Estimation of surface heat flux and temperature distributions in a multilayer tissue based on the hyperbolic model of heat conduction

In this study, an inverse algorithm based on the conjugate gradient method and the discrepancy principle is applied to solve the inverse hyperbolic heat conduction problem in estimating the unknown time-dependent surface heat flux in a skin tissue, which is stratified into epidermis, dermis, and subcutaneous layers, from the temperature measurements taken within the medium. Subsequently, the temperature distributions in the tissue can be calculated as well. The concept of finite heat propagation velocity is applied to the modeling of the bioheat transfer problem. The inverse solutions will be justified based on the numerical experiments in which two different heat flux distributions are to be determined. The temperature data obtained from the direct problem are used to simulate the temperature measurements. The influence of measurement errors on the precision of the estimated results is also investigated. Results show that an excellent estimation on the time-dependent surface heat flux can be obtained for the test cases considered in this study.     

On-line Estimation of the Rate of Sap Flow in Plant Stems Using Stationary Thermal Response Data

The heat pulse method for the measurement of the rate of sapflow in plants suffers from two drawbacks, viz. the discontinuousnature of the measurements and the lack of a precise mathematicalformulation of the heat fluxes. To overcome these drawbacksa random noise heat signal has been used as an input and twosensor pairs have been used for the measurement. A model isgiven that employs the signal from one sensor pair as inputand the signal from the second pair as output of a heat transportsystem. Thus the adverse effects of radial heat conduction havebeen eliminated. Simulation models with the rate of sap flowas one of the parameters have been fitted to the stationaryresponse data with an on-line parameter optimization algorithm.The method has been validated in applications to artificialdata and to real data obtained from a plastic tube and fromtomato plants. Key words: Sap flow, Heat pulse method, Continuous measurement     

A flow microcalorimetric method for enzyme activity measurements: Application to dihydrofolate reductase

A flow microcalorimetric method was developed for the analysis of enzymatic activities in crude tissue homogenates. It can be applied whenever a heat exchange is involved in an enzymatic reaction. The consequent sensitivity obviously depends on the enthalpy variation observed. Dihydrofolate reductase was chosen as an example; this enzyme is the molecular target of methotrexate, a widely used anticancer agent. This calorimetric method, whose sensitivity limit is 1.48 × 10⁻⁴ units of dihydrofolate reductase per milliliter of reactant medium, allows enzyme activity measurements in tissues with low dihydrofolate reductase levels. A few examples of measurements in animal tissues are given. These measurements are of some interest; indeed, increased activity and increased levels of this enzyme are two of the mechanisms which may explain resistance to methotrexate.     

Impact of acute exercise on brachial artery flow-mediated dilatation in young healthy people

Non-invasive measurement of splanchnic hemodynamics has been utilized in the clinical setting for diagnosis of gastro-intestinal disease, and for determining reserve blood flow (BF) distribution. However, previous studies that measured BF in a "single vessel with small size volume", such as the superior mesenteric and coeliac arteries, were concerned solely with the target organ in the gastrointestinal area, and therefore evaluation of alterations in these single arterial BFs under various states was sometimes limited to "small blood volumes", even though there was a relatively large change in flow. BF in the lower abdomen (BF_Ab) is potentially a useful indicator of the influence of comprehensive BF redistribution in cardiovascular and hepato-gastrointestinal disease, in the postprandial period, and in relation to physical exercise. BF_Ab can be determined theoretically using Doppler ultrasound by subtracting BF in the bilateral proximal femoral arteries (FAs) from BF in the upper abdominal aorta (Ao) above the coeliac trunk. Prior to acceptance of this method of determining a true BF_Ab value, it is necessary to obtain validated normal physiological data that represent the hemodynamic relationship between the three arteries. In determining BF_Ab, relative reliability was acceptably high (range in intra-class correlation coefficient: 0.85-0.97) for three arterial hemodynamic parameters (blood velocity, vessel diameter, and BF) in three repeated measurements obtained over three different days. Bland-Altman analysis of the three repeated measurements revealed that day-to-day physiological variation (potentially including measurement error) was within the acceptable minimum range (95% of confidence interval), calculated as the difference in hemodynamics between two measurements. Mean BF (ml/min) was 2951 ± 767 in Ao, 316 ± 97 in left FA, 313 ± 83 in right FA, and 2323 ± 703 in BF_Ab, which is in agreement with a previous study that measured the sum of BF in the major part of the coeliac, mesenteric, and renal arteries. This review presents the methodological concept that underlies BF_Ab, and aspects of its day-to-day relative reliability in terms of the hemodynamics of the three target arteries, relationship with body surface area, respiratory effects, and potential clinical usefulness and application, in relation to data previously reported in original dedicated research.     

