Anup K. Paul

Pulsatile arterial wall-blood flow interaction with wall pre-stress computed using an inverse algorithm

BackgroundThe computation of arterial wall deformation and stresses under physiologic conditions requires a coupled compliant arterial wall-blood flow interaction model. The in-vivo arterial wall motion is constrained by tethering from the surrounding tissues. This tethering, together with the average in-vivo pressure, results in wall pre-stress. For an accurate simulation of the physiologic conditions, it is important to incorporate the wall pre-stress in the computational model. The computation of wall pre-stress is complex, as the un-loaded and un-tethered arterial shape with residual stress is unknown. In this study, the arterial wall deformation and stresses in a canine femoral artery under pulsatile pressure was computed after incorporating the wall pre-stresses. A nonlinear least square optimization based inverse algorithm was developed to compute the in-vivo wall pre-stress.MethodsFirst, the proposed inverse algorithm was used to obtain the un-loaded and un-tethered arterial geometry from the unstressed in-vivo geometry. Then, the un-loaded, and un-tethered arterial geometry was pre-stressed by applying a mean in-vivo pressure of 104.5 mmHg and an axial stretch of 48% from the un-tethered length. Finally, the physiologic pressure pulse was applied at the inlet and the outlet of the pre-stressed configuration to calculate the in-vivo deformation and stresses. The wall material properties were modeled with an incompressible, Mooney-Rivlin model derived from previously published experimental stress-strain data (Attinger et al., 1968).ResultsThe un-loaded and un-tethered artery geometry computed by the inverse algorithm had a length, inner diameter and thickness of 35.14 mm, 3.10 mm and 0.435 mm, respectively. The pre-stressed arterial wall geometry was obtained by applying the in-vivo axial-stretch and average in-vivo pressure to the un-loaded and un-tethered geometry. The length of the pre-stressed artery, 51.99 mm, was within 0.01 mm (0.019%) of the in-vivo length of 52.0 mm; the inner diameter of 3.603 mm was within 0.003 mm (0.08%) of the corresponding in-vivo diameter of 3.6 mm, and the thickness of 0.269 mm was within 0.0015 mm (0.55%) of the in-vivo thickness of 0.27 mm. Under physiologic pulsatile pressure applied to the pre-stressed artery, the time averaged longitudinal stress was found to be 42.5% higher than the circumferential stresses. The results of this study are similar to the results reported by Zhang et al., (2005) for the left anterior descending coronary artery.ConclusionsAn inverse method was adopted to compute physiologic pre-stress in the arterial wall before conducting pulsatile hemodynamic calculations. The wall stresses were higher in magnitude in the longitudinal direction, under physiologic pressure after incorporating the effect of in-vivo axial stretch and pressure loading.

Predicting Temperature Changes During Cold Water Immersion and Exercise Scenarios: Application of a Tissue–Blood Interactive Whole-Body Model

A whole-body model with tissue–blood interaction was simulated to predict (1) cooling during cold water immersion of the human body in water temperatures of 18.5°C, 10°C, and 0°C and (2) heating of the human body at walking intensities of 0.9, 1.2, and 1.8 m/s for 30 min. The transient responses of body and blood temperature were obtained by simultaneously solving Pennes’ bioheat and energy balance equations. Predicted survival time at 0°C was around 39–50 min. During exercise with sweating, core body temperature was regulated within 0.25°C of its steady state value of 37.23°C.

Optimization of balloon obstruction for simulating equivalent pressure drop in physiological stenoses

The study of hemodynamics in an animal model simulating coronary stenosis has been limited due to the lack of a safe, accurate and reliable technique for creating an artificial stenosis. Creating artificial stenosis using occluders in an open-chest procedure has often caused myocardial infarction (MI) or severe injury to the vessel resulting in high failure rates. To minimize these issues, closed-chest procedures with internal balloon obstruction are often used to create an artificial stenosis. However, the hemodynamics in a blood vessel with internal balloon obstruction versus a physiological stenosis has not been compared. Hence, the aim of this research is to develop a relationship to predict the balloon obstruction equivalent to that of a physiological stenosis. The pressure drop in a balloon obstruction was evaluated and compared with that in a physiological stenosis. It was observed that the flow characteristics in balloon obstructions are more viscous dominated, whereas those in physiological stenoses are momentum dominated. Balloon radius was iteratively varied using a Design of Experiments (DOE) based optimization method to obtain a pressure drop equal to that of a physiological stenosis at mean hyperemic flow rates. A linear relation was obtained to predict equivalent balloon obstruction for a physiological stenosis. Further, the details were verified with our in vivo (animal) study data.

