Fick Principle Research Articles

Poor correlation of venous lactate with systemic oxygen saturation in the paediatric cardiac ICU: a pilot study.

Cardiac intensive care providers require a comprehensive understanding of cardiac output and oxygen delivery. The estimation of cardiac output in clinical practice often relies on thermodilution and the Fick principle. Central venous saturation and lactate levels are commonly used indicators for cardiac output assessment. However, the relationship between venous lactate levels and venous oxygen saturation in paediatric cardiac intensive care patients remains unclear. This is a single-centre retrospective pilot study aimed to investigate the correlation between venous lactate and venous oxygen saturation in paediatric patients. Data collected included venous saturation, heart rate, mean arterial blood pressure, arterial saturation by pulse oximetry, cerebral and renal near-infra-red spectroscopy values, and the presence of a functionally univentricular heart. Statistical analyses included Bayesian Pearson correlation and regression analyses. A total of 203 data points from 37 unique patients were included in the analysis. There was no significant correlation between serum lactate and venous saturation (correlation coefficient = -0.01; Bayes factor 10 = 0.06). Serum lactate also did not correlate with other haemodynamic metrics. Venous saturation showed correlations with arterial saturation and cerebral and renal near-infra-red spectroscopy. Regression analysis revealed that parallel circulation, arterial saturation, and cerebral near-infra-red spectroscopy were predictive of venous saturation. The following equation resulted from the regression analysis: 68.0 - (12.7 x parallel circulation) - (0.8 x arterial saturation) + (0.3 x cerebral near-infra-red spectroscopy). This model had a Bayes factor 10 of 0.03 and adjusted R-squared was 0.29. In paediatric cardiac intensive care patients, there is no significant correlation between venous lactate and venous saturation, suggesting that lactate may not be a reliable marker for assessing the adequacy of oxygen delivery in this population. Only a weak correlation could be identified once the venous saturation was 70% or lower. Additional research is needed to explore alternative markers for monitoring oxygen delivery in critically ill paediatric patients.

Mechanisms of adaptations in cardiorespiratory fitness with exercise prescriptions differing in volume and intensity in middle-age men

Background: To examine the mechanisms of adaptations in cardiorespiratory fitness with different dose of amount and intensity exercise training in middle-aged men. Methods: A total of 67 sedentary subjects aged 40-49 yr were assigned to participate for 12 weeks in a control group or in one of three exercise groups: 1) low volume/moderate intensity 2) low volume/vigorous intensity and 3) high volume/vigorous intensity. They were tested for VO2max, cardiac output (Q) and stroke volume (SV) before and after training and maximal arterial-venous oxygen difference (a-vO2diff) calculated by the Fick Equation. Results: Contrasted to control group, VO2max increased similar in both LVVI and HVVI groups after 12 weeks; It indicated that the intensity of exercise appears to make a greater benefit than the amount of exercise on VO2max. However, Maximal cardiac output (Qmax) and a-vO2diff contributed to increase VO2max were differences in both of vigorous intensity groups. In LVVI group, Qmax together with maximal a-vO2diff contributed to the greater VO2max; in HVVI group, the majority of the increment in VO2max was relied on larger Qmax whereas a widened a-vO2diff. Conclusion: It is appropriate to recommend vigorous intensity exercise to improve cardiorespiratory fitness and encourage higher amount to confer additional benefit for Qmax.

Differential impacts of body composition on oxygen kinetics and exercise tolerance of HFrEF and HFpEF patients