Evaluation of sap flow methods to determine water use by cultivated palms

Sustainable management of water resources allocated to palm crops requires reliable tools for measuring palm water use. Thermometric sap flow methods developed for woody dicot plants hold great potential for use in palms, but there have been few investigations to determine whether such methods can be used successfully in ‘woody’ monocots. Here, we evaluate two sap flow methods for measuring whole-plant water use by potted cocos palms (Syagrus romanzoffiana): the Heat Ratio Method (HRM) and the Compensation Heat Pulse Method (CHPM). Measurements of whole-plant water use from the HRM and the CHPM were compared to gravimetric measurements acquired from an electronic balance. Of the two methods, the HRM gave the most accurate results and it most precisely described patterns of transpiration with respect to environmental conditions and leaf morphology. Estimates of total daily water use from the HRM and the balance were highly correlated (R² = 0.92; P < 0.0001) and very near to a 1:1 relationship—an excellent result given the potential for error associated with each method. As expected, the CHPM was seriously limited at low flow rates, but it agreed well with the HRM at higher flow rates (heat pulse velocity >4 cm h⁻¹). Anatomical investigations revealed that vascular bundles in measured palm fronds were evenly distributed and the distance between bundles was comparable in scale to the diameter of probes of HRM sensors, and most likely an order of magnitude smaller than the probable zone of thermal influence for HRM measurements. This contention was supported by results of mathematical modeling suggesting that HRM heat pulse velocities in palm-like sapwood remain largely unaffected by increases in heterogeneity caused by larger xylem vessels and wider interstitial tissues. Although wounding models for heat pulse sap flow methods have not historically catered for the effects of discrete vascular bundles, they are sufficiently approximate given our empirical validations, and we conclude that palm sapwood is thermally homogenous enough for the HRM and the CHPM to be used without modification. Overall, we present strong evidence that heat pulse methods such as the HRM and the CHPM can be used successfully in woody monocots. Finally, we note that the CHPM is likely to perform better in cases of very high flow rates, while the HRM provides more comprehensive monitoring of the usual range of flow rates including at night, early morning and during water deficit.     

Simultaneous measurement of metabolic heat rate, CO2 production, and O2 consumption by microcalorimetry

This study describes methods and equipment for measurement of metabolic heat rates of cells and tissues under conditions that provide simultaneous determinations of the flux rates of both O2 and CO2. Isothermal measurement of metabolic heats are conducted in a sealed ampule. A trapping solution is employed to absorb metabolic CO2. Absorption of CO2 produces heat at a rate proportional to the rate of CO2 production. Under these conditions, O2 consumption by the tissue results in a decrease in the partial pressure of O2 within the sealed ampule. The decrease in pressure can be monitored with a pressure sensor and related to O2 consumption rates. The combined measurements of heat rates, CO2, and O2 fluxes provide important information on bioenergetic efficiency of cell metabolism. These data can also suggest possible shifts in metabolic pathways or substrate sources as cells develop, or are exposed to effectors, inhibitors, and environmental factors.     

Control of continuous polyhydroxybutyrate synthesis using calorimetry and flow cytometry

The substrate-carbon flow can be controlled in continuous bioreactor cultures by the medium composition, for example, by the C/N ratio. The carbon distribution is optimal when a maximum fraction flows into the desired product and the residual is just sufficient to compensate for the dilution of the microbial catalyst. Undershooting of the latter condition is reflected immediately by changes in the Gibbs energy dissipation and cellular states. Two calorimetric measurement principles were applied to optimize the continuous synthesis of polyhydroxybutyrate (PHB) by Variovorax paradoxus DSM4065 during growth with constantly increasing supply rates of fructose or toxic phenol. Firstly, the changed slope of the heat production rate in a complete heat balanced bioreactor (CHB) indicated optimum carbon channeling into PHB. The extent of the alteration depended directly on the toxic properties of the substrate. Secondly, a flow through calorimeter was connected with the bioreactor as a "measurement loop." The optimum substrate carbon distribution was indicated by a sudden change in the heat production rate independent of substrate toxicity. The sudden change was explained mathematically and exploited for the long-term control of phenol conversion into PHB. LASER flow cytometry measurements distinguished between subpopulations with completely different PHB-content. Populations grown on fructose preserved a constant ratio of two subpopulations with double and quadruple sets of DNA. Cells grown on phenol comprised a third subpopulation with a single DNA set. Rising phenol concentrations caused this subpopulation to increase. It may thus be considered as an indicator of chemostress.     

Intracellular flux analysis in hybridomas using mass balances and in vitro (13)C nmr

Intracellular fluxes are important in defining cellular physiology and its changes in response to environmental variations. Stoichiometric balances combined with extra cellular metabolite measurements were applied to the estimation of intracellular fluxes and the study of energy metabolism in the hybridoma cell line ATCC CRL 1606. Redundant measurements allowed the evaluation of the consistency of the stoichiometry, measurements, and pseudo-steady-state assumption leading to refinement of the assumed biochemistry and identification of measurement errors. To validate the flux estimates, two batch experiments were performed with glucose labeled in the 1 position with (13)C. The distribution of (13)C in secreted lactate was measured via nuclear magnetic resonance spectroscopy (NMR) and compared to that predicted from the estimated intracellular fluxes. There was good agreement between the measured and estimated isotope distributions, demonstrating the validity of the flux estimates obtained from stoichiometric balances. (c) 1995 John Wiley & Sons, Inc.     

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.     

Comparison of two hydrodensitometric methods for estimating percent body fat.

This study compared the two following hydrodensitometric methods for estimating percent body fat (%BF): 1) estimation of residual volume (RV) by helium dilution before and after measurement of immersed mass at RV, and 2) determination of immersed mass at a comfortable level of expiration (approximately functional residual capacity) with measurement of the associated gas volume by oxygen dilution. Twelve men [27.9 +/- 7.5 (SD) yr; 79.32 +/- 12.79 kg; 180.5 +/- 9.9 cm] were tested for %BF via both methods on each of two separate visits within 3 days by using a counterbalanced design. The two helium dilution measurements yielded a technical error of measurement of 0.2% BF and an intraclass correlation coefficient of 0.999. Corresponding values for the oxygen dilution method were 0.4% BF and 0.999, respectively. There was no difference (P = 0.80) between the helium dilution (16.9 +/- 9.3% BF) and oxygen dilution (16.9 +/- 9.4% BF) methods, and the individual differences ranged from -0.7 to 0.6% BF. The interclass correlation coefficient between the two methods was 0.999 with a SE of estimate of 0.4% BF. Whereas both methods were precise and reliable and yielded similar results, the oxygen dilution technique was more expedient and was preferred by the subjects because they were not required to exhale to RV.     

