied pressure of up to 7.1 kPa. Accurate measurements could be made within 30 min if suitable Gd-DTPA concentrations were selected. Due to the excellent repeatability and fast data acquisition time, this technique is very promising for future in vivo studies of species transport in tissue.     

A novel method for measuring the thermal conductivity of organisms

Based on the theories of tissue optics and artificial neural network, the relationship between the optical properties and biological parameters was studied, and a new experimental method was derived. The properties of the organism were obtained indirectly by a black-box model derived by self-study of the artificial neural network between optical parameters and thermo-physical properties without using the heat transfer equation. In this method, the energy of light in diffuse radiation, diffuse transmission and collimated transmission was absorbed by a dual-integrating sphere experimental system of a spectrometer, and the spectrogram of the energy was obtained. Combining these spectral data of the energy, the diffuse-reflecting power, the diffuse transmissivity and the collimated transmissivity were calculated. The calculated results were taken as the input parameters of a black-box model. The experimental results show that there are apparent differences between the spectrogram of the energy on the diffuse radiation, the diffuse transmission and the collimated transmission of different matters, while there is a little difference in the same matter. Each spectrogram has its own characteristic. The values of the four thermal properties including the density, the constant pressure specific heat, the thermal diffusivity and the viscosity were calculated using the black-box model. Compared with the real values the calculated one has an average relative error between −5% and 5%. The conductivity of the tongue is 0.68 W/(m K) that calculated from the value of the density, the constant pressure specific heat and the thermal diffusivity. The results also show that there is a little difference on the conductivities in the longitudinal cross-section and the transverse section, but the effect of temperature on the conductivity of the tongue is not apparent. The difference implies the anisotropy of the properties of the organism, which cannot be easily obtained by a conventional experimental method.     

Tracer measurements of non-equilibrium volumes of distribution

According to conventional theory the product of the transport flowrate and the mean transit time of a tracer through a system yields the equilibrium volume of distribution for the tracer, regardless of tracer kinetics or space geometry. Experimental results do not support this notion. The influence of measurement time on the volume measured with a bolus technique is addressed using systems theory to analyze a tissue-impedance form of the Sangren-Sheppard model. Assymptotic solutions show that the volume estimates are governed by a time constant, tau, related to diffusion in the tissue, to tissue capacity, and to wall permeability, and by a dimensionless ratio, f, describing a relation of tau to vascular transport time. A third parameter, g, describing the relative contributions to overall resistance to diffusion of effective permeability and of limited diffusivity in the tissue, is shown to be of less importance. The derived tau is similar to but not equivalent to the often cited "characteristic time". The "equilibrium" volume of distribution is defined as that which would be measured if equilibrium were allowed to establish. The "non-equilibrium" volume of distribution is defined as that which would be measured given finite times and is shown to approach the "equilibrium" volume as such times increase. Tracer equilibration is not required to accurately measure the "equilibrium" volume. When there is no flow limitation (f much less than 1) a measurement time of tau (plus vascular transit time) would yield a "non-equilibrium" volume only 33% of the "equilibrium" volume; a time of 2 tau would yield 55%; a time of 10 tau would yield effectively the total equilibrium volume. Finite diffusivity in tissue and permeability restrictions can have significant effects on the proportion of the volume measured.     

Thermal perturbation differential spectra of ribonucleic acids. I. Hydration effects.

A relatively important change in UV absorption is observed upon thermal perturbation of nucleotide solutions. Comparison of these thermal perturbation spectra of nucleic acid residues with solvent perturbation spectra of the same compounds suggests that this spectral change can most probably be attributed to temperature induced hydration change of the bases. This conclusion is confirmed by the results obtained from acid-base perturbation spectra of these nucleotides as well as thermal perturbation spectra of nucleotides containing modified bases. It is shown that this temperature dependent change in UV absorption is also present in dinucleoside monophosphates. In that case, this effect is superimposed upon the well known change in absorbance due to the unstacking of the bases during heating.     

Mechanobiology of low-density lipoprotein transport within an arterial wall—Impact of hyperthermia and coupling effects

The effects of hyperthermia, coupling attributes and property variations on Low-density lipoprotein (LDL) transport within a multi-layered wall while accounting for the fluid structure interaction (FSI) is analyzed in this work. To understand the potential impact of the hyperthermia process, thermo-induced attributes are incorporated, accounting for the plasma flow, mass transfer, as well as the elastic wall structure. The coupling effect of osmotic pressure, Soret and Dufour diffusion is discussed and their influence on LDL transport is examined, demonstrating that only the Soret effect needs to be accounted for. The effect of thermal expansion on changing the behavior of flow, mass transport, and elastic structure is illustrated and analyzed while incorporating the variations in the effective LDL diffusivity and consumption rate, as well as other dominating parameters. It is shown that hyperthermia results in an enhancement in LDL transport by increasing the concentration levels within the arterial wall.     