This study aims to (1) compare the kinetics of pulmonary oxygen uptake (VO2p), skeletal muscle deoxygenation ([HHb]), and microvascular O2 delivery (QO2mv) between heart failure (HF) patients with reduced ejection fraction (HFrEF) and those with preserved ejection fraction (HFpEF), and (2) explore the correlation between body composition, kinetic parameters, and exercise performance. Twenty-one patients (10 HFpEF and 11 HFrEF) underwent cardiopulmonary exercise testing to assess VO2 kinetics, with near-infrared spectroscopy (NIRS) employed to measure [HHb]. Microvascular O2 delivery (QO2mv) was calculated using the Fick principle. Dual-energy X-ray absorptiometry (DEXA) was performed to evaluate body composition. HFrEF patients exhibited significantly slower VO2 kinetics (time constant [t]: 63 ± 10.8 s vs. 45.4 ± 7.9 s; P < 0.05) and quicker [HHb] response (t: 12.4 ± 9.9 s vs. 25 ± 11.6 s; P < 0.05). Microvascular O2 delivery (QO2mv) was higher in HFrEF patients (3.6 ± 1.2 vs. 1.7 ± 0.8; P < 0.05), who also experienced shorter time to exercise intolerance (281.6 ± 84 s vs. 405.3 ± 96 s; P < 0.05). Correlation analyses revealed a significant negative relationship between time to exercise and both QO2mv (ρ= -0.51; P < 0.05) and VO2 kinetics (ρ= -0.63). Body adiposity was negatively correlated with [HHb] amplitude (ρ= -0.78) and peak VO2 (ρ= -0.54), while a positive correlation was observed between lean muscle percentage, [HHb] amplitude, and tau (ρ= 0.74 and 0.57; P < 0.05), respectively. HFrEF patients demonstrate more severely impaired VO2p kinetics, skeletal muscle deoxygenation, and microvascular O2 delivery compared to HFpEF patients, indicating compromised peripheral function. Additionally, increased adiposity and reduced lean mass are linked to decreased oxygen diffusion capacity and impaired oxygen uptake kinetics in HFrEF patients.

There is no limitation for CO2 excretion across the lung in exercising American alligators (Alligator mississippiensis).

Vertebrates utilize various respiratory organs like gills, lungs, and skin in combination with diverse cardiovascular structures, including single, three, and four-chambered hearts, to enable oxygen delivery and carbon dioxide removal. They also exhibit differences in aerobic and anaerobic metabolism during exertion, but the cardiorespiratory gas transport of all vertebrates follow is a similar a four-step process governed by Fick's Principle and Fick's Law of Diffusion over the entire range of metabolic rates. Hillman et al. (2013) suggested that previous exercise studies have focused too narrowly on mammals and proposed that the cardiorespiratory system's excess capacity serves an evolutionary role in enhancing CO2 excretion in non-mammalian vertebrates. In contrast, an analysis by Hicks and Wang (2021) concluded that vertebrates maintain effective gas exchange even at peak activity, finding no evidence of arterial hypercapnia at maximal oxygen consumption and thus challenging the proposal of significant limitations to pulmonary or branchial CO2 efflux. In the present study, we investigate the limits for CO2 exchange in exercising American alligators (Alligator mississippiensis) and provide evidence that the cardiorespiratory system is adequately built to sustain CO2 excretion during strenuous exercise and maintain arterial PCO2 , with no evidence of diffusion limitation for pulmonary CO2 excretion.

321 Application of the Fick Principle for the study of visceral nutrient absorption and metabolism

Abstract In 1870, Adolf Fick introduced the concept for the calculation of cardiac output by measuring gas exchange in the lungs at a meeting of the Würzburg Physiology and Medical Society. It was not until around 1930 after the development of cardiac catheterization that it was fully verified. Fick’s equation also serves as the basis for all indicator dilution methods for measuring blood flow and has been applied to several tissues throughout the body. By measuring the blood concentration of nutrients supplying and draining a tissue bed, coupled with the flow of blood, the net nutrient exchange can be calculated. Researchers first began investigating the movement of nutrients into the portal system of ruminants in the 1950s and the first method for measuring nutrient exchange in small ruminants was published in the 1960s. This approach requires the implantation of vascular catheters into an artery and the hepatic portal vein which drains the stomach, intestines, and spleen. An additional catheter is implanted upstream in a mesenteric vein for infusion of a blood flow marker, and the addition of a catheter in a hepatic vein allows the measure of blood flow and nutrient transfer in the liver. These methods were adapted for calves and dairy cows in the 1970s. The 1980s brought further refinement of the methodologies such as improved catheter materials allowing animals to be maintained for extended periods and, several researchers published data from cattle, sheep, and goats. These methods have been coupled with measures of ruminal and intestinal disappearance as well as isotopic tracers to examine nutrient exchange and metabolism by tissues. The goal of this presentation is to review the development of this approach for studying nutrient absorption in vivo, and to highlight specific advancements in its application.