Evaluation of sap flow methods to determine water use by cultivated palms

Sustainable management of water resources allocated to palm crops requires reliable tools for measuring palm water use. Thermometric sap flow methods developed for woody dicot plants hold great potential for use in palms, but there have been few investigations to determine whether such methods can be used successfully in ‘woody’ monocots. Here, we evaluate two sap flow methods for measuring whole-plant water use by potted cocos palms (Syagrus romanzoffiana): the Heat Ratio Method (HRM) and the Compensation Heat Pulse Method (CHPM). Measurements of whole-plant water use from the HRM and the CHPM were compared to gravimetric measurements acquired from an electronic balance. Of the two methods, the HRM gave the most accurate results and it most precisely described patterns of transpiration with respect to environmental conditions and leaf morphology. Estimates of total daily water use from the HRM and the balance were highly correlated (R² = 0.92; P < 0.0001) and very near to a 1:1 relationship—an excellent result given the potential for error associated with each method. As expected, the CHPM was seriously limited at low flow rates, but it agreed well with the HRM at higher flow rates (heat pulse velocity >4 cm h⁻¹). Anatomical investigations revealed that vascular bundles in measured palm fronds were evenly distributed and the distance between bundles was comparable in scale to the diameter of probes of HRM sensors, and most likely an order of magnitude smaller than the probable zone of thermal influence for HRM measurements. This contention was supported by results of mathematical modeling suggesting that HRM heat pulse velocities in palm-like sapwood remain largely unaffected by increases in heterogeneity caused by larger xylem vessels and wider interstitial tissues. Although wounding models for heat pulse sap flow methods have not historically catered for the effects of discrete vascular bundles, they are sufficiently approximate given our empirical validations, and we conclude that palm sapwood is thermally homogenous enough for the HRM and the CHPM to be used without modification. Overall, we present strong evidence that heat pulse methods such as the HRM and the CHPM can be used successfully in woody monocots. Finally, we note that the CHPM is likely to perform better in cases of very high flow rates, while the HRM provides more comprehensive monitoring of the usual range of flow rates including at night, early morning and during water deficit.     

Measuring Changes in Tactile Sensitivity in the Hind Paw of Mice Using an Electronic von Frey Apparatus

Measuring inflammation-induced changes in thresholds of hind paw withdrawal from mechanical pressure is a useful technique to assess changes in pain perception in rodents. Withdrawal thresholds can be measured first at baseline and then following drug, venom, injury, allergen, or otherwise evoked inflammation by applying an accurate force on very specific areas of the skin. An electronic von Frey apparatus allows precise assessment of mouse hind paw withdrawal thresholds that are not limited by the available filament sizes in contrast to classical von Frey measurements. The ease and rapidity of measurements allow for incorporation of assessment of tactile sensitivity outcomes in diverse models of rapid-onset inflammatory and neuropathic pain as multiple measurements can be taken within a short time period. Experimental measurements for individual rodent subjects can be internally controlled against individual baseline responses and exclusion criteria easily established to standardize baseline responses within and across experimental groups. Thus, measurements using an electronic von Frey apparatus represent a useful modification of the well-established classical von Frey filament-based assays for rodent mechanical allodynia that may also be applied to other nonhuman mammalian models.     

The recovery of terminal lymph flow following occlusion

The effects of external pressure on the relative terminal lymphatic flow rate following occlusion of the lymph system were studied. Sulfur colloid tagged with 99mTc was injected into the hind thigh of dogs prior to compressive loading. Initially, the lymphatic clearance of the tracer was measured for approximately forty minutes with no applied external pressure. The terminal lymph vessels were then occluded for thirty minutes with the application of an applied external pressure of 75 mm Hg. Finally, the lymphatic clearance following occlusion was measured with the application of a nonocclusive pressure. External pressures of 0, 30, and 45 mm Hg were tested to determine the effects of post-occlusive pressure application on terminal lymphatic clearance. Results indicated that terminal lymphatic clearance did not resume for an applied pressure of 45 mm Hg following occlusion. The relative lymphatic clearance rate at an external pressure of 30 mm Hg following occlusion was 54% of the clearance rate for a 0 mm Hg applied pressure prior to lymph occlusion. The results for a 0 mm Hg external pressure following occlusion indicated a 23 percent clearance rate compared to the pre-occlusive state. A two compartment model was utilized to determine the lymphatic clearance rate per unit tissue volume of subcutaneous tissue from the experimental data for each pressure phase.     

Role of ischemia and deformation in the onset of compression-induced deep tissue injury: MRI-based studies in a rat model.

