A three-dimensional variable geometry countercurrent model for whole limb heat transfer.

A new formulation of the combined macro and microvascular model for heat transfer in a human arm developed in Song et al. [1] is proposed using a recently developed approximate theory for the heat exchange between countercurrent vessels embedded in a tissue cylinder with surface convection [2]. The latter theory is generalized herein to treat an arm with an arbitrary variation in cross-sectional area and continuous bleed off from the axial vessels to the muscle and cutaneous tissue. The local microvascular temperature field is described by a "hybrid" model which applies the Weinbaum-Jiji [3] and Pennes [4] equations in the peripheral and deeper tissue layers, respectively. To obtain reliable end conditions at the wrist and other model input parameters, a plethysmograph-calorimeter has been used to measure the blood flow distribution between the arm and hand circulations, and hand heat loss. The predictions of the model show good agreement with measurements for the axial surface temperature distribution in the arm and confirm the minimum in the axial temperature variation first observed by Pennes [4] for an arm in a warm environment.     

A prototype segmental model for blood flow and heat transfer in the limb.

A general modeling technique for characterizing the blood flow and heat tranfer properties in the human limb is reported in this paper. The basic idea is to take the segmental approach so that a lumped model for each segment can be constructed. Consequently, a prototype segmental computer model is proposed which describes, in general terms, the interrelationships between the circulatory system and the thermal system of the limb. Simulation study of digital response to hand cooling is made and the results agree very well with the experimental data.     

A functional model for whole limb transplantation in the rat

To develop a functional model for the study of whole limb transplantation, inbred Lewis rats were used as both donors and recipients. In this model, the recipient biceps femoris muscle was elevated from its distal attachment to preserve part of the adductor function of the limb after surgery. The tibial, peroneal, and sural branches of the sciatic nerve were anastomosed separately to provide faster and more precise functional recovery. For control sensory evaluation, the saphenous branches of the femoral nerve were not reattached. A flat intramedullary pin stabilized with methyl methacrylate was used to rigidly immobilize the femur. The transplanted limbs started bearing weight at 17 to 22 days. Walking on the plantar surface of the hock and adduction of the toes gradually decreased, and the rats developed a normal walking pattern. Sciatic and tibial function indexes, based on walking track analysis, correlated well with clinical observations. In this study, a new model for limb transplantation was developed that provided good and reliable sensory and ambulatory recovery.     

Simulation of combined transfer of oxygen and heat through the skin using a capillary-loop model

A model of a microcirculatory unit has been developed to study oxygen exchange processes within the upper part of the skin. The model includes the loop-shaped capillary structure of stratum papillare, the nonlinear binding of oxygen by hemoglobin, and, in particular, the shift of the oxygen hemoglobin dissociation curve due to temperature variations. The corresponding nonlinear elliptic boundary value problem is defined and the existence of at least one solution assured. After describing the numerical procedure to calculate an approximation to the solution, results of several calculations representing different supply situations of the upper skin are presented and discussed.     

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

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

A stepwise model system for limb regeneration

The amphibian limb is a model that has provided numerous insights into the principles and mechanisms of tissue and organ regeneration. While later stages of limb regeneration share mechanisms of growth control and patterning with limb development, the formation of a regeneration blastema is controlled by early events that are unique to regeneration. In this study, we present a stepwise experimental system based on induction of limb regeneration from skin wounds that will allow the identification and functional analysis of the molecules controlling this early, critical stage of regeneration. If a nerve is deviated to a skin wound on the side of a limb, an ectopic blastema is induced. If a piece of skin is grafted from the contralateral side of the limb to the wound site concomitantly with nerve deviation, the ectopic blastema continues to grow and forms an ectopic limb. Our analysis of dermal cell migration, contribution, and proliferation indicates that ectopic blastemas are equivalent to blastemas that form in response to limb amputation. Signals from nerves are required to induce formation of both ectopic and normal blastemas, and the diversity of positional information provided by blastema cells derived from opposite sides of the limb induces outgrowth and pattern formation. Hence, this novel and convenient stepwise model allows for the discovery of necessary and sufficient signals and conditions that control blastema formation, growth, and pattern formation during limb regeneration.     

A theoretical model for peripheral tissue heat transfer using the bioheat equation of Weinbaum and Jiji

In this paper the new bioheat equation derived in Weinbaum and Jiji is applied to the three layer conceptual model of microvascular surface tissue organization proposed in. A simplified one-dimensional quantitative model of peripheral tissue energy exchange is then developed for application in limb and whole body heat transfer studies. A representative vasculature is constructed for each layer and the enhancement in the local tensor conductivity of the tissue as a function of vascular geometry and blood flow is examined. Numerical solutions for the boundary value problem coupling the three layers are presented and these results used to study the thermal behavior of peripheral tissue for a wide variety of physiological conditions from supine resting state to maximum exercise.     