Non-invasive assessment of the severity of aortic stenosis by Doppler derived aortic valve coefficient: a retrospective feasibility study in humans.

Background: Accurate assessment of the severity of stenosis is critical in patients with aortic stenosis. The ambiguities and imprecisions of the current diagnostic parameters can result in suboptimal clinical decisions. In this feasibility study, we investigate the functional diagnostic parameter AVC (Aortic Valve coefficient: ratio of the total transvalvular pressure drop to the proximal dynamic pressure) in the non-invasive assessment of the severity of aortic stenosis by correlating with the current diagnostic parameters. Original Research Article Paul et al.; BJMMR, 8(2): 177-191, 2015; Article no.BJMMR.2015.438 178 Methods and Results: AVC was calculated using Doppler measured diagnostic parameters obtained from retrospective chart reviews. A theoretical pressure recovery correction was applied to the pressure drop calculated from Doppler measurements to obtain AVC. A statistically significant and strong combined linear correlation (r = 0.93, p<0.001) of AVC with the transvalvular pressure drop and the left ventricular outflow tract velocity was observed. The mean values of AVC were shown to better delineate moderate and severe stenosis (54% difference) than the mean values of Doppler measured pressure drop and aortic valve area (22% and 25% difference, respectively), when the patients were categorized based on the catheterization measured pressure drop. Conclusion: The feasibility of using pressure and flow measurements obtained from Doppler measurements in a single combined diagnostic index for the assessment of aortic stenosis severity has been evaluated. The nondimensional clinical parameter, AVC, is expected to account for the variation in flow and pressure drop and thus improve the delineation of different grades of aortic stenosis. AVC must be further evaluated in a controlled prospective study.

Reducing the Inconsistency between Doppler and Invasive Measurements of the Severity of Aortic Stenosis Using Aortic Valve Coefficient: A Retrospective Study on Humans

Background. It is not uncommon to observe inconsistencies in the diagnostic parameters derived from Doppler and catheterization measurements for assessing the severity of aortic stenosis (AS) which can result in suboptimal clinical decisions. In this pilot study, we investigate the possibility of improving the concordance between Doppler and catheter assessment of AS severity using the functional diagnostic parameter called aortic valve coefficient (AVC), defined as the ratio of the transvalvular pressure drop to the proximal dynamic pressure. Method and Results. AVC was calculated using diagnostic parameters obtained from retrospective chart reviews. AVC values were calculated independently from cardiac catheterization () and Doppler measurements (). An improved significant correlation was observed between Doppler and catheter derived AVC (, ) when compared to the correlation between Doppler and catheter measurements of mean pressure gradient (, ) and aortic valve area (, ). The correlation between Doppler and catheter derived AVC exhibited a marginal improvement over the correlation between Doppler and catheter derived aortic valve resistance (, ). Conclusion. AVC is a refined clinical parameter that can improve the concordance between the noninvasive and invasive measures of the severity of aortic stenosis.

Comparison between experimental and Heart rate-derived core body temperatures using a 3D whole body model

Determination of core body temperature (Tc), a measure of metabolic rate, in firefighters is needed to avoid heat-stress related injury in real time. The measurement of Tc is neither routine nor trivial. This research is significant as thermal model to determine Tc is still fraught with uncertainties and reliable experimental data for validation are rare. The objective of this study is to develop a human thermoregulatory model that uses the heart rate measurements to obtain Tc for firefighters using a 3D whole body model. The hypothesis is that the heart rate-derived computed Tc correlates with the measured Tc during firefighting activities. The transient thermal response of the human body was calculated by simultaneously solving the Pennes’ bioheat and energy balance equations. The difference between experimental and numerical values of Tc was less than 2.6%. More importantly, a 6 10% alteration in heart rate was observed to have appreciable influence on Tc, resulting in a 6 1.2 C change. A 10% increase in the heart rate causes a significant relative % increase (52%) in Tc, considering its allowable/safe limit of 39.5 C. Routine acquisition of the heart rate data during firefighting scenario can be used to derive Tc of firefighters in real time using the proposed 3D whole body model. [DOI: 10.1115/1.4041594]

Evaluation of Hemodynamics in a Prestressed and Compliant Tapered Femoral Artery Using an Optimization-Based Inverse Algorithm.

