Effect of Blood Flow on Hemoglobin and Myoglobin Oxygenation in Contracting Muscle Using Near-Infrared Spectroscopy.

Insufficient O2 delivery to, and uptake by skeletal muscle can produce mobility limitations for patients with chronic diseases. Near-infrared spectroscopy (NIRS) can be used to noninvasively quantify the balance between skeletal muscle O2 delivery and utilization during contraction. However, it is not clear how the oxygenated or deoxygenated NIRS signal should be used to assess muscle O2 changes. This issue is related to the fact that the contributions of hemoglobin (Hb) and myoglobin (Mb) cannot be distinguished. This conundrum can be resolved by quantitative analysis of experimental data by computer simulations with a mechanistic, mathematical model. Model simulations distinguish dynamic responses of the oxygenated (HbO2, MbO2) and deoxygenated (HHb, HMb) contributions to the NIRS signal components (HbMbO2, HHbMb). Simulations of muscle O2 uptake and NIRS kinetics correspond closely to published experimental data (Hernández et al., J Appl Physiol 108: 1169-1176, 2010). Simulated muscle O2 uptake and oxygenation kinetics with different blood flows indicate (1) faster O2 delivery is responsible for slower muscle oxygenation kinetics; (2) Hb and Mb contributions to the HbMbO2 are similar (40-60%); and (3) Hb and Mb contributions to the HHbMb are significantly different, 80% and 20%, respectively. The effect of slow blood flow kinetics on oxygenated Hb and Mb contributions is minimal. However, the effect on the imbalance between O2 delivery and utilization rates causes significant overshoots and undershoots of deoxygenated Hb and Mb contributions. Model analysis in combination with NIRS measurements and information on hemodynamic and microvascular distribution can help to determine the use of NIRS signal in evaluating the factors limiting exercise tolerance in health and disease states.

Relating pulmonary oxygen uptake to muscle oxygen consumption at exercise onset: in vivo and in silico studies.

Assessment of the rate of muscle oxygen consumption, UO(2m), in vivo during exercise involving a large muscle mass is critical for investigating mechanisms regulating energy metabolism at exercise onset. While UO(2m) is technically difficult to obtain under these circumstances, pulmonary oxygen uptake, VO(2p), can be readily measured and used as a proxy to UO(2m). However, the quantitative relationship between VO(2p) and UO(2m) during the nonsteady phase of exercise in humans, needs to be established. A computational model of oxygen transport and utilization--based on dynamic mass balances in blood and tissue cells--was applied to quantify the dynamic relationship between model-simulated UO(2m) and measured VO(2p) during moderate (M), heavy (H), and very heavy (V) intensity exercise. In seven human subjects, VO(2p) and muscle oxygen saturation, StO(2m), were measured with indirect calorimetry and near infrared spectroscopy (NIRS), respectively. The dynamic responses of VO(2p) and StO(2m) at each intensity were in agreement with previously published data. The response time of muscle oxygen consumption, tauUO(2m) estimated by direct comparison between model results and measurements of StO(2m) was significantly faster (P < 0.001) than that of pulmonary oxygen uptake, tauVO(2p) (M: 13 +/- 4 vs. 65 +/- 7 s; H: 13 +/- 4 vs. 100 +/- 24 s; V: 15 +/- 5 vs. 82 +/- 31 s). Thus, by taking into account the dynamics of oxygen stores in blood and tissue and determining muscle oxygen consumption from muscle oxygenation measurements, this study demonstrates a significant temporal dissociation between UO(2m) and VO(2p) at exercise onset.

MRI-guided laser thermal ablation: model to predict cell death from MR thermometry images for real-time therapy monitoring.