Quantitative mapping of renal oxygen consumption using pseudo-continuous arterial spin labeling and quantitative susceptibility mapping in humans.

To propose a new method for quantitatively mapping the renal metabolic rate of oxygen (RMRO2) and to evaluate the proposed method using a caffeine challenge. Pseudo-continuous arterial spin labeling (pCASL) and QSM sequences were used to obtain MR images in the kidney. Six healthy volunteers were scanned on caffeine and control days. The pCASL and QSM images were registered using DICOM information and rigid translation. The Fick principle was applied to estimate RMRO2. The results on caffeine and control days were compared to evaluate the capability of the proposed method to estimate renal oxygen consumption. A paired t-test was used to assess the statistical significance. Estimated renal blood flow (RBF), QSM, and RMRO2 maps were consistent with those reported in the literature. RMRO2 values were higher than the cerebral metabolic rate of oxygen (CMRO2) and were significantly reduced on the caffeine days compared to the control days, consistent with findings from non-MRI literature. The feasibility of measuring renal oxygen consumption using pCASL and QSM images was demonstrated. To the best of our knowledge, this work provides quantitative maps of renal oxygen consumption in humans for the first time. The results were consistent with the literature, including the statistically significant reduction in renal oxygen consumption with caffeine challenge. These findings suggest the potential utility of our technique in measuring renal oxygen consumption noninvasively, especially for patients with complications associated with contrast agents.

Dynamics of Fourier's and Fick's laws on the convectively heated oscillatory sheet under Arrhenius kinetics: The finite-difference technique

The significance of chemical reaction with activation energy and convective boundary conditions on the fluid flow via an oscillatory stretchy surface in the presence of permeable media and radiation is analyzed in this study. This inspection presents Fourier and Fick's laws-based equations for heat, mass transport, and liquid flow through an oscillating stretchy sheet. Understanding these dynamics aids in the optimisation of catalytic reaction settings, where gradients greatly influence reaction rates in concentration and temperature. The governing differential equations of the current study are modelled and changed into their non-dimensional form by employing suitable similarity variables. The finite difference method (FDM) is also used to numerically solve the obtained dimensionless equations. The influence of many factors on the several profiles is portrayed with graphical representations. The outcome of the unsteadiness and porosity parameters on the velocity profile with time coordinate is depicted. The increase in the radiation parameter and Biot number upsurges the thermal profile. The temperature reduces as the unsteadiness parameter and temperature relaxation time parameter grow. The upsurge in the activation energy parameter intensifies the mass transport. The rise in concentration relaxation time parameter diminishes the concentration profile.

Exploring an Electrochemical Batch Reactor for Nutrient Recovery from Wastewater: Continuum Modeling Analysis of Hydrodynamics and Tertiary Current Distribution

