Incorporating neurophysiological concepts in mathematical thermoregulation models.

Skin blood flow (SBF) is a key player in human thermoregulation during mild thermal challenges. Various numerical models of SBF regulation exist. However, none explicitly incorporates the neurophysiology of thermal reception. This study tested a new SBF model that is in line with experimental data on thermal reception and the neurophysiological pathways involved in thermoregulatory SBF control. Additionally, a numerical thermoregulation model was used as a platform to test the function of the neurophysiological SBF model for skin temperature simulation. The prediction-error of the SBF-model was quantified by root-mean-squared-residual (RMSR) between simulations and experimental measurement data. Measurement data consisted of SBF (abdomen, forearm, hand), core and skin temperature recordings of young males during three transient thermal challenges (1 development and 2 validation). Additionally, ThermoSEM, a thermoregulation model, was used to simulate body temperatures using the new neurophysiological SBF-model. The RMSR between simulated and measured mean skin temperature was used to validate the model. The neurophysiological model predicted SBF with an accuracy of RMSR < 0.27. Tskin simulation results were within 0.37 °C of the measured mean skin temperature. This study shows that (1) thermal reception and neurophysiological pathways involved in thermoregulatory SBF control can be captured in a mathematical model, and (2) human thermoregulation models can be equipped with SBF control functions that are based on neurophysiology without loss of performance. The neurophysiological approach in modelling thermoregulation is favourable over engineering approaches because it is more in line with the underlying physiology.

Cold-induced vasoconstriction at forearm and hand skin sites: the effect of age.

During mild cold exposure, elderly are at risk of hypothermia. In humans, glabrous skin at the hands is well adapted as a heat exchanger. Evidence exists that elderly show equal vasoconstriction due to local cooling at the ventral forearm, yet no age effects on vasoconstriction at hand skin have been studied. Here, we tested the hypotheses that at hand sites (a) elderly show equal vasoconstriction due to local cooling and (b) elderly show reduced response to noradrenergic stimuli. Skin perfusion and mean arterial pressure were measured in 16 young adults (Y: 18-28 years) and 16 elderly (E: 68-78 years). To study the effect of local vasoconstriction mechanisms local sympathetic nerve terminals were blocked by bretylium (BR). Baseline local skin temperature was clamped at 33 degrees C. Next, local temperature was reduced to 24 degrees C. After 15 min of local cooling, noradrenaline (NA) was administered to study the effect of neural vasoconstriction mechanisms. No significant age effect was observed in vasoconstriction due to local cooling at BR sites. After NA, vasoconstriction at the forearm showed a significant age effect; however, no significant age effect was found at the hand sites. [Change in CVC (% from baseline): Forearm Y: -76 +/- 3 vs. E: -60 +/- 5 (P < 0.01), dorsal hand Y: -74 +/- 4 vs. E: -72 +/- 4 (n.s.), ventral hand Y: -80 +/- 7 vs. E: -70 +/- 11 (n.s.)]. In conclusion, in contrast to results from the ventral forearm, elderly did not show a blunted response to local cooling and noradrenaline at hand skin sites. This indicates that at hand skin the noradrenergic mechanism of vasoconstriction is maintained with age.

A model to predict patient temperature during cardiac surgery.

A core temperature drop after cardiac surgery slows down the patient's recuperation process. In order to minimize the amount of the so-called afterdrop, more knowledge is needed about the impaired thermoregulatory system during anesthesia and the effect of different protocols on temperature distribution. Therefore, a computer model has been developed that describes heat transfer during cardiac surgery. The model consists of three parts: (1) a passive part, which gives a simplified description of the human geometry and the passive heat transfer processes, (2) an active part that takes into account the thermoregulatory system as a function of the amount of anesthesia and (3) submodels, through which it is possible to adjust the boundary conditions. The validity of the new model was tested by comparing the model results to the measurement results of three surgical procedures. A good resemblance was found between simulation results and the experiments. Next, a model application was shown. A parameter study was performed to study the effect of different temperature protocols on afterdrop. It was shown that the effectiveness of forced-air heating is larger than the benefits resulting from increased environmental temperature or usage of a circulating water mattress. Ultimately, the model could be used to develop a monitoring decision system that advises clinicians what temperature protocol will be best for the patient.