Solid tumors and other pathologies can be treated using laser thermal ablation under interventional magnetic resonance imaging (iMRI) guidance. We developed a model to predict cell death from MR thermometry measurements and applied it to in vivo rabbit brain data. To align post-ablation T2-weighted spin-echo MR lesion images to gradient echo MR images, from which temperature is derived, we used a registration method that aligned fiducials placed near the thermal lesion. We used the outer boundary of the hyperintense rim in the post-ablation MR lesion image as the boundary for cell death, as verified from histology. Model parameters were simultaneously estimated using an iterative optimization algorithm applied to every interesting pixel in 328 images from multiple experiments having various temperature histories. For a necrotic region of 766 voxels across all lesions, the model gave a voxel specificity and sensitivity of 98.1% and 78.4%, respectively. Median distance between the segmented necrotic boundary and the mislabeled voxels was within one MR voxel. Furthermore, our model predicted fewer errors as compared to the critical temperature cell death model. This is good evidence that iMRI temperature maps can be used with our model to predict therapeutic regions in real-time.

Model transformations to evaluate transient thermal responses at a tissue surface.

For a spatially distributed model describing the transient temperature response of a thermistor-tissue system, Wei et al. [J. Biomech. Eng., 117:74-85, 1995] obtained an approximate transformation for fast analysis of the temperature response at the tissue surface. This approximate transformation reduces the model to a single ordinary differential equation. Here, we present an exact transformation that yields a single differential-integral equation. Numerical solutions from the approximate and exact transformations were compared to evaluate the differences with several sets of parameter values. The maximum difference between the exact and approximate solutions did not exceed 15 percent and occurred for only a short time interval. The root-mean-square error of the approximate solution was no more than 5 percent and within the level of experimental noise. Under the experimental conditions used by Wei et al., the approximate transformation is justified for estimating model parameters from transient thermal responses.

Comparison of algorithms for combining X-ray angiography images.

Using a one-dimensional convective-dispersive model of contrast agent flow in a blood vessel, we optimized and compared algorithms for combining a temporal sequence of X-ray angiography images, each with incomplete arterial filling, into a single-output image with fully opacified arteries. The four algorithms were: maximum opacity (MO) with a maximum over time at each spatial location; matched filtering (MAT); recursive filtering (REC) with a maximum opacity; and an approximate matched filter (AMF) consisting of a correlation with a kernel that approximates the matched filter kernel followed by a maximum opacity operation. Based on the contrast-to-noise ratio (CNR), MAT is theoretically the best algorithm. However, with spatially varying clinical images, a poorly matched MAT kernel greatly degraded CNR to the point of even inverting artery contrast. The practical AMF method maintained uniform CNR values over the entire field of view and gave >90% of the theoretical limit set by MAT. REC and MO created fully opacified arteries, but provided little CNR enhancement. By holding CNR at a nominal reference value, simulations predicted that AMF could be used with a contrast agent volume reduced by as much as 66%. Alternatively, X-ray exposure rate could be lowered. Although MO and REC are more easily implemented, the contrast enhancement with AMF makes it attractive for processing diagnostic angiography images acquired with a reduced contrast agent dose.

Temperature and perfusion responses of muscle and lung tissue during chronic heating in vivo.

For the first time, both temperature and perfusion responses have been obtained from in vivo studies of chronically heated lung and muscle tissue of calves. In each tissue, the spatial temperature distribution was measured by thermistors placed in needles at several distances from an implanted heated disc. A perfusion parameter was defined for a bioheat transfer model that describes temperature dynamics with distance from the heated disc. Estimates of perfusion were obtained by a least-squares fit of the model output to a step change in heat flux. Except for short transient experiments several times a week, a constant heat flux of 0.04, 0.06 or 0.08 Wcm(-2) was maintained at the disc surface for up to seven weeks. At the higher heat fluxes, the steady-state tissue temperature decreased with heating duration. Also, the characteristic time constants of the tissues decreased with heating duration. Muscle perfusion showed a statistically significant increase during chronic heating. Tissue adapts to chronic heating above 42 degrees C by allowing more capillary blood flow that increases heat loss to reduce tissue temperature.

Iterative optimal design of PET experiments for estimating beta-adrenergic receptor concentration.