A rat model was used to distinguish between the different factors that contribute to muscle tissue damage related to deep pressure ulcers that develop after compressive loading. The separate and combined effects of ischemia and deformation were studied. Loading was applied to the hindlimb of rats for 2 h. Muscle tissue was examined using MR imaging (MRI) and histology. An MR-compatible loading device allowed simultaneous loading and measurement of tissue status. Two separate loading protocols incorporated uniaxial loading, resulting in tissue compression and ischemic loading. Uniaxial loading was applied to the tibialis anterior by means of an indenter, and ischemic loading was accomplished with an inflatable tourniquet. Deformation of the muscle tissue during uniaxial loading was measured using MR tagging. Compression of the tissues for 2 h led to increased T2 values, which were correlated to necrotic regions in the tibialis anterior. Perfusion measurements, by means of contrast-enhanced MRI, indicated a large ischemic region during indentation. Pure ischemic loading for 2 h led to reversible tissue changes. From the MR-tagging experiments, local strain fields were calculated. A 4.5-mm deformation, corresponding to a surface pressure of 150 kPa, resulted in maximum shear strain up to 1.0. There was a good correlation between the location of damage and the location of high shear strain. It was concluded that the large deformations, in conjunction with ischemia, provided the main trigger for irreversible muscle damage.     

Quantification of Ceroid and Lipofuscin in Skeletal Muscle

Ceroid and lipofuscin are autofluorescent granules thought to be generated as a consequence of chronic oxidative stress. Because ceroid and lipofuscin are persistent in tissue, their measurement can provide a lifetime history of exposure to chronic oxidative stress. Although ceroid and lipofuscin can be measured by quantification of autofluorescent granules, current methods rely on subjective assessment. Furthermore, there has not been any evaluation of variables affecting quantitative measurements. The article describes a simple statistical approach that can be readily applied to quantitate ceroid and lipofuscin. Furthermore, it is shown that several factors, including magnification tissue thickness and tissue level, can affect precision and sensitivity. After optimizing for these factors, the authors show that ceroid and lipofuscin can be measured reproducibly in the skeletal muscle of dystrophic mice (ceroid) and aged mice (lipofuscin).     

Calorimetry with heat flux transducers: comparison with a suit calorimeter

Regional and total body heat loss rates of human subjects at rest were measured simultaneously by means of an array of heat flux transducers and with a tube suit calorimeter. Conditions ranged from thermal comfort to strong cooling. A high degree of correlation was found between heat loss rates determined by the two independent techniques. For the head and arms, the transducer array system measured less heat loss than the suit. For the torso and legs, measurements by the two methods were equivalent. For the whole body, the transducer system yielded a heat loss rate 87% of the suit calorimeter value.     

Characterization of a new substrate for protein kinase C: assay by continuous fluorometric monitoring and high performance liquid chromatography

A synthetic peptide derived from the phosphorylation site in the beta-subunit of phosphorylase kinase (RTKRSGSVYEPLKI) is an efficient substrate for rat brain protein kinase C: Km = 18 +/- 2 microM and Vmax = 2.1 +/- 0.1 mumol/min/mg. The phosphorylation of the peptide, which occurs at Ser7, can be followed by four independent procedures. 1. Standard measurement of 32P incorporation. 2. Reverse phase HPLC in a gradient system containing 0.1 M ammonium sulfate in the stationary phase. 3. Continuous fluorometric monitoring of the changes in intrinsic peptide fluorescence. 4. Continuous fluorometric determination of NADH oxidation in a coupled enzyme assay.     