Advancing electrochemical reactors for nutrient recovery from wastewater requires an integration of continuum modeling alongside experimental investigations to appropriately capture transport effects on electrode performance. This continuum modeling approach facilitates the comprehensive evaluation and optimization of electrochemical reactor performance, especially with respect to intricate phenomena that may be challenging to observe solely through experimentation. The optimization process not only enhances the efficacy of existing batch reactors but also lays the foundation for designing and scaling up continuous electrochemical reactors for nutrient recovery [1].A key transport phenomenon in electrochemistry is hydrodynamics because flow dynamics around electrodes dictate mass transport magnitude and uniformity, thereby impacting current distribution, efficiency, and electrolytic energy consumption during electrolysis. Achieving homogeneous velocity fields while avoiding undesirable flow features is essential to prevent non-uniform potential and current density distributions along the electrodes, mitigating side reactions and ensuring the overall efficacy of the electrochemical processes [2].In this study, a two-dimensional model of an electrochemical batch reactor was developed using COMSOL Multiphysics software to investigate reactor hydrodynamics, electrochemical reactions, and mass transfer of species. Employing the finite element method, the model incorporated the k-epsilon turbulence model for hydrodynamics simulation, widely used in literature for simulating fluid flow and mixing behavior [3]. Electrochemical reactions at the cathode (oxygen reduction) were modeled using the Butler-Volmer equation, while the Tafel equation was applied at the anode (hydrogen evolution). Boundary conditions were a grounded counter electrode (anode) and a potential of -1.1 vs Ag/AgCl(sat.) applied to the working electrode (cathode). Fick's second law diffusion-convective equation was employed to model the mass transfer of species, including hydroxide and oxygen.Preliminary findings indicate that while impellers contribute to turbulence and affect local conditions around electrodes, the impact on the backside of the modeled electrodes is relatively weak (Figure 1). This observation may adversely influence mass transfer rates and electrochemical reactions, underscoring the significance of integrating these results with electrochemical reactions for a comprehensive understanding of reactor behavior. Additional results will be presented at the meeting.

Validation of a Novel Method for Noninvasive Mixed Venous Oxygen Saturation Monitoring in Anesthetized Children.

Mixed venous oxygen saturation (SvO 2 ) is a critical variable in the assessment of oxygen supply and demand but is rarely used in children due to the invasive nature of pulmonary artery catheters. The aim of this prospective, observational study was to investigate the accuracy of noninvasively measured SvO 2 acquired by the novel capnodynamic method, based on differential Fick equation (Capno-SvO 2 ), against gold standard CO-oximetry. Capno-SvO 2 was compared to SvO 2 measured by pulmonary artery blood gas CO-oximetry in children undergoing cardiac catheter interventions and subjected to moderate hemodynamic challenges. Bland-Altman analysis was used to describe the agreement of absolute values between CO-oximetry and Capno-SvO 2 , and a concordance rate was calculated to evaluate the ability of Capno-SvO 2 to track change. Twenty-five procedures were included in the study. Capno-SvO 2 showed a bias toward CO-oximetry of +3 percentage points; upper and lower limits of agreement were +11 percentage points (95% confidence interval [CI], 9-14) and -5 percentage points (95% CI, -8 to -3), respectively. The concordance rate was 92% (95% CI, 89-96). In conclusion, this first clinical application of a novel concept for noninvasive SvO 2 monitoring without the need for a pulmonary artery catheter indicates that Capno-SvO 2 generates absolute values and trending capacity in close agreement with the gold standard reference method.

Longitudinal decline in peak V̇o2 with aging in a healthy population is associated with a reduction in peripheral oxygen utilization but not in cardiac output.

Aging is associated with a significant decline in aerobic capacity assessed by maximal exercise oxygen consumption (V̇o2max). The relative contributions of the specific V̇o2 components driving this decline, namely cardiac output (CO) and arteriovenous oxygen difference (A - V)O2, remain unclear. We examined this issue by analyzing data from 99 community-dwelling participants (baseline age: 21-96 yr old; average follow-up: 12.6 yr old) from the Baltimore Longitudinal Study of Aging, free of clinical cardiovascular disease. V̇o2peak, a surrogate of V̇o2max, was used to assess aerobic capacity during upright cycle ergometry. Peak exercise left ventricular volumes, heart rate, and CO were estimated using repeated gated cardiac blood pool scans. The Fick equation was used to calculate (A - V)O2diff,peak from COpeak and V̇o2peak. In unadjusted models, V̇o2peak, (A - V)O2diff,peak, and COpeak declined longitudinally over time at steady rates with advancing age. In multiple linear regression models adjusting for baseline values and peak workload, however, steeper declines in V̇o2peak and (A - V)O2diff,peak were observed with advanced entry age but not in COpeak. The association between the declines in V̇o2peak and (A - V)O2diff,peak was stronger among those ≥50 yr old compared with their younger counterparts, but the difference between the two age groups did not reach statistical significance. These findings suggest that age-associated impairment of peripheral oxygen utilization during maximal exercise poses a stronger limitation on peak V̇o2 than that of CO. Future studies examining interventions targeting the structure and function of peripheral muscles and their vasculature to mitigate age-associated declines in (A - V)O2diff are warranted.NEW & NOTEWORTHY The age-associated decline in aerobic exercise performance over an average of 13 yr in community-dwelling healthy individuals is more closely associated with decreased peripheral oxygen utilization rather than decreased cardiac output. This association was more evident in older than younger individuals. These findings suggest that future studies with larger samples examine whether these associations vary across the age range and whether the decline in cardiac output plays a greater role earlier in life. In addition, studies focused on determinants of peripheral oxygen uptake by exercising muscle may guide the selection of preventive strategies designed to maintain physical fitness with advancing age.