Modelling of temperature and perfusion during scalp cooling.

Hair loss is a feared side effect of chemotherapy treatment. It may be prevented by cooling the scalp during administration of cytostatics. The supposed mechanism is that by cooling the scalp, both temperature and perfusion are diminished, affecting drug supply and drug uptake in the hair follicle. However, the effect of scalp cooling varies strongly. To gain more insight into the effect of cooling, a computer model has been developed that describes heat transfer in the human head during scalp cooling. Of main interest in this study are the mutual influences of scalp temperature and perfusion during cooling. Results of the standard head model show that the temperature of the scalp skin is reduced from 34.4 degrees C to 18.3 degrees C, reducing tissue blood flow to 25%. Based upon variations in both thermal properties and head anatomies found in the literature, a parameter study was performed. The results of this parameter study show that the most important parameters affecting both temperature and perfusion are the perfusion coefficient Q10 and the thermal resistances of both the fat and the hair layer. The variations in the parameter study led to skin temperature ranging from 10.1 degrees C to 21.8 degrees C, which in turn reduced relative perfusion to 13% and 33%, respectively.

Hybrid method coupling molecular dynamics and Monte Carlo simulations to study the properties of gases in microchannels and nanochannels.

We combine molecular dynamics (MD) and Monte Carlo (MC) simulations to study the properties of gas molecules confined between two hard walls of a microchannel or nanochannel. The coupling between MD and MC simulations is introduced by performing MD near the boundaries for accuracy and MC in the bulk because of the low computational cost. We characterize the influence of different densities and molecule sizes on the equilibrium properties of the gas in the microchannel. The effect of the particle size on the simulation results is very small in the case of a dilute gas and increases with the density. The hybrid MD-MC simulation method is validated by comparing the results for density and temperature profiles with those of pure MD and pure MC simulations. These results compare well for pure MD and pure MC, as well as hybrid MD-MC, both in the bulk and near the boundaries, when hard-sphere interactions are used. When Lennard-Jones potentials are used to accurately model the interactions between the gas and wall molecules instead, the results of pure MD simulations differ significantly from the pure MC simulations near the boundaries, but the results of the hybrid method compare well with the pure MD results near the wall, and with the pure MC and pure MD results in the middle of the channel. The hybrid method also very accurately simulates the interface between the MD and MC simulation domains. Comparisons between MD, MC, and hybrid MD-MC computational costs are outlined. The speedup when using 50% of the domain for MD simulations and 50% for MC simulations is very small compared to pure MD simulations times, but this speedup increases drastically for more realistic situations where the region near the wall is small compared to the bulk region.

Seasonal changes in metabolic and temperature responses to cold air in humans.

The metabolic and temperature response to mild cold were investigated in summer and winter in a moderate oceanic climate. Subjects were 10 women and 10 men, aged 19-36 years and BMI 17-32 kg/m2. Metabolic rate (MR) and body temperatures were measured continuously in a climate chamber with an ambient temperature of 22 degrees C for 1 h and subsequently 3 h of 15 degrees C. The average metabolic response during cold exposure, measured as the increase in kJ/min over time, was significantly higher in winter (11.5%) compared to summer (7.0%, P < .05). The temperature response was comparable in both seasons. The metabolic response in winter was significantly related to the response in summer (r2 = .47, P < .001). Total heat production during cold exposure was inversely related to the temperature response in both seasons (summer, r2 = .39, P < .01; winter r2 = .32, P < .05). In conclusion, the observed higher metabolic response in winter compared to summer indicates cold adaptation. The magnitude of the cold response varies, but the relative contribution of metabolic and temperature response was subject specific and consistent throughout the seasons, which can have implications for energy balance and body composition.

Experimental and numerical analyses of the steady flow field around an aortic Björk-Shiley standard valve prosthesis.