Environmental Synthesis of Few Layers Graphene Sheets Using Ultrasonic Exfoliation with Enhanced Electrical and Thermal Properties

In this paper, we report how few layers graphene that can be produced in large quantity with low defect ratio from exfoliation of graphite by using a high intensity probe sonication in water containing liquid hand soap and PVP. It was founded that the graphene powder obtained by this simple exfoliation method after the heat treatment had an excellent exfoliation into a single or layered graphene sheets. The UV-visible spectroscopy, FESEM, TEM, X-ray powder diffraction and Raman spectroscopy was used to analyse the graphene product. The thermal diffusivity of the samples was analysed using a highly accurate thermal-wave cavity photothermal technique. The data obtained showed excellent enhancement in the thermal diffusivity of the graphene dispersion. This well-dispersed graphene was then used to fabricate an electrically conductive polymer-graphene film composite. The results demonstrated that this low cost and environmental friendly technique allowed to the production of high quality layered graphene sheets, improved the thermal and electrical properties. This may find use in the wide range of applications based on graphene.     

Thermally induced increase in energy transport capacity of silkworm silks

This work reports on the first study of thermally induced effect on energy transport in single filaments of silkworm (Bombyx mori) fibroin degummed mild (type 1), moderate (type 2), to strong (type 3). After heat treatment from 140 to 220°C, the thermal diffusivity of silk fibroin type 1, 2, and 3 increases up to 37.9, 20.9, and 21.5%, respectively. Our detailed scanning electron microscopy study confirms that the sample diameter change is almost negligible before and after heat treatment. Raman analysis is performed on the original and heat‐treated (at 147°C) samples. After heat treatment at 147°C, the Raman peaks at 1081, 1230, and 1665 cm^?1 become stronger and narrower, indicating structural transformation from amorphous to crystalline. A structure model composed of amorphous, crystalline, and laterally ordered regions is proposed to explain the structural change by heat treatment. Owing to the close packing of more adjacent laterally ordered regions, the number and size of the crystalline regions of Bombyx mori silk fibroin increase by heat treatment. This structure change gives the observed significant thermal diffusivity increase by heat treatment. © 2014 Wiley Periodicals, Inc. Biopolymers 101: 1029–1037, 2014.     

Effects of Fiber Type and Size on the Heterogeneity of Oxygen Distribution in Exercising Skeletal Muscle

The process of oxygen delivery from capillary to muscle fiber is essential for a tissue with variable oxygen demand, such as skeletal muscle. Oxygen distribution in exercising skeletal muscle is regulated by convective oxygen transport in the blood vessels, oxygen diffusion and consumption in the tissue. Spatial heterogeneities in oxygen supply, such as microvascular architecture and hemodynamic variables, had been observed experimentally and their marked effects on oxygen exchange had been confirmed using mathematical models. In this study, we investigate the effects of heterogeneities in oxygen demand on tissue oxygenation distribution using a multiscale oxygen transport model. Muscles are composed of different ratios of the various fiber types. Each fiber type has characteristic values of several parameters, including fiber size, oxygen consumption, myoglobin concentration, and oxygen diffusivity. Using experimentally measured parameters for different fiber types and applying them to the rat extensor digitorum longus muscle, we evaluated the effects of heterogeneous fiber size and fiber type properties on the oxygen distribution profile. Our simulation results suggest a marked increase in spatial heterogeneity of oxygen due to fiber size distribution in a mixed muscle. Our simulations also suggest that the combined effects of fiber type properties, except size, do not contribute significantly to the tissue oxygen spatial heterogeneity. However, the incorporation of the difference in oxygen consumption rates of different fiber types alone causes higher oxygen heterogeneity compared to control cases with uniform fiber properties. In contrast, incorporating variation in other fiber type-specific properties, such as myoglobin concentration, causes little change in spatial tissue oxygenation profiles.     

Analysis of thermal stress in cryosurgery of kidneys

In this study, the thermal stress distribution in cryosurgery of kidney was investigated using a multiphysics finite element model developed in ANSYS (V8.1). The thermal portion of the model was verified using experimental data and the mechanics portion of the model (elastic) was verified using classic analytical solutions. Temperature dependent thermal and mechanical properties were used in the model. Moreover, the model accounts for thermal expansion due to both thermal expansion in single phase and volumetric expansion associated with phase change of tissue water to ice. For a clinical cylindrical cryoprobe inserted into the renal cortex from the top-middle renal capsule, it was found that the thermal stress distributions along the radial position are very different at different depths from the top renal capsule. The thermal stress is much higher at both ends than in the middle of the cryoprobe surface. It was found that there might be more tissue next to the top renal capsule than other region undergoing microcrack formation or plastic deformation. Furthermore, it was found that macrocrack formation is more likely to occur in tissue adjacent to the cryoprobe surface (especially on the sharp point tip) and during the thawing phase of cryosurgery. It was further found that the volumetric expansion associated with phase change induced much higher thermal stress than thermal expansion in a single phase and might therefore be the main cause of the frequently observed crack formation shortly after initiation of thawing in cryosurgery. Because the thermal stress adjacent to the cryoprobe is much higher than the yield stress of frozen renal tissue, a plastic stress model is required for better modeling of the thermal stress distribution in cryosurgery of kidney in future. However the computational effort will then be drastically increased due to the strong nonlinear nature of the plastic model and more experimental studies are indispensable for better understanding of the mechanical behavior of frozen tissue in cryosurgery.