Determination of Cardiac Output in a Porcine Model for Ex Vivo Pulmonary Perfusion.

Due to their physiological similarities to humans, pigs are used as experimental models for ex vivo lung perfusion (EVLP). EVLP is a technique that perfuses lungs that are not suitable for transplantation via an extracorporeal circulation pump to improve their function and increase their viability. Existing EVLP protocols are differentiated by the type of perfusion solution and perfusion flow, which varies from 40%-100% of the estimated cardiac output (CO) according to the body surface area (BSA). Devices for measuring CO use simple physical principles and other mathematical models. Thermodilution in animal models continues to be the reference standard for estimating CO because of its simplicity and ease of reproduction. Therefore, the objective of this study was to reproduce the measurement of CO by thermodilution in pigs and compare its precision and accuracy with those obtained by the BSA, weight, and Fick's method, to establish perfusion flow during EVLP. In 23 pigs, a thermodilution catheter was placed in the right jugular vein, and the carotid artery on the same side was cannulated. Blood samples were obtained for gasometry, and CO was estimated by thermodilution, adjusted body surface area, Fick's principle, and per body weight. The CO obtained by the BSA was greater (p = 0.0001, ANOVA, Tukey) than that obtained by the other methods. We conclude that although the methods used in this study to estimate CO are reliable, there are significant differences between them; therefore, each method must be evaluated by the investigator to determine which meets the needs of the protocol.

Research on multi‐mechanism synergistic effects of gas cross‐scale percolation in tight gas reservoirs of Yanchang oilfield

AbstractRevealing the gas transport patterns at the microscale and nanoscale is of great scientific and engineering significance for unconventional oil and gas exploration and development. This paper first systematically analyzes the properties of gas transport mechanism under different Knudsen number conditions. Second, the coupling modes of the cross‐scale multi‐drive mechanism are systematically categorized, and three typical coupling calculation methods are pointed out. Again, the rationality of the cross‐scale multi‐agency coupling is quantitatively calculated. The results show that (a) Under the influence of Fick's diffusion equation, when Knr &gt; 0, the coupled ‘slip flow–Fick diffusion–Knudsen diffusion’ equation does not converge to the Knudson diffusion equation. (b) The ‘Fick diffusion–Knudsen diffusion’ coupled equation is calculated to be more than 102 times as large as the Knudsen diffusion equation.

Non-arterial line cardiac output calculation misclassifies exercise pulmonary hypertension and increases risk of data loss particularly in black, scleroderma and Raynaud's patients during invasive exercise testing.