To develop a numerical method for the description of the flow field around a Björk-Shiley (BS) standard valve prosthesis in aortic position, detailed experimental measurements and numerical calculations are performed under steady flow conditions. The experiment was conducted at Reynolds numbers up to 800. In order to perform LDA measurement of velocity in the vicinity of the valve with a curved sinus boundary, a mixture of oil and kerosine was used as the fluid which exactly matches the refractive index of the perspex aortic model. The velocity profiles at six positions in the vicinity and downstream of the valve were measured, including both axial and radial velocity components. The results show very clearly the existence of two nearly symmetric spiral vortex streams downstream of the valve. There is no recirculation area in the aorta downstream and also no obvious stagnation area in the minor orifice region near the valve when Re less than or equal to 800. Theoretically, the flow field of a BS valve is simulated by the flow pattern around a circular plate with an angle of incidence to the approaching stream. The numerical calculations were carried out by means of a 2-D model using the FEM together with the penalty function method. The maximum Reynolds number is 700. The results agree with the experimental results in the plane of symmetry when the Reynolds number is small. However, as the Reynolds number increases, the difference becomes evident. Our conclusion is that the steady flow field of a BS valve is completely 3-dimensional, featured by two spiral vortices. It cannot be simulated exactly by 2-D numerical calculations. To get more detailed and complete information about the flow field of this valve, 3-D numerical calculations are needed.

Linear propagation of pulsatile waves in viscoelastic tubes.

An experimental and theoretical analysis is made of pulsatile wave propagation in deformable latex tubes as a model of the propagation of pressure pulses in arteries. A quasi one-dimensional linear model is used in which, in particular, attention is paid to the viscous phenomena in fluid and tube wall. The agreement between experimental and theoretical results is satisfactory. It appeared that the viscoelastic behaviour of the tube wall dominates the damping of the pressure pulse. Several linear models are used to describe the wall behaviour. No significant differences between the results of these models were found.

An experimental analysis of the flow field in a three-dimensional model of the human carotid artery bifurcation.

Steady flow measurements were carried out in a rigid three-dimensional model of the human carotid artery bifurcation at a Reynolds number of 640 and a flow division ratio of 50/50. Both axial and secondary velocities were measured with a laser-Doppler anemometer. In the bulb opposite to the flow divider a zone with negative axial velocities was found with a maximal diameter of about 60% of the local diameter of the branch and a cross-sectional extent of about 25% of the local cross-sectional area. In the bulb the maximum axial velocity shifted towards the divider wall and at the end of the bulb an axial velocity plateau arose near the non-divider wall. Halfway through the bulb, secondary flow showed a vortex through which fluid flowed towards the divider wall near the bifurcation plane and back towards the non-divider wall near the upper walls.

A mechanical analysis of the closed Hancock heart valve prosthesis.

In order to obtain mechanical specifications for the design of an artificial leaflet valve prosthesis, a geometrically non-linear numerical model is developed of a closed Hancock leaflet valve prosthesis. In this model, the fibre reinforcement of the leaflet and the viscoelastic properties of frame and leaflets are incorporated. The calculations are primarily restricted to 1/6 part of the valve and a time varying pressure load is applied. The calculations are verified experimentally by measuring the commissure displacements and leaflet centre displacement of a Hancock valve. The numerically obtained commissure displacements are found to be linearly dependent on the pressure load, and the slope of the curves is hardly dependent on loading type and loading velocity. Experimentally a difference is found between the three commissure displacements, which is also predicted numerically using a simplified asymmetric total valve model. Besides, experimentally a clear dependency of commissure displacements on frame size is found. For the leaflet centre displacement, a qualitative agreement exists between numerical prediction and experimental result, although the numerical predicted values are systematically higher. The numerically obtained stress distributions revealed that the maximum von Mises intensity in the membranes occurs in the vicinity of the commissure in the free leaflet area (0.2 N mm-2). Wrinkling of the membranes may occur in the coaptation area near the leaflet suspension. The maximum fibre stress is found near the aortic ring in the fibres which form the boundaries of the coaptation area (0.64 N mm-2). These locations seem to correlate with some common regions of tissue valve failure.

A numerical analysis of steady flow in a three-dimensional model of the carotid artery bifurcation.

A finite element approximation of steady flow in a rigid three-dimensional model of the carotid artery bifurcation is presented. A Reynolds number of 640 and a flow division ratio of about 50/50, simulating systolic flow, was used. To limit the CPU- and I/O-times needed for solving the systems of equations, a mesh-generator was developed, which gives full control over the number of elements into which the bifurcation is divided. A mini-supercomputer, based on parallel and vector processing techniques, was used to solve the system of equations. The numerical results of axial and secondary flow compare favorably with those obtained from previously performed laser-Doppler velocity measurements. Also, the influence of the Reynolds number, the flow division ratio, and the bifurcation angle on axial and secondary flow in the carotid sinus were studied in the three-dimensional model. The influence of the interventions is limited to a relatively small variation in the region with reversed axial flow, more or less pronounced C-shaped axial velocity contours, and increasing or decreasing axial velocity maxima.

In vitro closing behaviour of Björk-Shiley, St Jude and Hancock heart valve prostheses in relation to the in vivo recorded aortic valve closure.

To compare prosthetic valve behaviour with that of the natural aortic valve, experiments were performed in vitro as well as in vivo. In a mock circulation system, cinematographic high-speed recordings of the valvular behaviour were made for Björk-Shiley, St Jude and Hancock heart valve prostheses. Simultaneously with the film recording, the aortic flow and the left ventricular and aortic pressures were measured. The closing behaviour of the natural aortic valve was recorded in in vivo experiments following the same measuring technique. Comparison of the film frames with the aortic flow signal revealed that the mechanical prostheses mainly close due to the back flow in the early phase of diastole; they close only for 5% of their cross-sectional area during systolic ejection. The Hancock bioprosthesis closes already for 45% during the flow deceleration phase of systole, which is however significantly less than the corresponding closure of the aortic valve as recorded in vivo (74%). The change in fluid viscosity from 3.10(-3) Ns/m2 to 1.10(-3) Ns/m2 does not affect the closing behaviour of the mechanical prostheses. Reducing the peak value of systolic aortic flow by a factor two decreases the cross-sectional area of the prosthetic valves at peak systole. When the natural aortic valve closing mechanism is applied to a disc-valve prosthesis, a partial (30%) systolic valve closure is found.

Model studies on the influence of nonstationary flow on the mean flow estimate with the indicator-dilution technique.

The applicability of the indicator-dilution technique for the estimate of the mean flow under circumstances of nonstationary flow is investigated by model studies. The studies comprise experiments using a hydrodynamical model as well as calculations with a compartmental approach. The main conclusions are: (1) The influence of nonstationary flow on the mean flow estimate with the indicator-dilution technique can be described accurately by a mathematical model based on a mixing-chamber approach. (2) The relative error in the mean flow estimate by a single measurement is dependent on the system parameters (number and time constant of mixing chambers) and the flow parameters (relative amplitude and relative frequency of flow variation and the phase with respect to the variation at the moment of injection). (3) Errors due to cyclic nonstationarities of the flow can be reduced strongly by averaging over two measurements with injection at two points of time with phases pi radians apart.

Design of a system for the accelerated loading of heart valve prostheses.

In this paper an equipment is described for the loading of heart valve prostheses under physiological pressure conditions at a frequency of 10 Hz. The system consists essentially of two reservoirs between which a housing is mounted for holding the valve prosthesis. The reservoirs are partly filled with liquid. The physiological pressure variation across the valve is obtained by pressure control within the two reservoirs. A phase difference between the pressures in the two reservoirs compensates for the mass-inertia effects which normally occur at these high frequencies. The system without a valve has been analysed on the basis of simplified relationships between pressure and flow. The predicted values for the phase difference between the flow and the pressure curves within the valve housing, have been verified experimentally for various values of phase difference and amplitude ratios of the pressure variations within the reservoirs. The agreement between theory and experiment is fair. For the system with a valve the experimentally observed patterns closely resemble the theoretically predicted ones. From experiments with a Björk-Shiley ( 21ABP ) and a Hancock (242-A21) valve prosthesis it is concluded that the valves open and close completely and that the pressure and flow patterns around the valves mimic the essential features of the in-vivo signals.

