Physical Principles of Cardiovascular Function – Contents



The 2 videos below depict an intensive application of physical principles to model the complexity of fluid flow through a rectangular conduit with an asymmetric branch point (the "side" branch is at \(90^{\circ}\) to the straight branch.  Is this like cardiology?? Naw.  But it helps for understanding physical principles!  That's what this website is about. (I know how to make these models be more relevant in appearance but I'm busy with my day job too.  Just so's you know )

The first high-def video (above) starts by step-slicing through the structure to show velocity contours at various locations within.  Next it starts to step through from the inlet of the conduit showing velocity vectors associated with each slice.  Within a short distance of the inlet, the video begins an animation of a distorting fluid surface as it flows through the branch point.  The first video is at Reynolds number 500 and with equal flow division between the 2 branches.

Next is a high-def video of flow through the bifurcation that starts out by labeling fluid that has already entered into the straight branch.  Because the fluid is close to the "suction zone" (a force due to a pressure gradient acts on the fluid), it flows upstream along the sides of the conduit and flows out the side branch.  Yep, that happens.

The latter video is at Reynolds number 500 but with 75% of the flow going to the side branch.


Philosophy, Models and Science 

Mathematical Background

     What's the Function?  (under construction)    

     The Order of Things

     Linear vs Nonlinear

     The Similarity Priniciple

     The Shape of Things

     Similarity Examples

     Cardiac Size

     Allometric, Isometric, all that Jazz

     Ejection Fraction

     Calculus Fundamentals

     Differential Equations - An Introduction

     Vector and Scalar Fields

     Complex Numbers

     The Fourier Transform

     Some Useful Tools

     The Weighted Average(under construction)

     The Well-Posed Problem

Physical Background

      Equations vs Formulas

      Physical Units and Analyses

      The Conservation Law



      Pressure Vessels - Laplace and Beyond

            Thin-Walled Sphere

            Thin-Walled Cylinder

            Thick-Walled Sphere

            Thick-Walled Cylinder

Linear Hemodynamics

      Physical Hemodynamics

      Fluid Statics

      Poiseuille Flow

            The No Slip Condition


      Preliminary Background on Sinusoids

      Impedance and the Electrical Analogy for Fluid Flow




      Fluid filled catheter

      Dynamic pressure measurements

      Simplified (Lumped Parameter) Circulatory Models

      Pulsatile Flow in Straight Cylindrical Tubes

      Fluid Velocity in Pulsatile Flow

      Longitudinal Impedance

      Transverse Impedance

      Introduction to Wave Transmission

      The Transmission Line 

      Characteristic Impedance 

      Understanding Pulsatile Pressue and Flow

      Traveling Waves (Attenuation, Dispersion, Wave Velocity)

      Pressure Pulse and Flow Wave Reflection  

      Input Impedance 

Nonlinear Hemodynamics (Fluid Dynamics)

      Potential Flow

      Ideal Fluid-- An approximation useful in understanding cardiovascular applications

      Mathematical Models-- General Comments about mathematical determination of complicated outcomes

      Velocity and Pressure Distribution for Flow over a Cylinder

      Model Limitations-- Boundary layer separation and turbulence

      Streamlines and Stream Tubes

      Continuity/Conservation of Mass

      Circulation and Lift

      The Continuum Approximation

      The Navier-Stokes Equations

      The Bernoulli Equation

      Dynamic Similarity and the Ubiquitous Reynolds Number

      Entrance Flow in Straight Cylindrical Tubes

      Flow in Curved Conduits


      Stenosis Flow

            Stenosis Qualitative

            The Gorlin Formula

            Stenosis Flow-Dependence

            It's Not Just Stenosis Area

            Control Volume Stenosis Analysis

            Clinical Relevance

     Flow in Arterial Bifurcations

Computational Fluid Dynamics

     CFD Examples

     Lid Driven Cavity

Extensive Cardiovascular Models (Don't expect I'll live this long)

Scaling the Cardiovascular System

Active Figures and Downloads

     CFD 3D View

     CFD Examples

     Joukowski Airfoil


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