The direct Fick principle is the standard for calculating cardiac output (CO) to detect CO-dependent conditions like exercise pulmonary hypertension (ePH). Fick COarterial incorporates arterial haemoglobin (Hba) and oxygen saturation (S aO2 ) with oxygen consumption from exercise testing, while Fick COnon-arterial substitutes mixed venous haemoglobin (Hbmv) and peripheral oxygen saturation (S pO2 ) in the absence of an arterial line. The decision to employ an arterial catheter for exercise testing varies, and discrepancies in oxygen saturation and haemoglobin between arterial and non-arterial methods may lead to differences in Fick CO, potentially affecting ePH classification. We performed a retrospective analysis of 296 consecutive invasive cardiopulmonary exercise testing (iCPET) studies comparing oxygen saturation from pulse oximetry (S pO2 ) and radial arterial (S aO2 ), Hba and Hbmv, and CO calculated with arterial (COarterial) and non-arterial (COnon-arterial) values. We assessed the risk of misclassification of pre- and post-capillary ePH and data loss due to inaccurate S pO2 . When considering all stages from rest to peak exercise, Hba and Hbmv demonstrated high correlation, while S pO2 and S aO2 as well as COarterial and COnon-arterial demonstrated low correlation. Data loss was significantly higher across all stages of exercise for S pO2 (n=346/1926 (18%)) compared to S aO2 (n=17/1923 (0.88%)). We found that pre- and post-capillary ePH were misclassified as COnon-arterial data (n=7/41 (17.1%) and n=2/23 (8.7%), respectively). Patients with scleroderma and/or Raynaud's (n=11/33 (33.3%)) and black patients (n=6/19 (31.6%)) had more S pO2 data loss. Reliance upon S pO2 during invasive exercise testing results in the misclassification of pre- and post-capillary ePH, and unmeasurable S pO2 for black, scleroderma and Raynaud's patients can preclude accurate exercise calculations, thus limiting the diagnostic and prognostic value of invasive exercise testing without an arterial line.

Investigation of MHD fractionalized viscous fluid and thermal memory with slip and Newtonian heating effect: a fractional model based on Mittag-Leffler kernel

This paper introduces an innovative approach for modelling unsteady incompressible natural convection flow over an inclined oscillating plate with an inclined magnetic effect that employs the Atangana-Baleanu time-fractional derivative (having a non-singular and non-local kernel) and the Mittag-Leffler function. The fractional model, which includes Fourier and Fick's equations, investigates memory effects and is solved using the Laplace transform. The Mittag-Leffler function captures power-law relaxation dynamics, which improves our understanding of thermal and fluid behaviour. Graphical examination shows the influence of fractional and physically involved parameters, leading to the conclusion that concentration, temperature, and velocity profiles initially grow and then decrease asymptotically with time. Moreover, the study emphasizes the impact of effective Prandtl and Schmidt numbers on temperature, concentration, and velocity levels in the fluid.

A one-dimensional diffusive transport model to evaluate H2S generation in salt caverns hydrogen storage sites

Salt caverns are considered a potential hydrogen storage site given the ductility, tightness, and chemical inertness of halite. In addition, unlike porous media, salt caverns require less cushion gas and allow more cycles of injection and production within a year. However, hydrogen is an electron donor for many hydrogenotrophic microorganisms including halophilic sulfate-reducing microbes (SRM) and hydrogen sulfide (H2S) can be generated in a cavern once sulfate and hydrogen become available in the aqueous phase. As salt deposits are often associated with large amounts of impurities such as anhydrite and gypsum, their dissolution during the leaching phase can release the required sulfate ions for SRMs to produce H2S once hydrogen diffuses and dissolves in the brine at the bottom of the cavern. In this study, a one-dimensional diffusive transport model was developed using PHREEQC to simulate sulfate reduction and H2S generation in a cavern at the gas-brine interface. The solution of Fick's diffusion equation was used to calculate the hydrogen concentration at each level of the 1D model while the kinetic rates of reactions were derived from reported experimental and field site observations of brine samples taken from salt caverns. The results obtained indicated that hydrogen consumption at the gas-brine interface can trigger H2S and methane formations. This is followed by a reduction in sulfate and carbonate concentration and a slight increase in pH due to the reduction of protons in the solution. It was also observed that the presence of Fe2+ ions can reduce the amount of the hydrogen sulfide production while Ca2+ ions slightly favour sulfate reduction due to the production of methane. Although the kinetic reaction rate of the reactions in the model is subject to a certain degree of uncertainty, the workflow and results this study can serve as a guide for the future storage of hydrogen in salt caverns.