The mechanical properties of porcine aortic valve tissues.

In uniaxial tensile experiments in vitro mechanical properties of the different parts of porcine aortic valves, i.e. the leaflets, the sinus wall and the aortic wall, have been dealt with. Tissue strips cut in different directions were investigated. The collagen bundles in the leaflets show a stiffening effect and cause a marked anisotropy: within the physiological range of strains the largest slopes of the stress-strain curves of leaflet specimens in the bundle direction are a factor of about 20 larger than those of specimens taken along the perpendicular direction. For the sinus and aortic tissues, these values are 50-200 times smaller than those obtained from the leaflet specimens in the bundle direction. Two aspects of viscoelastic behaviour were examined: the strain rate sensitivity of the stress-strain curves and the relaxation behaviour. The stress-strain curves of the different valve parts appeared to be rather insensitive to the strain rate: the most pronounced sensitivity observed in our experiments, was a doubling of the stress at the same strain caused by a hundredfold increase of the strain rate. In analyzing the relaxation behaviour, use was made of the relaxation model proposed by Fung (1972, in Biomechanics, its Foundations and Objectives; Fung, Perrone and Anliker. Prentice Hall). In the leaflets, about 45% stress relaxation was found whereas this amounted to 30% in the sinus and aortic walls. Predictions based upon the model indicate that on cyclic loading the larger viscous losses have to be expected in the leaflets.

Numerical analysis of steady generalized Newtonian blood flow in a 2D model of the carotid artery bifurcation.

The stationary flow of blood in a two-dimensional model of the bifurcation of the human carotid artery is simulated numerically using a finite element method. The Reynolds number is taken as equal to 300, corresponding to the value during the end-diastolic phase of the heart cycle. As constitutive equations, the Newtonian model and the non-Newtonian power-law and Casson models are used. The chosen model parameters corresponded with blood. The flow in this geometry is determined by the branching of the artery and the existence of a reversed flow area in the internal carotid artery. From the results of this problem, we conclude that the general flow structure is not influenced by the generalized (non-)Newtonian models. However, there are differences that cannot be neglected. First, the generalized Newtonian models result in axial and secondary velocity profiles that have 5-10% lower maximum values compared to the Newtonian model. Second, the pressure has higher values in the case of the generalized Newtonian models, especially in the internal carotid artery where these models give maximal 25% higher pressure values. Third, along the divider wall, the wall shear stresses are lower for the generalized Newtonian models; near the apex, this difference is maximal 40% in case of the power-law model. The generalized Newtonian models give higher wall shear stresses along the non-divider wall than the Newtonian model, the maximum difference being 5%. And fourth, in the internal carotid artery the reversed flow area is 10% reduced by the generalized Newtonian models. In general, the differences are more pronounced in the case of the power-law model.

A two-dimensional numerical analysis of unsteady flow in the carotid artery bifurcation. A comparison with three-dimensional in-vitro measurements and the influence of minor stenoses.

In the present study a two-dimensional finite element model for incompressible Newtonian flow is applicated to the modelling of carotid artery flow. In earlier studies, the numerical model was validated experimentally for several flow configurations. In general the pulsatile flow is characterized by reversed flow regions at the non-divider side walls of both the internal and external carotid arteries. The unsteadiness of the flow is associated with rather complex spatial and temporal velocity distributions and leads to temporal variations of the location and length of the reversed flow regions. As a consequence, pronounced spatial and temporal variations in the wall shear stresses are found. At the non-divider side walls, wall shear stresses are relatively low and exhibits an oscillatory behaviour in space and time. At the divider side walls, wall shear stresses are relatively high and approximately follow the flow rate distribution in time. The aim of this study is not only to present two-dimensional calculations but also to compare the calculated two-dimensional velocity profiles with those from three-dimensional experiments. It is observed that in the common carotid artery and in the proximal parts of the internal and external carotid arteries, the two-dimensional numerical model provides valuable information with respect to the three-dimensional configuration. In the more distal parts of especially the internal carotid artery, deviations are found between the two-dimensional numerical and three-dimensional experimental model. These deviations can mainly be attributed to the neglect of the secondary velocity distribution in the two-dimensional model. In the two-dimensional numerical model the influence of a minor stenosis in the internal carotid artery is hardly distinguishable from a minor geometrical variation without stenosis. Full three-dimensional analyses of the influence of minor stenoses are needed to prove numerically whether in-vivo measurements of the axial velocity distribution are useful in the detection of minor stenoses.

