Individualized estimation of human core body temperature using noninvasive measurements.

A rising core body temperature (Tc) during strenuous physical activity is a leading indicator of heat-injury risk. Hence, a system that can estimate Tc in real time and provide early warning of an impending temperature rise may enable proactive interventions to reduce the risk of heat injuries. However, real-time field assessment of Tc requires impractical invasive technologies. To address this problem, we developed a mathematical model that describes the relationships between Tc and noninvasive measurements of an individual's physical activity, heart rate, and skin temperature, and two environmental variables (ambient temperature and relative humidity). A Kalman filter adapts the model parameters to each individual and provides real-time personalized Tc estimates. Using data from three distinct studies, comprising 166 subjects who performed treadmill and cycle ergometer tasks under different experimental conditions, we assessed model performance via the root mean squared error (RMSE). The individualized model yielded an overall average RMSE of 0.33 (SD = 0.18)°C, allowing us to reach the same conclusions in each study as those obtained using the Tc measurements. Furthermore, for 22 unique subjects whose Tc exceeded 38.5°C, a potential lower Tc limit of clinical relevance, the average RMSE decreased to 0.25 (SD = 0.20)°C. Importantly, these results remained robust in the presence of simulated real-world operational conditions, yielding no more than 16% worse RMSEs when measurements were missing (40%) or laden with added noise. Hence, the individualized model provides a practical means to develop an early warning system for reducing heat-injury risk. NEW & NOTEWORTHY A model that uses an individual's noninvasive measurements and environmental variables can continually "learn" the individual's heat-stress response by automatically adapting the model parameters on the fly to provide real-time individualized core body temperature estimates. This individualized model can replace impractical invasive sensors, serving as a practical and effective surrogate for core temperature monitoring.

Assessing Airflow Sensitivity to Healthy and Diseased Lung Conditions in a Computational Fluid Dynamics Model Validated In Vitro.

Computational models are useful for understanding respiratory physiology. Crucial to such models are the boundary conditions specifying the flow conditions at truncated airway branches (terminal flow rates). However, most studies make assumptions about these values, which are difficult to obtain in vivo. We developed a computational fluid dynamics (CFD) model of airflows for steady expiration to investigate how terminal flows affect airflow patterns in respiratory airways. First, we measured in vitro airflow patterns in a physical airway model, using particle image velocimetry (PIV). The measured and computed airflow patterns agreed well, validating our CFD model. Next, we used the lobar flow fractions from a healthy or chronic obstructive pulmonary disease (COPD) subject as constraints to derive different terminal flow rates (i.e., three healthy and one COPD) and computed the corresponding airflow patterns in the same geometry. To assess airflow sensitivity to the boundary conditions, we used the correlation coefficient of the shape similarity (R) and the root-mean-square of the velocity magnitude difference (Drms) between two velocity contours. Airflow patterns in the central airways were similar across healthy conditions (minimum R, 0.80) despite variations in terminal flow rates but markedly different for COPD (minimum R, 0.26; maximum Drms, ten times that of healthy cases). In contrast, those in the upper airway were similar for all cases. Our findings quantify how variability in terminal and lobar flows contributes to airflow patterns in respiratory airways. They highlight the importance of using lobar flow fractions to examine physiologically relevant airflow characteristics.

An Integrated Musculoskeletal-Finite-Element Model to Evaluate Effects of Load Carriage on the Tibia During Walking.

Prior studies have assessed the effects of load carriage on the tibia. Here, we expand on these studies and investigate the effects of load carriage on joint reaction forces (JRFs) and the resulting spatiotemporal stress/strain distributions in the tibia. Using full-body motion and ground reaction forces from a female subject, we computed joint and muscle forces during walking for four load carriage conditions. We applied these forces as physiological loading conditions in a finite-element (FE) analysis to compute strain and stress. We derived material properties from computed tomography (CT) images of a sex-, age-, and body mass index-matched subject using a mesh morphing and mapping algorithm, and used them within the FE model. Compared to walking with no load, the knee JRFs were the most sensitive to load carriage, increasing by as much as 26.2% when carrying a 30% of body weight (BW) load (ankle: 16.4% and hip: 19.0%). Moreover, our model revealed disproportionate increases in internal JRFs with increases in load carriage, suggesting a coordinated adjustment in the musculature functions in the lower extremity. FE results reflected the complex effects of spatially varying material properties distribution and muscular engagement on tibial biomechanics during walking. We observed high stresses on the anterior crest and the medial surface of the tibia at pushoff, whereas high cumulative stress during one walking cycle was more prominent in the medioposterior aspect of the tibia. Our findings reinforce the need to include: (1) physiologically accurate loading conditions when modeling healthy subjects undergoing short-term exercise training and (2) the duration of stress exposure when evaluating stress-fracture injury risk. As a fundamental step toward understanding the instantaneous effect of external loading, our study presents a means to assess the relationship between load carriage and bone biomechanics.