A functional model of microvascular thrombosis

A new model of microvascular thrombosis is presented, with the evaluation of single-dose heparin in the prevention of microvascular thrombosis. The technique, which involves arterial crushing and an arteriotomy with intimal abrasion, was performed on the superficial femoral artery of the rat. The model was applied to a series of 30 consecutive rat superficial femoral arteries. A 100 percent thrombosis rate was seen immediately and at 24 hours in 10 nonheparinized animals. An operator control group of 10 vessels without intimal abrasion had a patency rate of 100 percent immediately and at 24 hours. Ten vessels following single-dose heparin and intimal abrasion were all patent initially, with 7 remaining patent at 24 hours. Reproducibility of the model was documented by a second operator with similar results. Utilizing this model, single-dose heparin was effective in maintaining vessel patency.     

A neural network model for limb trajectory formation

This paper deals with the problem of representing and generating unconstrained aiming movements of a limb by means of a neural network architecture. The network produced time trajectories of a limb from a starting posture toward targets specified by sensory stimuli. Thus the network performed a sensory-motor transformation. The experimenters trained the network using a bell-shaped velocity profile on the trajectories. This type of profile is characteristic of most movements performed by biological systems. We investigated the generalization capabilities of the network as well as its internal organization. Experiments performed during learning and on the trained network showed that: (i) the task could be learned by a three-layer sequential network; (ii) the network successfully generalized in trajectory space and adjusted the velocity profiles properly; (iii) the same task could not be learned by a linear network; (iv) after learning, the internal connections became organized into inhibitory and excitatory zones and encoded the main features of the training set; (v) the model was robust to noise on the input signals; (vi) the network exhibited attractor-dynamics properties; (vii) the network was able to solve the motorequivalence problem. A key feature of this work is the fact that the neural network was coupled to a mechanical model of a limb in which muscles are represented as springs. With this representation the model solved the problem of motor redundancy.     

A theoretical model for immobilized whole cell enzyme

A method of estimating effectiveness factor for immobilized whole cells is developed by considering microbial cells as microspheres containing enzyme activity dispersed in the gel phase of the support matrix. The proper model equations describing the system are solved and the corresponding effectiveness factors calculated for various bead sizes, and numbers and activities of cells. The cell wall resistance (permeability) is found to be one of most important variables in the system. The model is applied in predicting the experimental data of other investigators.     

A Bayesian antedependence model for whole genome prediction

Hierarchical mixed effects models have been demonstrated to be powerful for predicting genomic merit of livestock and plants, on the basis of high-density single-nucleotide polymorphism (SNP) marker panels, and their use is being increasingly advocated for genomic predictions in human health. Two particularly popular approaches, labeled BayesA and BayesB, are based on specifying all SNP-associated effects to be independent of each other. BayesB extends BayesA by allowing a large proportion of SNP markers to be associated with null effects. We further extend these two models to specify SNP effects as being spatially correlated due to the chromosomally proximal effects of causal variants. These two models, that we respectively dub as ante-BayesA and ante-BayesB, are based on a first-order nonstationary antedependence specification between SNP effects. In a simulation study involving 20 replicate data sets, each analyzed at six different SNP marker densities with average LD levels ranging from r(2) = 0.15 to 0.31, the antedependence methods had significantly (P < 0.01) higher accuracies than their corresponding classical counterparts at higher LD levels (r(2) > 0. 24) with differences exceeding 3%. A cross-validation study was also conducted on the heterogeneous stock mice data resource (http://mus.well.ox.ac.uk/mouse/HS/) using 6-week body weights as the phenotype. The antedependence methods increased cross-validation prediction accuracies by up to 3.6% compared to their classical counterparts (P < 0.001). Finally, we applied our method to other benchmark data sets and demonstrated that the antedependence methods were more accurate than their classical counterparts for genomic predictions, even for individuals several generations beyond the training data.     

A two-phase model for water and heat transfer within an intermittently-mixed solid-state fermentation bioreactor with forced aeration

A two-phase dynamic model is developed that describes heat and mass transfer in intermittently-mixed solid-state fermentation bioreactors. The model predicts that in the regions of the bed near the air inlet there can be significant differences in the air and solid temperatures, while in the remainder of the bed the gas and solid phases are much closer to equilibrium, although there can be differences in water activity of around 0.05. The increase in the temperature of the gas as it flows through the bed means that it is impossible to prevent the bed from drying out, even if saturated air is used at the air inlet. The substrate can dry to water activities that severely limit growth, unless the bed is intermittently mixed, with the addition of water to bring the water activity back to the desired value. Under the conditions assumed for the simulation, which was designed to mimic the growth of Aspergillus niger on corn, two mixing events were necessary, one at 17.4 and the other at 27.9 h. Even though such a strategy can minimize the restriction of growth by water-limitation, temperature-limitation remains a problem due to the rapid heating dynamics. The model is obviously a useful tool that can be used to guide scale-up and to test control strategies. Such a model, describing the non-equilibrium situation between the gas and solid phases, has not previously been proposed for solid-state fermentation bioreactors. Models in the literature that assume gas-solid temperature and moisture equilibrium cannot describe the large temperature differences between the gas and solid phase which occur within the bed near the air inlet.     

UTCI-Fiala multi-node model of human heat transfer and temperature regulation

The UTCI-Fiala mathematical model of human temperature regulation forms the basis of the new Universal Thermal Climate Index (UTC). Following extensive validation tests, adaptations and extensions, such as the inclusion of an adaptive clothing model, the model was used to predict human temperature and regulatory responses for combinations of the prevailing outdoor climate conditions. This paper provides an overview of the underlying algorithms and methods that constitute the multi-node dynamic UTCI-Fiala model of human thermal physiology and comfort. Treated topics include modelling heat and mass transfer within the body, numerical techniques, modelling environmental heat exchanges, thermoregulatory reactions of the central nervous system, and perceptual responses. Other contributions of this special issue describe the validation of the UTCI-Fiala model against measured data and the development of the adaptive clothing model for outdoor climates.     

A computational model of intussusceptive microvascular growth and remodeling

Non-sprouting angiogenesis, also known as intussusceptive angiogenesis (IA), is an important modality of blood vessel morphogenesis in growing tissues. We present a novel computational framework for simulation of IA to answer some of the questions concerning the underlying mechanisms of the remodeling process. The model relies on mechanical interactions between blood and tissue, includes the structural maturation of the vessel wall, and is controlled by stimulating or inhibiting chemical agents. The model provides a simple explanation for the formation of microvessels and bifurcations from capillaries via IA, allowing for both maintenance and avoidance of shunt vessels. Detailed hemodynamic and transport properties for oxygen, metabolites or growth factors can be predicted. The model is an in silico framework for testing certain conceptual ideas about the mechanisms of intussusceptive growth and remodeling, in particular those related to mechanical and transport phenomena.     

An improved model of heat transfer through penguin feathers and down

Penguins, mostly live in the extremely cold Antarctic, are known to have feathers and down, which are light weight, compact and extremely efficient in preventing heat loss. Nevertheless, the mechanisms of heat transfer through the penguin feathers and down, and how the unique characteristics of penguin feathers and down make them such good thermal insulators are not fully understood. In this paper, an integrated model of heat transfer through the penguin feathers and down is developed and computed using finite volume method, with the geometrical structure of the barbules being considered. Monte-Carlo method is adopted to determine the radiative absorption and emission constant in the integrated model. The effective thermal conductance of penguin feathers and down computed from our model compared well with the experimentally measured value reported in the literature. Three models (penguin model, random fibre model (fibre radius=3microm) and random fibre model (fibre radius=10microm)) are further simulated and compared. Results showed that the relative small radius of the barbules of penguin feather and their geometrical structure are responsible for the reduction of heat loss in cold environment.     

A general model for the propagation of uncertainty in measurements into heat transfer simulations and its application to cryosurgery

This report presents a technique for estimating the propagation of uncertainty in measurements into mathematical simulations of heat transfer. The motivation for this report is to show the dramatic uncertainty associated with estimating the value of the so-called "lethal temperature," even in a case where a perfect correlation appears to exist between histo-pathologic observations and a corresponding heat transfer simulation. Although the example presented in this report relates to cryosurgery, the technique proposed in this report is rather general and can be applied to any heat transfer problem. The uncertainty analysis presented in this report can be considered as an extension of the well-known concept of the rule of the square root of the sum of the square errors. A comparison of the new technique with the worst case scenario concept is also presented. In conclusion, it is recommended that the proposed technique be routinely applied when presenting simulated results, whether as a part of a theoretical study, or in comparison with experimental data.