To estimate in vivo myocardial beta-adrenergic receptor concentration with sufficient precision and to reduce the experimental complexities in positron emission tomography (PET), an iterative optimal design method is applied. An initial three-injection protocol, utilising [F-18]-labelled (R)- and (S)-fluorocarazolol and unlabelled (S)-fluorocarazolol, is optimised for ligand dosages and administration times to maximise the precision of all model parameters using the D-optimal criterion. Using this experimental protocol, PET data are collected in porcine studies, and model parameters are estimated. All model parameters are identified with satisfactory precision. The in vivo myocardial beta-receptor concentration is 7.5+/-0.6 pmol x ml(-1), which corresponds to the in vitro result of 10.1+/-1.3 pmol x ml(-1). With more accurate parameter values, a simplified two-injection protocol is optimally designed, utilising only radiolabelled and unlabelled (S)-fluorocarazolol, based on a new criterion to maximise the precision of the beta-receptor concentration. This revised optimum design predicts that the in vivo beta-receptor concentration can be estimated with good precision but reduced experiment complexity.

Lactate metabolism during exercise: analysis by an integrative systems model.

To provide a framework for quantitative analysis of metabolic and transport processes associated with ATP production during exercise, we adapted a recently developed model that links cellular metabolism and its control to whole body responses at rest. The enhanced model is based on dynamic mass balances for glycogen, glucose, pyruvate (PY), lactate (LA), O(2), and CO(2) and is solved numerically to simulate responses to acute (<20 min), moderate exercise (i.e., below the LA threshold, less than approximately 60% maximal rate of O(2) uptake). Simulations of responses to a step change in muscle ATP turnover predict substrate changes in muscle, splanchnic, and other tissues compartments, as well as changes in other metabolites (e.g., NADH, ADP) whose reactions are coupled to the main reactions. Even a significant (64%) decrease in muscle O(2) concentration (C(m, O(2))) did not affect muscle O(2) consumption. Model simulations of moderate exercise show that 1) muscle oxygenation is sufficient (C(m, O(2)) >2 mM) even during the transient state; 2) transient increases in concentration of muscle LA and arterial concentration of LA are associated with increases in glycolysis from increases in ADP/ATP and in LA production associated with a rise in NADH/NAD; 3) muscle ADP/ATP reaches a higher steady state that stimulates glycolysis, glycogenolysis, and oxidative phosphorylation to match the ATP demand; and 4) muscle NADH/NAD reaches a lower steady state that stimulates LA oxidation. It is suggested that the continuous stimulation of ATP synthesis processes during moderate exercise is mainly due to a higher ADP/ATP, not to a higher NADH/NAD. Critical measurements needed to quantify metabolic control mechanisms are identified.

Single cell model for simultaneous drug delivery and efflux.

Multidrug resistance (MDR) of some cancer cells is a major challenge for chemotherapy of systemic cancers to overcome. To experimentally uncover the cellular mechanisms leading to MDR, it is necessary to quantitatively assess both drug influx into, and efflux from, the cells exposed to drug treatment. By using a novel molecular microdelivery system to enforce continuous and adjustable drug influx into single cells by controlled diffusion through a gel plug in a micropipet tip, drug resistance studies can now be performed on the single cell level. Our dynamic model of this scheme incorporates drug delivery, diffusive mixing, and accumulation inside the cytoplasm, and efflux by both passive and active membrane transport. Model simulations using available experimental information on these processes can assist in the design of MDR related experiments on single cancer cells which are expected to lead to a quantitative evaluation of mechanisms. Simulations indicate that drug resistance of a cancer cell can be quantified better by its dynamic response than by steady-state analysis.

A model analysis of lactate accumulation during muscle ischemia.

PURPOSE: The mechanistic basis of the relationship between tissue [O2] and tissue or blood lactate (LA) concentration during tissue hypoxia are not fully understood. However, blood and tissue lactate accumulation are still used as indicators of tissue hypoxia in critically ill patients. To investigate this relationship, we applied a previously developed mathematical model of human bioenergetics to simulate the integrated responses (cellular, tissue, and whole body) to moderate (10% to 45%) and severe (50% to 80%) reductions in muscle blood flow. MATERIALS AND METHODS: Model simulations of muscle ischemia predicted metabolite concentration changes in muscle, splanchnic bed, and other tissues, and were compared with experimental data in humans for model validation. RESULTS: In general, simulations closely predicted the pattern of change in substrates and control metabolites to that observed experimentally. Specifically, simulations showed that most of the increase in muscle LA production during moderate ischemia was due to an increase in pyruvate (PY) and notto the change in redox state induced by a small decrease in O2 consumption. However, during severe ischemia, changes in [LA]/[PY] ratio in venous blood corresponded very closely to changes in tissue redox state. Because both blood [LA] and [LA]/[PY] tracked changes in tissue redox state very well, these can be used reliably as indices of tissue hypoxia during severe muscle ischemia. CONCLUSIONS: Based on the simulations, the commonly used threshold value for venous [LA]/[PY] = 14 as evidence of tissue hypoxia seems appropriate during severe ischemia.