Computational Study of Thrombus Formation and Clotting Factor Effects under Venous Flow Conditions.

A comprehensive understanding of thrombus formation as a physicochemical process that has evolved to protect the integrity of the human vasculature is critical to our ability to predict and control pathological states caused by a malfunctioning blood coagulation system. Despite numerous investigations, the spatial and temporal details of thrombus growth as a multicomponent process are not fully understood. Here, we used computational modeling to investigate the temporal changes in the spatial distributions of the key enzymatic (i.e., thrombin) and structural (i.e., platelets and fibrin) components within a growing thrombus. Moreover, we investigated the interplay between clot structure and its mechanical properties, such as hydraulic resistance to flow. Our model relied on the coupling of computational fluid dynamics and biochemical kinetics, and was validated using flow-chamber data from a previous experimental study. The model allowed us to identify the distinct patterns characterizing the spatial distributions of thrombin, platelets, and fibrin accumulating within a thrombus. Our modeling results suggested that under the simulated conditions, thrombin kinetics was determined predominantly by prothrombinase. Furthermore, our simulations showed that thrombus resistance imparted by fibrin was ∼30-fold higher than that imparted by platelets. Yet, thrombus-mediated bloodflow occlusion was driven primarily by the platelet deposition process, because the height of the platelet accumulation domain was approximately twice that of the fibrin accumulation domain. Fibrinogen supplementation in normal blood resulted in a nonlinear increase in thrombus resistance, and for a supplemented fibrinogen level of 48%, the thrombus resistance increased by ∼2.7-fold. Finally, our model predicted that restoring the normal levels of clotting factors II, IX, and X while simultaneously restoring fibrinogen (to 88% of its normal level) in diluted blood can restore fibrin generation to ∼78% of its normal level and hence improve clot formation under dilution.

Untangling the Effect of Head Acceleration on Brain Responses to Blast Waves.

Multiple injury-causing mechanisms, such as wave propagation, skull flexure, cavitation, and head acceleration, have been proposed to explain blast-induced traumatic brain injury (bTBI). An accurate, quantitative description of the individual contribution of each of these mechanisms may be necessary to develop preventive strategies against bTBI. However, to date, despite numerous experimental and computational studies of bTBI, this question remains elusive. In this study, using a two-dimensional (2D) rat head model, we quantified the contribution of head acceleration to the biomechanical response of brain tissues when exposed to blast waves in a shock tube. We compared brain pressure at the coup, middle, and contre-coup regions between a 2D rat head model capable of simulating all mechanisms (i.e., the all-effects model) and an acceleration-only model. From our simulations, we determined that head acceleration contributed 36-45% of the maximum brain pressure at the coup region, had a negligible effect on the pressure at the middle region, and was responsible for the low pressure at the contre-coup region. Our findings also demonstrate that the current practice of measuring rat brain pressures close to the center of the brain would record only two-thirds of the maximum pressure observed at the coup region. Therefore, to accurately capture the effects of acceleration in experiments, we recommend placing a pressure sensor near the coup region, especially when investigating the acceleration mechanism using different experimental setups.

Mathematical modeling of the heat-shock response in HeLa cells.