Gas-surface interactions using accommodation coefficients for a dilute and a dense gas in a micro- or nanochannel: heat flux predictions using combined molecular dynamics and Monte Carlo techniques.

The influence of gas-surface interactions of a dilute gas confined between two parallel walls on the heat flux predictions is investigated using a combined Monte Carlo (MC) and molecular dynamics (MD) approach. The accommodation coefficients are computed from the temperature of incident and reflected molecules in molecular dynamics and used as effective coefficients in Maxwell-like boundary conditions in Monte Carlo simulations. Hydrophobic and hydrophilic wall interactions are studied, and the effect of the gas-surface interaction potential on the heat flux and other characteristic parameters like density and temperature is shown. The heat flux dependence on the accommodation coefficient is shown for different fluid-wall mass ratios. We find that the accommodation coefficient is increasing considerably when the mass ratio is decreased. An effective map of the heat flux depending on the accommodation coefficient is given and we show that MC heat flux predictions using Maxwell boundary conditions based on the accommodation coefficient give good results when compared to pure molecular dynamics heat predictions. The accommodation coefficients computed for a dilute gas for different gas-wall interaction parameters and mass ratios are transferred to compute the heat flux predictions for a dense gas. Comparison of the heat fluxes derived using explicit MD, MC with Maxwell-like boundary conditions based on the accommodation coefficients, and pure Maxwell boundary conditions are discussed. A map of the heat flux dependence on the accommodation coefficients for a dense gas, and the effective accommodation coefficients for different gas-wall interactions are given. In the end, this approach is applied to study the gas-surface interactions of argon and xenon molecules on a platinum surface. The derived accommodation coefficients are compared with values of experimental results.

Increased systolic blood pressure after mild cold and rewarming: relation to cold-induced thermogenesis and age.

AIM: Higher winter mortality in elderly has been associated with augmented systolic blood pressure (SBP) response and with impaired defense of core temperature. Here we investigated whether the augmented SBP upon mild cold exposure remains after a rewarming period, and whether SBP changes are linked to thermoregulation. Therefore, we tested the following hypotheses: cold-induced increase in SBP (1) remains augmented after rewarming in elderly compared to young adults (2) is related to non-shivering thermogenesis (NST) upon mild cold (3) is related to vasoconstriction upon mild cold. METHODS: Blood pressure, energy expenditure (EE), skin and core temperature, skin perfusion (abdomen, forearm, both sides of hand) and % body fat were measured in 12 young adults (Y) and 12 elderly (E). Supine subjects were exposed to a thermoneutral baseline 0.5 h (T(air) = 30.1°C), 1 h mild cold (T(air) = 20.7°C), 1 h rewarming (T(air) = 34.8°C) and 1 h baseline (T(air) = 30.5°C). RESULTS: Upon mild cold only the young adults showed significant NST (Y: +2.5 ± 0.6 W m(-2), P < 0.05). No significant age effects in vasoconstriction were observed. After rewarming per cent change in SBP (%ΔSBP) remained significantly increased in both age groups and was augmented in elderly (Y: +5.0% ± 1.2% vs. E: +14.7% ± 3.1%, P < 0.05). Regression analysis revealed that %ΔSBP significantly related to ΔEE upon mild cold (P < 0.01, r(2) = 0.35) and in elderly also to %body fat (P < 0.02, r(2) = 0.57). CONCLUSION: Individual changes in SBP after rewarming correlate negatively to NST. Elderly did not show NST, which explains the greater SBP increase in this group. In elderly a relatively large %body fat protected against the adverse effects of mild cold.