System for dynamic measurements of membrane capacitance in intact epithelial monolayers.

Dynamic measurements of exocytosis have been difficult to perform in intact epithelial monolayers. We have designed a system that estimates with +/-1% accuracy (99% confidence) the total membrane capacitance of monolayers represented by a lumped model. This impedance measurement and analysis system operates through a conventional transepithelial electrophysiology clamp, performing all signal measurements as frequently as every 5 s. Total membrane capacitance (the series combination of apical and basolateral membranes) is the inverse of one of three unique coefficients that describe the monolayer impedance. These coefficients are estimated using a weighted, nonlinear, least-squares algorithm. Using the estimated coefficients, solution ranges for individual membrane parameters are calculated, frequently providing results within +/-20% of true values without additional electrophysiological measurements. We determined the measurement system specifications and statistical significance of estimated parameters using 1) analytical testing with circuit simulation software and equation-generated data; 2) a system noise analysis combined with Monte Carlo simulations; and 3) analog model circuits for calibration of the electronic system and to check equation-generated results. Finally, the time course of capacitance changes associated with purinergically stimulated mucin exocytosis are quantified in monolayers of the colonic goblet cell-like cell line HT29-CI.16E.

A mechanistic model of plasma filtration.

A model describing the sieving and transmembrane pressure behavior of plasma filtration is developed and numerically simulated. The model assumes a mechanistic criteria for particle passage through a membrane with cylindrical pores. The initial pore diameter distribution and porosity are assumed to be known. Model inputs include the particle diameter distribution, concentration and total flow rate of the permeate plasma solution. Outputs of the model include transmembrane pressure, the time-averaged sieving coefficients, and size distributions of the deposited particles and accumulated filtrate particles. Optimal filtration is characterized by high, stable sieving coefficients for desired particles, high retention of larger particles and relatively small increases in transmembrane pressure. These characteristics are realized for membranes with mean pore diameters equal to or slightly larger than mean permeate particle diameters. Simulations demonstrate that the incorporation of membrane properties into models of plasma filtration is both significant and readily possible.

Characterization of tissue morphology, angiogenesis, and temperature in the adaptive response of muscle tissue to chronic heating.

Previous investigations on the in vivo effects of chronic heat on tissue suggest a response whereby heated tissue temperatures decrease over time. This response occurred in conjunction with localized angiogenesis, which possibly contributed to the temperature decreases by increasing local perfusion and enhancing tissue heat transfer. Our own studies were the first to use a chronic heat source to heat tissue at initial interfacial temperatures between 40 degrees C and 46 degrees C. Initial temperatures above 45.3+/-2.2 degrees C caused necrosis of adjacent tissue. Through an adaptive response, the necrosis was removed by 7 weeks and replaced by a highly vascularized tissue capsule at 41.8+/-0.5 degrees C. The present study sought to characterize the spatial distribution, number of capillaries, and temperatures associated with this adaptive response. Heated and control muscle tissue sections were removed after 2, 4, and 7 weeks of heating at 0.08 W/cm2. Tissue layer thicknesses and capillary densities were measured and correlated with corresponding tissue temperatures. Necrosis was present adjacent to the heat source at 2 and 4 weeks; however by 7 weeks, a highly vascularized fibrous tissue capsule had replaced nearly all necrosis. Capillary densities, particularly near the heat source, were significantly greater at 7 weeks than at either 2 or 4 weeks. Capillary densities in heated tissue capillary fronts tripled from 2 to 7 weeks (106.4+/-14.3 caps/mm2 versus 39.1+/-18.5 caps/mm2). Furthermore, a mean temperature of 41.7+/-0.9 degrees C was measured in heated tissue capillary fronts at all durations, suggesting that this may be a threshold temperature for heat-induced angiogenesis or endothelial cell survival. These findings more completely characterize the perfusion component of the current mathematical model for heat transfer in tissue and will help to establish guidelines for the functional heat loss that an implantable, heat-producing device may allow.