The heat-shock response is a key factor in diverse stress scenarios, ranging from hyperthermia to protein folding diseases. However, the complex dynamics of this physiological response have eluded mathematical modeling efforts. Although several computational models have attempted to characterize the heat-shock response, they were unable to model its dynamics across diverse experimental datasets. To address this limitation, we mined the literature to obtain a compendium of in vitro hyperthermia experiments investigating the heat-shock response in HeLa cells. We identified mechanisms previously discussed in the experimental literature, such as temperature-dependent transcription, translation, and heat-shock factor (HSF) oligomerization, as well as the role of heat-shock protein mRNA, and constructed an expanded mathematical model to explain the temperature-varying DNA-binding dynamics, the presence of free HSF during homeostasis and the initial phase of the heat-shock response, and heat-shock protein dynamics in the long-term heat-shock response. In addition, our model was able to consistently predict the extent of damage produced by different combinations of exposure temperatures and durations, which were validated against known cellular-response patterns. Our model was also in agreement with experiments showing that the number of HSF molecules in a HeLa cell is roughly 100 times greater than the number of stress-activated heat-shock element sites, further confirming the model's ability to reproduce experimental results not used in model calibration. Finally, a sensitivity analysis revealed that altering the homeostatic concentration of HSF can lead to large changes in the stress response without significantly impacting the homeostatic levels of other model components, making it an attractive target for intervention. Overall, this model represents a step forward in the quantitative understanding of the dynamics of the heat-shock response.

Patterns of gene expression associated with recovery and injury in heat-stressed rats.

BACKGROUND: The in vivo gene response associated with hyperthermia is poorly understood. Here, we perform a global, multiorgan characterization of the gene response to heat stress using an in vivo conscious rat model. RESULTS: We heated rats until implanted thermal probes indicated a maximal core temperature of 41.8°C (Tc,Max). We then compared transcriptomic profiles of liver, lung, kidney, and heart tissues harvested from groups of experimental animals at Tc,Max, 24 hours, and 48 hours after heat stress to time-matched controls kept at an ambient temperature. Cardiac histopathology at 48 hours supported persistent cardiac injury in three out of six animals. Microarray analysis identified 78 differentially expressed genes common to all four organs at Tc,Max. Self-organizing maps identified gene-specific signatures corresponding to protein-folding disorders in heat-stressed rats with histopathological evidence of cardiac injury at 48 hours. Quantitative proteomics analysis by iTRAQ (isobaric tag for relative and absolute quantitation) demonstrated that differential protein expression most closely matched the transcriptomic profile in heat-injured animals at 48 hours. Calculation of protein supersaturation scores supported an increased propensity of proteins to aggregate for proteins that were found to be changing in abundance at 24 hours and in animals with cardiac injury at 48 hours, suggesting a mechanistic association between protein misfolding and the heat-stress response. CONCLUSIONS: Pathway analyses at both the transcript and protein levels supported catastrophic deficits in energetics and cellular metabolism and activation of the unfolded protein response in heat-stressed rats with histopathological evidence of persistent heat injury, providing the basis for a systems-level physiological model of heat illness and recovery.

A virtual rat for simulating environmental and exertional heat stress.

Severe cases of environmental or exertional heat stress can lead to varying degrees of organ dysfunction. To understand heat-injury progression and develop efficient management and mitigation strategies, it is critical to determine the thermal response in susceptible organs under different heat-stress conditions. To this end, we used our previously published virtual rat, which is capable of computing the spatiotemporal temperature distribution in the animal, and extended it to simulate various heat-stress scenarios, including 1) different environmental conditions, 2) exertional heat stress, 3) circadian rhythm effect on the thermal response, and 4) whole body cooling. Our predictions were consistent with published in vivo temperature measurements for all cases, validating our simulations. We observed a differential thermal response in the organs, with the liver experiencing the highest temperatures for all environmental and exertional heat-stress cases. For every 3°C rise in the external temperature from 40 to 46°C, core and organ temperatures increased by ∼0.8°C. Core temperatures increased by 2.6 and 4.1°C for increases in exercise intensity from rest to 75 and 100% of maximal O2 consumption, respectively. We also found differences as large as 0.8°C in organ temperatures for the same heat stress induced at different times during the day. Even after whole body cooling at a relatively low external temperature (1°C for 20 min), average organ temperatures were still elevated by 2.3 to 2.5°C compared with normothermia. These results can be used to optimize experimental protocol designs, reduce the amount of animal experimentation, and design and test improved heat-stress prevention and management strategies.

A computational study of the respiratory airflow characteristics in normal and obstructed human airways.