The important factors that affect the arterial wall compliance are the tissue properties of the arterial wall, the in vivo pulsatile pressure, and the prestressed condition of the artery. It is necessary to obtain the load-free geometry for determining the physiological level of prestress in the arterial wall. The previously developed optimization-based inverse algorithm was improved to obtain the load-free geometry and the wall prestress of an idealized tapered femoral artery of a dog under varying arterial wall properties. The compliance of the artery was also evaluated over a range of systemic pressures (72.5-140.7 mmHg), associated blood flows, and artery wall properties using the prestressed arterial geometry. The results showed that the computed load-free outer diameter at the inlet of the tapered artery was 6.7%, 9.0%, and 12% smaller than the corresponding in vivo diameter for the 25% softer, baseline, and 25% stiffer arterial wall properties, respectively. In contrast, the variations in the prestressed geometry and circumferential wall prestress were less than 2% for variable arterial wall properties. The computed compliance at the inlet of the prestressed artery for the baseline arterial wall property was 0.34%, 0.19%, and 0.13% diameter change/mmHg for time-averaged pressures of 72.5, 104.1, and 140.7 mmHg, respectively. However, the variation in compliance due to the change in arterial wall property was less than 6%. The load-free and prestressed geometries of the idealized tapered femoral artery were accurately (error within 1.2% of the in vivo geometry) computed under variable arterial wall properties using the modified inverse algorithm. Based on the blood-arterial wall interaction results, the arterial wall compliance was influenced significantly by the change in average pressure. In contrast, the change in arterial wall property did not influence the arterial wall compliance.

Influence Of Exercise Condition On Tissue Blood Temperature Using Whole Body Model

Predicting thermal responses of the human body accurately during different exercise conditions is of increasing importance. Computing changes in the core body temperature (Tc) during exercise require detailed modeling of both the body tissue temperature and the time-dependent blood temperature. Predicting changes in Tc is challenging because the model needs to respond effectively to the changes in perfusion or sweating. Our study was to demonstrate the ability of a recently developed whole body heat transfer model. It simulates the tissue-blood interaction to predict the thermal response of the human body under different exercise intensities. The cases simulated were of a human being walking on a treadmill at 0.9, 1.2 and 1.8 m/s for 30 minutes. It was shown that Tc was effectively regulated within 0.17 °C of the steady state value of 37.23 °C for the three cases by means of adjusting the cardiac output; varying between 15 to 25 liters per minute.Copyright

Theoretical Predictions of Body Tissue and Blood Temperature During Cold Water Immersion Using a Whole Body Model

Understanding the thermal response of the human body under various environmental and thermal stress conditions is of growing importance. Calculation of the core body temperature and the survivability of the body during immersion in cold water require detailed modeling of both the body tissue and the time-dependent blood temperature. Predicting body temperature changes under cold stress conditions is considered challenging since factors like thickness of the skin and blood perfusion within the skin layer become influential. Hence, the aim of this research was to demonstrate the capability of a recently developed whole body heat transfer model that simulates the tissue-blood interaction to predict the cooling of the body during immersion in cold water. It was shown that computed drop in core temperature agrees within 0.57 °C of the results calculated using a detailed network model. The predicted survival time in 0 °C water was less than an hour whereas in 18.5 °C water, the body attained a relatively stable core temperature of 34 °C in 2.5 hours.© 2013 ASME

Assessment of Aortic Stenosis Severity Using Pressure Drop Coefficient: A Retrospective Study in Humans

Accurate assessment of the stenosis severity is critical in patients with aortic stenosis (AS). The ambiguities and reduced sensitivities of the current diagnostic parameters can result in sub-optimal clinical decision making. In this preliminary study, we investigate the functional diagnostic parameter CDP (ratio of the transvalvular pressure drop to the proximal dynamic pressure) for the assessment of AS severity by correlating with the current diagnostic parameters. CDP was calculated using diagnostic parameters obtained from retrospective chart reviews. CDP values were calculated independently from Doppler and catheterization measurements. CDP exhibited better correlation with transvalvular pressure drop and jet velocity simultaneously, than when correlated independently with the same diagnostic parameters. CDP increases with increasing AS severity, which is consistent with hydrodynamic principles. This retrospective study is a prelude to a prospective study to evaluate CDP for AS severity assessment.Copyright