Wagner diagram for modeling O2 pathway—calculation and graphical display by the Helsinki O2 Pathway Tool

Objective. Maximal O2 uptake ( V˙O2max ) reflects the individual’s maximal rate of O2 transport and utilization through the integrated whole-body pathway composed of the lungs, heart, blood, circulation, and metabolically active tissues. As such, V˙O2max is strongly associated with physical capacity as well as overall health and thus acts as one predictor of physical performance and as a vital sign in determination of status and progress of numerous clinical conditions. Quantifying the contribution of single parts of the multistep O2 pathway to V˙O2max provides mechanistic insights into exercise (in)tolerance and into therapy-, training-, or disuse-induced adaptations at individual or group levels. We developed a desktop application (Helsinki O2 Pathway Tool—HO2PT) to model numerical and graphical display of the O2 pathway based on the ‘Wagner diagram’ originally formulated by Peter D. Wagner and his colleagues. Approach. The HO2PT was developed and programmed in Python to integrate the Fick principle and Fick’s law of diffusion into a computational system to import, calculate, graphically display, and export variables of the Wagner diagram. Main results. The HO2PT models O2 pathway both numerically and graphically according to the Wagner diagram and pertains to conditions under which the mitochondrial oxidative capacity of metabolically active tissues exceeds the capacity of the O2 transport system to deliver O2 to the mitochondria. The tool is based on the Python open source code and libraries and freely and publicly available online for Windows, macOS, and Linux operating systems. Significance. The HO2PT offers a novel functional and demonstrative platform for those interested in examining V˙O2max and its determinants by using the Wagner diagram. It will improve access to and usability of Wagner’s and his colleagues’ integrated physiological model and thereby benefit users across the wide spectrum of contexts such as scientific research, education, exercise testing, sports coaching, and clinical medicine.

Exercise limitation in hypertrophic cardiomyopathy: combined stress echocardiography and cardiopulmonary exercise test.

The study aims to investigate exercise-limiting factors in hypertrophic cardiomyopathy (HCM) using combined stress echocardiography and cardiopulmonary exercise test. A symptom-limited ramp bicycle exercise test was performed in the semi-supine position on a tilting dedicated ergometer. Echocardiographic images were obtained concurrently with gas exchange measurements along predefined stages of exercise. Oxygen extraction was calculated using the Fick equation at each activity level. Thirty-six HCM patients (mean age 67±6years, 72% men, 18 obstructive HCM) were compared with age and sex-matched 29 controls. At rest, compared with controls, E/E' ratio (6.26±2.3 vs. 14±2.5, P<0.001) and systolic pulmonary artery pressures (SPAP) (22.6±3.4 vs. 34±6.2mmHg, P=0.023) were increased. Along with the stages of exercise (unloaded; anaerobic threshold; peak), diastolic function worsened (E/e' 8.9±2.6 vs. 13.8±3.6 P=0.011; 9.4±2.3 vs. 18.6±3.3 P=0.001; 8.7±1.9 vs. 21.5±4, P<0.001), SPAP increased (23±2.7 vs. 33±4.4, P=0.013; 26±3.2 vs. 40±2.9, P<0.001; 26±3.5 vs. 45±7mmHg, P<0.001), and oxygen consumption (6.6±1.7 vs. 6.8±1.6, P=0.86; 18.1±2.2 vs. 14.6±1.5, P=0.008; 20.3±3 vs. 15.1±2.1mL/kg/min, P=0.01) was reduced. Oxygen pulse was blunted (6.3±1.8 vs. 6.2±1.9, P=0.79; 10±2.1 vs. 8.8±1.6, P=0.063; 12.2±2 vs. 8.2±2.3mL/beat, P=0.002) due to an insufficient increase in both stroke volume (92.3±17 vs. 77.3±14.5 P=0.021; 101±19.1 vs. 87.3±15.7 P=0.06; 96.5±12.2 vs. 83.6±16.1mL, P=0.034) and oxygen extraction (0.07±0.03 vs. 0.07±0.02, P=0.47; 0.13±0.02 vs. 0.10±0.03, P=0.013; 0.13±0.03 vs. 0.11±0.03, P=0.03). Diastolic dysfunction, elevated SPAP, and the presence of atrial fibrillation were associated with reduced exercise capacity. Both central and peripheral cardiovascular limitations are involved in exercise intolerance in HCM. Diastolic dysfunction seems to be the main driver for this limitation.