Role of O2 in regulation of lactate dynamics during hypoxia: mathematical model and analysis.

The mechanistic basis of the relationship between O2 and lactate concentration in muscle is not fully understood. Although hypoxia can cause lactate (LA) accumulation, it is possible for LA accumulation to occur without hypoxia. Nevertheless, during conditions of low O2 availability, blood and tissue LA accumulation are used as indicators of hypoxia. To provide a framework for analyzing changes in energy metabolism and its regulation, we developed a mathematical model of human bioenergetics that links cellular metabolic processes to whole-body responses. Our model is based on dynamic mass balances and mechanistic kinetics in muscle, splanchnic and other body tissues for many substrates (glycogen, glucose, pyruvate, LA, O2, CO2, etc.) and control metabolites (e.g., ATP) through coupled reaction processes. Normal substrate concentrations in blood and tissues as well as model parameters are obtained directly or estimated indirectly from physiological observation in the literature. The model equations are solved numerically to simulate substrate concentration changes in tissues in response to disturbances. One key objective is to examine and quantify the mechanisms that control LA accumulation when O2 availability to the muscle is lowered. Another objective is to quantify the contribution of different tissues to an observed increase in blood lactate concentration. Simulations of system responses to respiratory hypoxia were examined and compared to physiological observations. Model simulations show patterns of change for substrates and control metabolites that behave similarly to those found experimentally. From the simulations, it is evident that a large decrease can occur in muscle O2 concentration, without affecting muscle respiration (Um,O2) significantly. However, a small decrease in Um,O2 (1%-2%) can result in a large increase in LA production (50%-100%). The cellular rate of oxygen consumption, Um,O2, which is coupled to ATP formation and NADH oxidation, can regulate other processes (e.g., glycolysis, pyruvate reduction) with high sensitivity through its effects on ADP/ATP and NADH/NAD. Thus, although LA metabolism does not depend directly on O2 concentration, it is indirectly affected by Um,O2, through changes in ADP/ATP, and NADH/NAD. Arterial LA concentration (Ca,LA) follows the pattern of change of muscle LA concentration (Cm,LA). Nevertheless, changes in Ca,LA, due to Cm,LA, are unlikely to be detected experimentally because changes in Cm,LA are small relative to the total LA concentrations in other tissues.

Macromolecular transport in the arterial intima: comparison of chronic and acute injuries.

Hypertension is a known risk factor for the development of atherosclerosis, which is characterized by the abnormal accumulation of low-density lipoprotein and other plasma-borne macromolecules. The goal of this study was to measure accumulation of a plasma-borne macromolecular marker, horseradish peroxidase (HRP; 44 kDa), in the aortic intima and media of chronically hypertensive rats. HRP transport in 2-yr-old spontaneously hypertensive rats (SHR) was compared with that in age-matched Wistar-Kyoto rats (WKY) under conditions in which blood pressures were not significantly different during the 15-min HRP circulation. Intimal accumulation and medial HRP concentration profiles were obtained from methacrylate-embedded sections after reaction with 3,3'-diaminobenzidine and H2O2. Data were analyzed using a mathematical model of macromolecular transport to quantify the permeabilities of endothelium and internal elastic lamina (IEL). Chronic hypertension increased endothelial permeability without a change in IEL permeability. An apparent convective flux of HRP into the intima of SHR raised intimal HRP to a concentration higher than that of HRP in the plasma. Our results suggest that the intimal accumulation of plasma-borne macromolecules from pressure-driven convection is normally minimized by an intact endothelium. Similar changes resulted from acute injury by lipopolysaccharide, suggesting endothelial injury could account for transport changes associated with hypertension. After either chronic or acute endothelial damage, transport of macromolecules into the intima increases, but the IEL continues to retard transport of macromolecules beyond the intima, resulting in increased intimal accumulation.

Sensitivity analysis of one-dimensional heat transfer in tissue with temperature-dependent perfusion.

