scholarly journals Blood flow in venules: A mathematical model including valves inertia

2019 ◽  
Vol 8 (3) ◽  
Author(s):  
Matteo Cardini ◽  
Angiolo Farina ◽  
Antonio Fasano ◽  
Alberto Caggiati
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Blood Flow ◽  
Velocity Profile ◽  
Present Model ◽  
Pressure Pulse ◽  
Venous Blood ◽  
Critical Role ◽  
Respiratory Rhythm ◽  
Peristaltic Pumps

It is well known that venules equipped with valves play a critical role in regulating blood flow. Essentially they are peristaltic pumps that increase the efficiency of venous blood return to the heart, thanks to the presence of valves preventing backflow. Inspired by two recent papers, we have modeled the venule as a vessel with valves placed at its ends and walls animated by radial oscillations that are independent of heart pulsation and respiratory rhythm. Differently from the previous papers, the present model takes into account the valves inertia allowing, for progressive closing/opening stages. The numerical simulations produce a pressure pulse and a velocity profile which agree almost perfectly with the experimental data of Dongaonkar et al., eliminating the discrepancies found in Farina et al., arising from the hypothesis that valves act instantaneously.

Modeling Heat Transfer in Human Arm and Forearm: Effect of Countercurrent Heat Exchange and Superficial Veins

2008 ◽  
Author(s):  
Maurício S. Ferreira ◽  
Jurandir I. Yanagihara
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Blood Flow ◽  
Heat Exchange ◽  
Heat Sink ◽  
Human Tissue ◽  
Thermal Equilibrium ◽  
Venous Blood ◽  
Perfusion Rate ◽  
Human Arm

In 1948, Pennes [1] presented a mathematical model of heat transfer in human tissue. The effect of blood flow on heat transfer was modeled as heat sink or source whose magnitude is proportional to the volumetric perfusion rate and difference between arterial and venous temperature [2]. Pennes assumed that thermal equilibrium occurs in the capillary beds, although Chen [3] showed that it occurs in bigger vessels before the blood enters the beds. Weinbaum et al. [2] and Zhu et al. [4] studied the thermal effect of vessels in the range of 50 to 1,000 μm on muscle tissue, and recognized the importance of countercurrent heat exchange. Hirata et al. [5] showed that the heat loss in the forearm is enhanced by the venous blood returning through the superficial veins and that arterious-venous anastomoses (AVAs) presented in the hands are important to thermoregulation.

scholarly journals Blood pressure and blood flow variation during postural change from sitting to standing: model development and validation

2005 ◽  
Vol 99 (4) ◽  
pp. 1523-1537 ◽  
Author(s):  
Mette S. Olufsen ◽  
Johnny T. Ottesen ◽  
Hien T. Tran ◽  
Laura M. Ellwein ◽  
Lewis A. Lipsitz ◽  
...  
Keyword(s):  
Blood Pressure ◽  
Mathematical Model ◽  
Blood Flow ◽  
Young Subject ◽  
Venous Blood ◽  
Cardiovascular Responses ◽  
Physiological Data ◽  
Postural Change ◽  
Metabolic Demand ◽  
Arterial Blood

Short-term cardiovascular responses to postural change from sitting to standing involve complex interactions between the autonomic nervous system, which regulates blood pressure, and cerebral autoregulation, which maintains cerebral perfusion. We present a mathematical model that can predict dynamic changes in beat-to-beat arterial blood pressure and middle cerebral artery blood flow velocity during postural change from sitting to standing. Our cardiovascular model utilizes 11 compartments to describe blood pressure, blood flow, compliance, and resistance in the heart and systemic circulation. To include dynamics due to the pulsatile nature of blood pressure and blood flow, resistances in the large systemic arteries are modeled using nonlinear functions of pressure. A physiologically based submodel is used to describe effects of gravity on venous blood pooling during postural change. Two types of control mechanisms are included: 1) autonomic regulation mediated by sympathetic and parasympathetic responses, which affect heart rate, cardiac contractility, resistance, and compliance, and 2) autoregulation mediated by responses to local changes in myogenic tone, metabolic demand, and CO2 concentration, which affect cerebrovascular resistance. Finally, we formulate an inverse least-squares problem to estimate parameters and demonstrate that our mathematical model is in agreement with physiological data from a young subject during postural change from sitting to standing.