Obstructive lung diseases in the lower airways are a leading health concern worldwide. To improve our understanding of the pathophysiology of lower airways, we studied airflow characteristics in the lung between the 8th and the 14th generations using a three-dimensional computational fluid dynamics model, where we compared normal and obstructed airways for a range of breathing conditions. We employed a novel technique based on computing the Pearson׳s correlation coefficient to quantitatively characterize the differences in airflow patterns between the normal and obstructed airways. We found that the airflow patterns demonstrated clear differences between normal and diseased conditions for high expiratory flow rates (>2300ml/s), but not for inspiratory flow rates. Moreover, airflow patterns subjected to filtering demonstrated higher sensitivity than airway resistance for differentiating normal and diseased conditions. Further, we showed that wall shear stresses were not only dependent on breathing rates, but also on the distribution of the obstructed sites in the lung: for the same degree of obstruction and breathing rate, we observed as much as two-fold differences in shear stresses. In contrast to previous studies that suggest increased wall shear stress due to obstructions as a possible damage mechanism for small airways, our model demonstrated that for flow rates corresponding to heavy activities, the wall shear stress in both normal and obstructed airways was <0.3Pa, which is within the physiological limit needed to promote respiratory defense mechanisms. In summary, our model enables the study of airflow characteristics that may be impractical to assess experimentally.

A 3-D mathematical model to identify organ-specific risks in rats during thermal stress.

Early prediction of the adverse outcomes associated with heat stress is critical for effective management and mitigation of injury, which may sometimes lead to extreme undesirable clinical conditions, such as multiorgan dysfunction syndrome and death. Here, we developed a computational model to predict the spatiotemporal temperature distribution in a rat exposed to heat stress in an attempt to understand the correlation between heat load and differential organ dysfunction. The model includes a three-dimensional representation of the rat anatomy obtained from medical imaging and incorporates the key mechanisms of heat transfer during thermoregulation. We formulated a novel approach to estimate blood temperature by accounting for blood mixing from the different organs and to estimate the effects of the circadian rhythm in body temperature by considering day-night variations in metabolic heat generation and blood perfusion. We validated the model using in vivo core temperature measurements in control and heat-stressed rats and other published experimental data. The model predictions were within 1 SD of the measured data. The liver demonstrated the greatest susceptibility to heat stress, with the maximum temperature reaching 2°C higher than the measured core temperature and 95% of its volume exceeding the targeted experimental core temperature. Other organs also attained temperatures greater than the core temperature, illustrating the need to monitor multiple organs during heat stress. The model facilitates the identification of organ-specific risks during heat stress and has the potential to aid in the development of improved clinical strategies for thermal-injury prevention and management.

Experimental and analytical temperature distributions during oven-based convection heating.

Mathematical models, combined with experimental evaluation, provide an approach to understand, design, and optimize food process operations. Magnetic resonance imaging (MRI), as an experimental technique, is used extensively in both medical and engineering applications to measure and quantify transport processes. Magnetic resonance (MR) was used in this study to assess a mathematical model based on Fourier's second law. The objective was to compare analytical solutions for the prediction of internal temperature distributions in foods during oven-based convective heating to experimental temperature measurements and determine at what point during the heating process a coupled heat and mass transport process should be considered. Cylindrical samples of a model food gel, Russet potato and rehydrated mashed potato were heated in a convection oven for specified times. Experimentally measured internal temperatures were compared to the internal temperatures predicted by the analytical model. Temperatures distributions in the axial direction compared favorably for the gel and acceptably for the Russet and mashed potato samples. The MR-acquired temperatures in the radial direction for the gel resulted in a shallower gradient than predicted but followed the expected trend. For the potato samples, the MR-acquired temperatures in the radial direction were not qualitatively similar to the analytical predictions due to moisture loss during heating. If temperature resolution is required in the radial direction, moisture losses merit the use of transport models that couple heat and mass transfer.

Finite-element model of interaction between fungal polysaccharide and monoclonal antibody in the capsule of Cryptococcus neoformans.

Many microorganisms such as bacteria and fungi possess so-called capsules made of polysaccharides which protect these microorganisms from environmental insults and host immune defenses. The polysaccharide capsule of Cryptococcus neoformans, a human pathogenic yeast, is capable of self-assembly, composed mostly of glucuronoxylomannan (GXM), a polysaccharide with a molecular weight of approximately 2,000,000, and has several layers with different densities. The objective of this study was to model pore-hindered diffusion and binding of the GXM-specific antibody within the C. neoformans capsule. Using the finite-element method (FEM), we created a model which represents the in vivo binding of a GXM-specific antibody to a C. neoformans cell taking into account the intravenous infusion time of antibody, antibody diffusion through capsular pores, and Michaelis-Menten kinetics of antibody binding to capsular GXM. The model predicted rapid diffusion of antibody to all regions of the capsule where the pore size was greater than the Stokes diameter of the antibody. Binding occurred primarily at intermediate regions of the capsule. The GXM concentration in each capsular region was the principal determinant of the steady-state antibody-GXM complex concentration, while the forward binding rate constant influenced the rate of complex formation in each region. The concentration profiles predicted by the model closely matched experimental immunofluorescence data. Inclusion of different antibody isotypes (IgG, IgA, and IgM) into the modeling algorithm resulted in similar complex formation in the outer capsular regions, but different depths of binding at the inner regions. These results have implications for the development of new antibody-based therapies.