Diffusion capability of Cs-137 in compacted soil and bentonite under groundwater-saturated condition

Several researches have been studied the diffusion coefficient (Da) of radionuclide in soil samples in varies location around the world; however, the effect of cations in groundwater as a medium of saturation for Cs-137 diffusion in soil and bentonite remains to be accomplished. Compacted soil and bentonite layers are utilized in the construction of radioactive waste disposal sites, which serve to prevent the release of Cs-137 from the repository to the unsaturated zone. The samples used were soil from the prospective disposal site in SP4—Serpong Nuclear Center (SNC) and bentonite taken from Santrijaya, Tasikmalaya. The diffusion coefficient (Da) is used as indicator of Cesium-137 diffusion in the samples. Experimental measurements were conducted on a diffusion column unit that varied in diffusion time and density conditions to determine diffusion coefficients. The samples were cut into slices and analyzed using Multichannel Analyzer (MCA) unit to measure Cs-137 radioactivity. The measurement results were then incorporated into Fick's Law equation to obtain the value of the diffusion coefficient (Da) of Cs-137 in soil and bentonite. The experimental results showed that the diffusion coefficients of samples with groundwater simulation are in the range of 10–12 m2 s−1 for the local soil and bentonite samples, respectively. Compare to the similar experiment that was conducted previously, the results indicated that the groundwater content could slightly impact the increase in the diffusion coefficient value of Cs-137.

Analysis of a nonlocal diffusion model with a weakly singular kernel

We establish that for any fixed horizonδ>0, the solution of a nonlocal diffusion model with a weakly singular kernel pδ converges asymptotically to the solution of the corresponding Fickian diffusion equation. The diffusion tensor of the Fickian equation is determined by half of the covariance matrix, with pδ serving as the probability density function. Numerical experiments are performed to validate our findings. Additionally, we observe that the mean square displacement of the nonlocal diffusion model exhibits a linear relationship with respect to time t.

A mathematical model of tissue axial and radial diffusion in the microvasculature for intravascular microscopy and phosphorescence quenching data

This study aims to extend earlier Krogh Cylinder Models of an oxygen profile by considering axial diffusion and analytically solving Fick's Law Partial Differential Equation with novel boundary conditions via the separation of variables. We next prospectively collected a total of 20 animals, which were randomly assigned to receive either fresh or two-week-old stored red blood cell (RBC) transfusions and PQM oxygen data were measured acutely (90 min) or chronically (24 h). Transfusion effects were evaluated in vivo using intravital microscopy of the dorsal skinfold window chamber in Golden Syrian Hamsters. Hamsters were initially hemorrhaged by 50% of total blood volume and resuscitated 1-h post hemorrhage. PQM data were subsequently collected and fit the derived 2D Krogh cylinder model. Systemic hemodynamics (mean arterial pressure, heart rate) were similar in both pre and post-transfusion with either stored or fresh cells. Transfusion with stored cells was found to impair axial and radial oxygen gradients as quantified by our model and consistent with previous studies. Specifically, we observed a statistically significant decrease in the arteriolar tissue radial oxygen gradient after transfusion with stored RBCs at 24 h compared with fresh RBCs (0.33 ± 0.17 mmHg μ m-1 vs, 0.14 ± 0.12 mmHg μ m-1; p = 0.0280). We also observed a deficit in the arteriolar tissue oxygen gradient (0.03 ± 0.01 mmHg μ m-1 fresh vs. 0.018 ± 0.007 mmHg μ m-1 stored; p = 0.0185). We successfully derived and validated an analytical 2D Krogh cylinder model in an animal model of microhemodynamic oxygen diffusion aberration secondary to storage lesions.