Analysis of oxygen diffusion from arteriolar networks

1979 ◽  
Vol 237 (6) ◽  
pp. H681-H689 ◽  
Author(s):  
A. S. Popel ◽  
J. F. Gross
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Blood Flow ◽  
Oxygen Diffusion ◽  
Blood Flow Rate ◽  
Cheek Pouch ◽  
Oxygen Distribution ◽  
Hamster Cheek Pouch ◽  
Longitudinal Gradients ◽  
Po2 Gradients

A mathematical model of oxygen transport in the precapillary microcirculation is presented. The theory is then used to simulate oxygen distribution in the arteriolar network of the hamster cheek pouch. Theoretical prediction of transmural and longitudinal oxygen tension (PO2) gradients is in qualitative agreement with available experimental data. The effect of the variation of inlet network PO2, blood flow rate, blood hematocrit, and other parameters on the transport characteristics is studied. The calculations predict that the luminal PO2 in small arterioles is practically independent of the inlet network PO2 leve if the latter is sufficiently high; when this inlet PO2 level is low, then the longitudinal gradients of luminal PO2 vanish. It is further shown that retardation of blood flow may cause a significant increase in precapillary oxygen losses.

scholarly journals Mathematical Model of VOCs Emission in Three-layer Building Materials

2021 ◽  
Vol 257 ◽  
pp. 03047
Author(s):  
Zhehua Du ◽  
Xin Lin
Keyword(s):  
Experimental Data ◽  
Boundary Layer ◽  
Mathematical Model ◽  
Building Materials ◽  
Present Model ◽  
Transfer Resistance ◽  
Model Predictions ◽  
Layer Resistance ◽  
Boundary Layer Resistance ◽  
Good Agreement

A simple mathematical model is proposed to account for emissions of Volatile Organic Compounds (VOCs) from three-layer building materials. The model considers both the diffusion within three layer building materials and the mass transfer resistance through the air boundary layer. A general solution method based on Laplace transform is presented. Compared to other models capable of accounting for emissions of VOCs from multi layer building materials, the present model is fully analytical instead of being numerical. The present model was validated by the experimental data from the specially designed test. The results indicated that there was a good agreement between the model predictions and the experimental data. It can also be seen from calculation that model ignoring the boundary layer resistance cannot fully reflect the real situation.

Enhanced global mathematical model for studying cerebral venous blood flow

2014 ◽  
Vol 47 (13) ◽  
pp. 3361-3372 ◽  
Author(s):  
Lucas O. Müller ◽  
Eleuterio F. Toro
Keyword(s):  
Mathematical Model ◽  
Blood Flow ◽  
Venous Blood ◽  
Venous Blood Flow

scholarly journals Sufficiency of unidirectional allostery in KaiC in generating the cyanobacterial circadian rhythm

2020 ◽  
Author(s):  
Shin-ichi Koda ◽  
Shinji Saito
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Circadian Rhythm ◽  
Atpase Activity ◽  
Protein Concentration ◽  
Present Model ◽  
Conformational Transitions ◽  
Functional Roles ◽  
Domain Specific ◽  
Clock Protein

AbstractThe clock protein of cyanobacteria KaiC forms a homohexamer with two ring-shaped domains, C1 and C2. These domains undergo several domain-specific conformational transitions and allosterically communicate to generate a circadian rhythm. Interestingly, experiments show a possibility that C2 is independent of C1. However, detailed interplay among them remains elusive. Here we propose a mathematical model, which explicitly considers the interplay. The allostery in KaiC is here modeled to be unidirectional from C2 to C1. We demonstrate that the unidirectional allostery is sufficient for the circadian rhythm by showing the quantitative reproducibility of various experimental data, including temperature dependence of both phosphorylation oscillation and ATPase activity. Based on the present model, we further discuss possible functional roles of the unidirectional allostery particularly in the period robustness against both protein concentration and temperature.

scholarly journals Mathematical model of cavitation under the influence of a single stretching pulse

2019 ◽  
Vol 27 (1) ◽  
pp. 49-59
Author(s):  
Nikolay Yu Kravchenko ◽  
Dmitry S Kulyabov
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Time Dependence ◽  
Vapor Phase ◽  
Negative Pressure ◽  
Carrier Phase ◽  
Pressure Pulse ◽  
Cavitation Bubbles ◽  
Temperature And Pressure ◽  
Good Agreement

This paper describes the created mathematical model that allows you to explore the dynamics of cavitation bubbles under the influence of a single negative pressure pulse. The time dependence and coordinates of the parameters of the carrier phase, the temperature and pressure of the vapor phase, the concentration and size of the bubbles are determined numerically. It is concluded that the model created gives a good agreement between the calculated and experimental data.