Design criteria for implantable heat-generating devices such as the total artificial heart require the determination of safe thresholds for chronic heating. This involves in-vivo experiments in which tissue temperature distributions are obtained in response to known heat sources. Prior to experimental studies, simulation using a mathematical model can help optimize the design of experiments. In this paper, a theoretical analysis of heat transfer is presented that describes the dynamic, one-dimensional distribution of temperature from a heated surface. Loss of heat by perfusion is represented by temperature-independent and temperature-dependent terms that can reflect changes in local control of blood flow. Model simulations using physiologically appropriate parameter values indicate that the temperature elevation profile caused by a heated surface adjacent to tissue may extend several centimeters into the tissue. Furthermore, sensitivity analysis indicates the conditions under which temperature profiles are sensitive to changes in thermal diffusivity and perfusion parameters. This information provides the basis for estimation of model parameters in different tissues and for prediction of the thermal responses of these tissues.

Exogenous oxidized low-density lipoprotein injures and alters the barrier function of endothelium in rats in vivo.

Oxidation converts low-density lipoprotein (LDL) into a cytotoxin in vitro. Oxidized LDL exists in vivo in atherosclerotic lesions and possibly in plasma. Many cell functions are altered in vitro by oxidized LDL, but few have been examined in vivo. To test whether oxidized LDL could injure endothelial cells and alter endothelial permeability to macromolecules in vivo, we infused oxidized LDL, native LDL, or their solvent intravenously into rats. Subsequently, endothelial cell injury and proliferation were measured, and the transport into the aorta wall of the macromolecule horseradish peroxidase (HRP) was quantified. Transport data were analyzed using mathematical models of macromolecular transport; parameters were estimated by optimally fitting model-predicted HRP concentrations to experimental data. Compared with native LDL or solvent control infusion, oxidized LDL infusion increased (1) the number of injured aortic endothelial cells fivefold to sixfold at 36 hours, (2) proliferation of endothelial cells at 48 hours, (3) intimal and medial accumulations of HRP twofold to threefold at 48 hours, and (4) the permeability coefficient of the endothelium to HRP fourfold to fivefold at 48 hours. Hence, oxidized LDL administered in vivo can injure the endothelium, despite the presence of endogenous antioxidants, compromising the function of the endothelium as a permeability barrier.

Dynamic model of oxygen transport for transcutaneous PO2 analysis.

A dynamic model of oxygen transport through the outer skin layers and a polarographic sensor was developed for the analysis of transcutaneous oxygen tension (tcPO2). It provides a basis for quantifying the factors that determine the relationship between tcPO2 and arterial oxygen tension (PaO2). Model simulations show the importance of stratum papillare metabolic oxygen consumption; the oxygen permeability of the skin relative to that of the sensor membrane and electrolyte; and temperature and the oxyhemoglobin dissociation curve. These simulations were consistent with experimental data obtained by using microcathode transcutaneous oxygen sensors, which were placed on the skin of 10 healthy adults. Furthermore, the model indicates that accurate evaluation of arterial oxygen tension by using transcutaneous measurements requires continuous estimation of skin perfusion. On the basis of tcPO2 measurements made during arterial occlusion, simulations indicate that quantitative evaluation of the metabolic oxygen consumption of the viable skin tissues is possible only when the oxygen permeabilities of the skin and sensor are known.

Optimal experiment design for PET quantification of receptor concentration.

The mathematical models used to analyze positron emission tomography (PET) data obtained for receptor quantitation have many unknown parameters which must be estimated from the data. Obtaining unique and precise estimates of the model parameters from PET data is difficult as a result of the complex interdependence of the parameters. Here the authors address the task of estimating the concentration of myocardial beta-adrenergic receptors using unlabeled and (18)F-labeled S(-)-fluorocarazolol as the receptor ligand. For a three-injection study the authors have optimized the ligand injection times and dosages using the D-optimal criterion for estimating receptor concentration. They found that in optimizing a three-injection experimental design, the dose of ligand in the third injection approaches zero so that the optimal three-injection design is actually a two-injection experiment. Using this optimal experiment, the authors demonstrate estimates of receptor concentration that are almost five times as precise as compared to an empirically designed three-injection experiment.