Simulation of turbulent airflow using a CT based upper airway model of a racehorse.

Computational model for airflow through the upper airway of a horse was developed. Previous flow models for human airway do not hold true for horses due to significant differences in anatomy and the high Reynolds number of flow in the equine airway. Moreover, models that simulate the entire respiratory cycle and emphasize on pressures inside the airway in relation to various anatomical diseases are lacking. The geometry of the airway was created by reconstructing images obtained from computed tomography scans of a thoroughbred racehorse. Different geometries for inhalation and exhalation were used for the model based on the difference in the nasopharynx size during the two phases of respiration. The Reynolds averaged Navier-Stokes equations were solved for the isothermal flow with the standard k-epsilon model for turbulence. Transient pressure boundary conditions for the entire breathing cycle were obtained from past experimental studies on live horses. The flow equations were solved in a commercial finite volume solver. The flow rates, computed based on the applied pressure conditions, were compared to experimentally measured flow rates for model validation. Detailed analysis of velocity, pressure, and turbulence characteristics of the flow was done. Velocity magnitudes at various slices during inhalation were found to be higher than corresponding velocity magnitudes during exhalation. The front and middle parts of the nasopharynx were found to have minimum intraluminal pressure in the airway during inhalation. During exhalation, the pressures in the soft palate were higher compared to those in the larynx, epiglottis, and nasopharynx. Turbulent kinetic energy was found to be maximum at the entry to the airway and gradually decreased as the flow moved inside the airway. However, turbulent kinetic energy increased in regions of the airway with abrupt change in area. Based on the analysis of pressure distribution at different sections of the airway, it was concluded that the front part of the nasopharynx requires maximum muscular activity to support it during inhalation. During exhalation, the soft palate is susceptible to displacements due to presence of high pressures. These can serve as critical information for diagnosis and treatment planning of diseases known to affect the soft palate and nasopharynx in horses, and can potentially be useful for human beings.

Computational model predicts effective delivery of 188-Re-labeled melanin-binding antibody to metastatic melanoma tumors with wide range of melanin concentrations.

Metastatic melanoma is almost always deadly and new methods of treatment are urgently needed. Recently, we established the feasibility of radioimmunotherapy (RIT) for experimental melanoma in mice using a 188-rhenium (188Re)-labeled monoclonal antibody (mAb) 6D2 (IgM) to melanin. Our objective was to determine the effects of varying tumor melanin concentration and of different diffusivities and lymphatic clearance rates of the normal tissue, on the absorbed dose to the tumor in simulated therapy, in preparation for a clinical trial of RIT for melanoma. Using finite element analysis (FEA), we created a pharmacokinetic model that describes melanin-targeting RIT of a melanoma micrometastasis (1.3-mm radius) imbedded in normal tissue (14.3-mm radius). Our method incorporates antibody plasma kinetics, transcapillary transport, interstitial diffusion, and lymphatic clearance. Michaelis-Menten kinetics was used to model mAb binding to tumor melanin for melanin concentrations of 76, 7.6, 0.76, 0.076, and 0.0076 micromol/l. An absorbed dose was calculated, after accounting for direct and crossfire irradiation, on the basis of a 7.4-GBq intravenous dose of 188Re-6D2. The results showed that penetration of mAb into the tumor was inversely proportional to tumor melanin concentration. Decreased diffusivity and increased lymphatic clearance of the surrounding normal tissue decreased the dose to the tumor. The formation of mAb-melanin complex was remarkably similar within a 1000-fold range of melanin concentration, resulting in total doses of 2840, 2820, 2710, and 1990 cGy being delivered to tumors with melanin concentrations of 76, 7.6, 0.76, and 0.076 micromol/l, respectively. In conclusion, RIT of metastatic melanoma can be effective over a wide range of tumor melanin concentrations. The results can be useful in the design of a clinical trial of melanin-targeting RIT in patients with metastatic melanoma.