Geometry of compact plain knitted structures

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Gamini Lanarolle
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Present Model ◽  
Major Axis ◽  
Minor Axis ◽  
Loop Length ◽  
Knitted Fabrics ◽  
Content Type ◽  
Mathematical Relationships ◽  
The Mathematical Model

Purpose The purpose of this paper is to develop mathematical relationships to calculate the loop length to knit compact plain knitted fabrics and to validate the model using the fabric parameters of commercial fabrics. Design/methodology/approach Ellipse defines the shape of the head of a knitted loop and straight lines define the arms of a knitted loop. The mathematical relationships developed relate the yarn count to the loop length of compact knitted fabrics. The experimental data and the data from previous similar research validate the accuracy of the mathematical model. Findings The model can calculate loop lengths to knit compact plain knitted fabrics in terms of thickness of the yarn and the coefficient defined to express the ratio of minor axis to major axis of the ellipse that defines the shape of the head of the loop. The mathematical model can deliver several loop lengths to produce compact plain knitted fabrics for different values of this coefficient. For commercial fabrics the error of the model was 0.53%. Originality/value The present model defines the head of the loop as an ellipse. The uniqueness of the present model is that several ellipses can exist for any given yarn thickness for a range of values assigned to the minor axis of the ellipse. The accuracy of the model against experimental data ascertains that the model is closer to the reality for commercial fabrics and proves the uniqueness of the model. Further, this model is an ideal and a simple model to introduce knitted loop configurations in teaching knitted fabric geometry.

Assessment of the incorporation of revascularized fibula grafts used for mandibular reconstruction with F-18-PET

2001 ◽  
Vol 40 (02) ◽  
pp. 51-58 ◽  
Author(s):  
H. Schliephake ◽  
van den Hoff ◽  
W. H. Knapp ◽  
G. Berding
Keyword(s):  
Blood Flow ◽  
Regional Blood Flow ◽  
Venous Blood ◽  
Mandibular Reconstruction ◽  
Reference Region ◽  
Osteoblastic Activity ◽  
Non Union ◽  
Range Of Values ◽  
Measured Input

Summary Aim: Determination of the range of regional blood flow and fluoride influx during normal incorporation of revascularized fibula grafts used for mandibular reconstruction. Evaluation, if healing complications are preceded by typical deviations of these parameters from the normal range. Assessment of the potential influence of using “scaled population-derived” instead of “individually measured” input functions in quantitative analysis. Methods: Dynamic F-l 8-PET images and arterialized venous blood samples were obtained in 11 patients early and late after surgery. Based on kinetic modeling regional blood flow (K1) and fluoride influx (Kmlf) were determined. Results: In uncomplicated cases, early postoperative graft K1 - but not Kmlf -exceeded that of vertebrae as reference region. Kmn values obtained in graft necrosis (n = 2) were below the ranges of values observed in uncomplicated healing (0.01 13-0.0745 ml/min/ml) as well as that of the reference region (0.0154-0.0748). Knf values in mobile non-union were in the lower range - and those in rigid non-union in the upper range of values obtained in stable union (0.021 1-0.0694). If scaled population-derived instead of measured input functions were used for quantification, mean deviations of 23 ± 17% in K1 and 12 ± 16% in Kmlf were observed. Conclusions: Normal healing of predominantly cortical bone transplants is characterized by relatively low osteoblastic activity together with increased perfusion. It may be anticipated that transplant necrosis can be identified by showing markedly reduced F− influx. In case that measured input functions are not available, quantification with scaled population-derived input functions is appropriate if expected differences in quantitative parameters exceed 70%.

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