Measurements of tumor tissue oxygen tension using a time-resolved luminescence-based optical oxylite probe: comparison with a paired survival assay

Recently, a system that measures tissue oxygen tension using time-resolved luminescence-based optical sensors has become available commercially (Oxford Optronix, Oxford, England). Two experiments were conducted using this system. First, the oxygen tension distribution was measured in two tumor lines: a spontaneous mouse fibrosarcoma, FSa-II, and a human squamous cell carcinoma xenograft, FaDu. The area in which the pO(2) was equal to or lower than 2.5 mmHg was defined as the hypoxic lesion, and the hypoxic cell fraction was taken as the fraction of these measurements in a tumor. The measured hypoxic cell fractions were compared with those determined by the paired cell survival assay for tumors of various sizes. Second, the tumor tissue pO(2) was measured continuously after administration of two different anesthetics to evaluate the effect of these drugs on tissue pO(2). Results indicated a good agreement between the hypoxic cell fractions measured by this system and those determined by the paired cell survival curve assay for tumors smaller than approximately 500 mm(3). For tumors larger than approximately 500 mm(3), the hypoxic cell fractions measured by the oxygen probe system were higher than those measured by the paired cell survival assay. This may suggest that the hypoxic cell fraction measured by the oxygen probes included both hypoxic and necrotic areas in large tumors where necrotic lesions occupied a significant portion of the tumor. Continuous measurements of pO(2) after anesthesia (Nembutal, or ketamine plus xylazine) showed a consistent rise in the pO(2) during the first 20-30 min of measurement. Subsequently, the pO(2) values became constant or continued to rise slowly. For comparison, the tumor cell survivals were assayed after a dose of 20 Gy given in air at 5, 20 and 60 min after anesthesia. The result showed a decrease in cell survival only in tumors irradiated 20 min after an injection of Nembutal.     

Measurement error in heat tolerance assays

Biological measurements inherently involve some measurement error (ME), which is a major concern because measurement accuracy (how closely a measurement reproduces the true value of the attribute being measured) and statistical power steadily decrease with increasing ME. However, ME has been largely overlooked in the thermal biology literature, which can be explained by the fact that thermotolerance estimates often involve the collapse or death of the tested individuals and measurements cannot be repeated in vivo with the same specimen under identical conditions. Here we assess inter- and intra-researcher (test-retest) reliability of heat tolerance measured as knockdown time from digital recordings of Drosophila subobscura flies individually assayed in vials with a dynamic method. We provide a summary of various estimators used to compute measurement reliability (the degree to which the measurement is affected by ME) together with their statistical properties. Our results indicate that the estimation of heat knockdown time has poor reliability: intra-researcher ME=29% and inter-researcher ME=34%. This difference is attributed to lack of ‘accurateness’ (the difference in the marginal distributions of the measurements taken by the two researchers) because measurement imprecision was essentially the same in both estimates (27%). In view of our results we conclude that thermal biologists should report the reliability of thermotolerance estimates and, when necessary, adopt some straightforward guidelines suggested here to improve measurement reliability.     

Kinetic and Physical Studies of Cell Death Induced By Chemotherapeutic Agents Or Hyperthermia

The kinetics of three physical parameters: cell density, relative cytoplasmic viscosity and DNA stability to denaturation have been measured during the period preceding cell death induced by hyperthermia, methylprednisolone and a series of cancer chemotherapeutic agents. This series of measurements employed cultured human lymphoblastoid cells as an experimental system to establish the changes that can be observed in the early stages of cell death, prior to applying such measurements to tissue biopsies from solid human tumours. Cell death, induced by hyperthermia up to 43°C, methylprednisolone, vincristine, 5-fluorouracil, BCNU and melphalan, showed essentially identical and reproducible changes corresponding to those which characterize programmed cell death (apoptosis). Such changes could also be observed following hyperthermia above 43°C, but reproducibility was poor and increasing damage to the cell membranes was evident. In cells treated with adriamycin or methotrexate, cell sub-populations showing an increase in cell density were not detected. Measurements of DNA stability were readily performed by flow cytofluorometry thus allowing rapid quantitation of the fraction of cells in the early stages of cell death. Modified flow cytometric instrumentation would further allow measurement of cytoplastic viscosity as an additional parameter to indicate entry into programmed cell death. This suggests that these measurements could readily be applied to cell suspensions derived from tumour tissue biopsies for a more accurate assessment of tumour growth rate, and to allow monitoring of response to therapy in sequential tumour biopsies.