caa a22 4500 469122404 CHVBK 20180323133142.0 cr unu---uuuuu 170328e19920101xx s 000 0 eng 10.1007/BF02368504 doi (NATIONALLICENCE)springer-10.1007/BF02368504 Numerical modeling of ventricular filling [Elektronische Daten] [James Thomas, Arthur Weyman] The fluid dynamical and physiological assumptions underlying general mathematical modeling of ventricular filling are outlined. We then describe the use of a lumped parameter model and computer simulation to study how the early transmitral velocity profile is affected by isolated changes in ventricular compliance and relaxation, atrial pressure and compliance, and valvular morphology. We show that the transmitral velocity is fundamentally affected by twophysical determinants: the transmitral pressure difference and the net compliance of the atrium and the ventricle. These physical determinants in turn are specified by the variousphysiologic parameters of interest. This approach has shown that peak velocity is most strongly affected by initial left atrial pressure, lowered somewhat by prolonged relaxation, low atrial and ventricular compliance, and systolic dysfunction. Peak acceleration is directly affected by atrial pressure and inversely affected by the time constant of isovolumic relaxation, with little influence of compliance, whereas the deceleration rate is almost purely given by mitral valve area divided by instantaneous atrioventricular compliance at the end of the rapid filling wave. Pergamon Press plc, 1992 Diastole nationallicence Diastolic function nationallicence Echocardiography nationallicence Doppler nationallicence Mitral valve nationallicence Relaxation nationallicence Compliance nationallicence Mathematical modeling nationallicence a m : maximal acceleration, cm/s2 nationallicence a t or AT : acceleration time (from start of flow to peak velocity), msec nationallicence A or MVA : effective mitral valve area, cm2 nationallicence A(s) : cross-sectional area of the chambers as a function of distance from the atrium, cm2 nationallicence A MV : narrowest cross-sectional area at mitral valvevena contracta (equivalent in general toA), cm2 nationallicence B : body force (such as gravity) acting on fluid nationallicence C : chamber compliance, cm3/(dyne/cm2) or cm3/mm Hg nationallicence d m : negative maximal deceleration, cm/s2 nationallicence d t or DT : deceleration time (from peak velocity to end of E-wave), msec nationallicence E : peak E-wave velocity (same asv m ), cm/sec nationallicence ESV : end-systolic ventricular volume, cm3 nationallicence IVRT : isovolumic relaxation time, msec nationallicence L : effective acceleration length of mitral blood flow, cm nationallicence M : mitral inertance (given by σL), g/cm2 nationallicence p : chamber pressure, dyne/cm2 or mm Hg nationallicence Δ p : atrioventricular pressure difference, dyne/cm2 or mm Hg nationallicence Δ P 0 : initial atrioventricular pressure difference, dyne/cm2 or mm Hg nationallicence pA : atrial pressure dyne/cm2 or mm Hg nationallicence pA 0 or LAP : initial LA pressure dyne/cm2 or mm Hg nationallicence pV : ventricular pressure, dyne/cm2 or mm Hg nationallicence pk : chamber pressure at 0 volume, dyne/cm2 or mm Hg nationallicence pAk : atrial pressure at 0 volume, dyne/cm2 or mm Hg nationallicence pvk : ventricular pressure at 0 volume, dyne/cm2 or mm Hg nationallicence q : transmitral flow nationallicence s : location along streamline from atrium to ventricle nationallicence s : distance along streamline from atrium to ventricle nationallicence S : chamber stiffness, (dyne/cm2)/cm3 or mm Hg/cm3 nationallicence S A : atrial stiffness, (dyne/cm2)/cm3 or mm Hg/cm3 nationallicence S V : ventricular stiffness, (dyne/cm2)/cm3 or mm Hg/cm3 nationallicence S n : netstiffness (dyne/cm2)/cm3 or mm Hg/cm3 nationallicence v : velocity vector at arbitrary point within the heart, cm/sec nationallicence v : scalar velocity, usually within the mitral apparatus, cm/sec nationallicence v(s) : velocity (scalar) as a function of distance along the central streamline through the mitral valve, cm/sec nationallicence v i or VTI : time velocity integral of E-wave, cm nationallicence v M : "potential” peak velocity, if the initial gradient were completely converted to velocity, (2Δp/ρ)1/2, cm/sec nationallicence v m : actual peak velocity, cm/sec nationallicence v A : speed within the atrium, cm/sec nationallicence v V : speed within the mitral apparatus, generally replaced byv throughout the article, cm/sec nationallicence V : chamber volume, cm3 nationallicence V k : chamber volume constant, volume required to raise pressure bye (2.718) nationallicence V Ak : atrial volume constant, volume required to raise pressure bye (2.718) nationallicence V vk : ventricular volume constant, volume required to raise pressure bye (2.718) nationallicence V vo : end-systolic ventricular volume, cm3 nationallicence x j : independent parameters input into mathematical model (valve area, chamber compliance, initial pressure, etc.) nationallicence y i : dependent parameters resulting from mathematical model (peak velocity, acceleration, deceleration, etc.) nationallicence Γ : "activation” constant for the ventricle. Att=0 (usually aortic valve closure), this represents one less than the ratio between ventricular pressure and the pressure which would be observed at that volume in the fully relaxed ventricle, dimensionless nationallicence μ : blood viscosity, 0.03 Poise nationallicence ρ : blood density, 1.05 g/cm3 nationallicence τ : time constant of isovolumic relaxation nationallicence Thomas James Noninvasive Cardiac Laboratory, Massachusetts General Hospital Harvard Medical School, Zero Emerson Place, Suite 2F, 02114, Boston, MA aut Weyman Arthur Noninvasive Cardiac Laboratory, Massachusetts General Hospital Harvard Medical School, Zero Emerson Place, Suite 2F, 02114, Boston, MA aut Annals of Biomedical Engineering Kluwer Academic Publishers 20/1(1992-01-01), 19-39 0090-6964 20:1<19 1992 20 10439 https://doi.org/10.1007/BF02368504 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02368504 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Thomas James Noninvasive Cardiac Laboratory, Massachusetts General Hospital Harvard Medical School, Zero Emerson Place, Suite 2F, 02114, Boston, MA aut NATIONALLICENCE 700 1- Weyman Arthur Noninvasive Cardiac Laboratory, Massachusetts General Hospital Harvard Medical School, Zero Emerson Place, Suite 2F, 02114, Boston, MA aut NATIONALLICENCE 773 0- Annals of Biomedical Engineering Kluwer Academic Publishers 20/1(1992-01-01), 19-39 0090-6964 20:1<19 1992 20 10439 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer