scholarly journals Alternative diastolic function models of ventricular longitudinal filling velocity are mathematically identical

2020 ◽  
Vol 318 (5) ◽  
pp. H1059-H1067 ◽  
Author(s):  
Druv Bhagavan ◽  
William M. Padovano ◽  
Sándor J. Kovács
Keyword(s):  
Diastolic Function ◽  
Longitudinal Velocity ◽  
Force Balance ◽  
Balance Model ◽  
Diastolic Filling ◽  
Restoring Force ◽  
Suction Pump ◽  
Restoring Forces ◽  
Pdf Model

The spatiotemporal features of normal in vivo cardiac motion are well established. Longitudinal velocity has become a focus of diastolic function (DF) characterization, particularly the tissue Doppler e′-wave, manifesting in early diastole when the left ventricle (LV) is a mechanical suction pump (dP/dV < 0). To characterize DF and elucidate mechanistic features, several models have been proposed and have been previously compared algebraically, numerically, and in their ability to fit physiological velocity data. We analyze two previously noncompared models of early rapid-filling lengthening velocity (Doppler e′-wave): parametrized diastolic filling (PDF) and force balance model (FBM). Our initial numerical experiments sampled FBM-generated e′( t) contours as input to determine PDF model predicted fit. The resulting exact numerical agreement [standard error of regression (SER) = 9.06 × 10−16] was not anticipated. Therefore, we analyzed all published FBM-generated e′( t) contours and observed identical agreement. We re-expressed FBM’s algebraic expressions for e′( t) and observed for the first time that model-based predictions for lengthening velocity by the FBM and the PDF model are mathematically identical: e′( t) = γe−α tsinh(β t), thereby providing exact algebraic relations between the three PDF parameters and the six FBM parameters. Previous pioneering experiments have independently established the unique determinants of e′( t) to be LV relaxation, restoring forces (stiffness), and load. In light of the exact intermodel agreement, we conclude that the three PDF parameters, relaxation, stiffness (restoring forces), and load, are unique determinants of DF and e′( t). Thus, we show that only the PDF formalism can compute the three unique, independent, physiological determinants of long-axis LV myocardial velocity from e′( t). NEW & NOTEWORTHY We show that two separate, independently derived physiological (kinematic) models predict mathematically identical expressions for LV-lengthening velocity (Doppler e′-wave), indicating that damped harmonic oscillatory motion is a physiologically accurate model of diastolic function. Although both models predict the same “overdamped” velocity contour, only one model solves the “inverse problem” and generates unique, lumped parameters of relaxation, stiffness (restoring force), and load from the e′-wave.

scholarly journals Pericentric chromatin loops function as a nonlinear spring in mitotic force balance

2013 ◽  
Vol 200 (6) ◽  
pp. 757-772 ◽  
Author(s):  
Andrew D. Stephens ◽  
Rachel A. Haggerty ◽  
Paula A. Vasquez ◽  
Leandra Vicci ◽  
Chloe E. Snider ◽  
...  
Keyword(s):  
Chromosome Segregation ◽  
Spindle Assembly Checkpoint ◽  
Force Balance ◽  
Nonlinear Spring ◽  
Sister Chromatids ◽  
Spindle Dynamics ◽  
Restoring Forces ◽  
Cross Links ◽  
Mean And Variance

The mechanisms by which sister chromatids maintain biorientation on the metaphase spindle are critical to the fidelity of chromosome segregation. Active force interplay exists between predominantly extensional microtubule-based spindle forces and restoring forces from chromatin. These forces regulate tension at the kinetochore that silences the spindle assembly checkpoint to ensure faithful chromosome segregation. Depletion of pericentric cohesin or condensin has been shown to increase the mean and variance of spindle length, which have been attributed to a softening of the linear chromatin spring. Models of the spindle apparatus with linear chromatin springs that match spindle dynamics fail to predict the behavior of pericentromeric chromatin in wild-type and mutant spindles. We demonstrate that a nonlinear spring with a threshold extension to switch between spring states predicts asymmetric chromatin stretching observed in vivo. The addition of cross-links between adjacent springs recapitulates coordination between pericentromeres of neighboring chromosomes.

scholarly journals Ase1/Prc1-dependent spindle elongation corrects merotely during anaphase in fission yeast

2009 ◽  
Vol 187 (3) ◽  
pp. 399-412 ◽  
Author(s):  
Thibault Courtheoux ◽  
Guillaume Gay ◽  
Yannick Gachet ◽  
Sylvie Tournier
Keyword(s):  
Fission Yeast ◽  
Mechanical Model ◽  
Elongation Rate ◽  
Force Balance ◽  
Balance Model ◽  
Spindle Poles ◽  
Sister Chromatids ◽  
Spindle Elongation ◽  
Dependent Mechanism

Faithful segregation of sister chromatids requires the attachment of each kinetochore (Kt) to microtubules (MTs) that extend from opposite spindle poles. Merotelic Kt orientation is a Kt–MT misattachment in which a single Kt binds MTs from both spindle poles rather than just one. Genetic induction of merotelic Kt attachment during anaphase in fission yeast resulted in intra-Kt stretching followed by either correction or Kt disruption. Laser ablation of spindle MTs revealed that intra-Kt stretching and merotelic correction were dependent on MT forces. The presence of multiple merotelic chromosomes linearly antagonized the spindle elongation rate, and this phenomenon could be solved numerically using a simple force balance model. Based on the predictions of our mechanical model, we provide in vivo evidence that correction of merotelic attachment in anaphase is tension dependent and requires an Ase1/Prc1-dependent mechanism that prevents spindle collapse and thus asymmetric division and/or the appearance of the cut phenotype.

Evaluation of diastolic function with Doppler echocardiography: the PDF formalism

1987 ◽  
Vol 252 (1) ◽  
pp. H178-H187 ◽  
Author(s):  
S. J. Kovacs ◽  
B. Barzilai ◽  
J. E. Perez
Keyword(s):  
Harmonic Oscillator ◽  
Diastolic Function ◽  
Doppler Echocardiography ◽  
Diastolic Filling ◽  
Doppler Velocity ◽  
Elastic Recoil ◽  
Initial Displacement ◽  
Suction Pump ◽  
Forcing Term ◽  
Damped Harmonic Oscillator

A new parametrized diastolic filling (PDF) formalism for evaluation of holodiastolic (left and right) ventricular function via Doppler echocardiography is presented. It is motivated by the empiric observation that during diastole the heart behaves as a suction pump whose dynamics, in certain respects, are those of a damped harmonic oscillator. An expression for elastic recoil (suction) initiated ventricular diastolic fluid inflow velocity v(t) is obtained by differentiation from the solution x(t) of the linear differential equation that describes the motion of a forced, damped harmonic oscillator. It is solved for “over-damped” motion, for zero initial velocity and initial displacement = xo cm. An explicit forcing term F(t) = Fosin(omega t) is included to account for late diastolic (atrial) filling. The quantitative parameters of the model include inertia (mass; m), viscosity (damping constant; c), source of stored energy for suction (spring constant; k), and its initial displacement xo, the amplitude and frequency of the (atrial) forcing term Fo, omega. The mathematical behavior of the solution v(t) and its dependence on the parameters xo, c, and k, which characterize the contour of the Doppler velocity profile (DVP), is discussed. When clinical examples of normal and abnormal transmitral DVPs are compared with v(t) calculated using the harmonic oscillator model, excellent agreement [DVP-v(t)]/v(t) approximately 0.05 is obtained throughout diastole. Thus the model allows accurate qualitative and quantitative characterization of global ventricular diastolic behavior by noninvasive means in a variety of normal and abnormal stiffness-compliance states. In addition, it may serve as a prototype for a class of mathematical models that can encompass the essential dynamic elements of ventricular diastolic function that couple to flow and further enhance the role of the heart as a suction pump.

Effects of Angiotensin II and Aldosterone on Diastolic Function In Vivo in Normal Man

1994 ◽  
Vol 87 (4) ◽  
pp. 397-401 ◽  
Author(s):  
P. B. M. Clarkson ◽  
N. M. Wheeldon ◽  
C. MacLeod ◽  
M. Tennent ◽  
T. M. MacDonald
Keyword(s):  
Blood Pressure ◽  
Angiotensin Ii ◽  
Diastolic Function ◽  
Left Ventricular ◽  
Diastolic Filling ◽  
Normal Male ◽  
Normal Man ◽  
Male Subjects ◽  
Left Ventricular Diastolic Filling

1. Doppler echocardiographic indices of diastolic function and systemic haemodynamics were studied in response to infusions of angiotensin II (1, 2, 5 and 10 ng min−1 kg−1), D-aldosterone (2, 4, 10 and 20 ng min−1 kg−1) and placebo [0.9% (w/v) NaCl] in ten normal male subjects. 2. Dose-related increases in systolic and diastolic blood pressure were observed with angiotensin II infusion at rates of 2 ng min−1 kg−1 and above, whereas no changes in blood pressure occurred with D-aldosterone. No changes in aortic stroke distance or heart rate were seen with either angiotensin II or aldosterone infusion. 3. Compared with placebo, angiotensin II infusion produced a dose-related prolongation of the isovolumic relaxation time [mean and 95% confidence intervals 12.0 (8.2–15.8) ms, P < 0.001] at 10 ng min−1 kg−1, and a significant reduction in the ratio between early and late transmitral flow velocity integrals at 2 ng min−1 kg−1, [−0.84 (−1.63 to −0.05), P < 0.05] and 5 ng min−1 kg−1 [−0.76 (−1.47 to −0.05), P < 0.05]. No changes in Doppler echocardiographic indices of diastolic function were observed with D-aldosterone infusion. 4. These data suggest that angiotension II, even at a sub-pressor concentration, produces an impairment of left ventricular diastolic filling, which occurs independently of its effect on aldosterone release.

scholarly journals Prometaphase spindle maintenance by an antagonistic motor-dependent force balance made robust by a disassembling lamin-B envelope

2010 ◽  
Vol 188 (1) ◽  
pp. 49-68 ◽  
Author(s):  
Gul Civelekoglu-Scholey ◽  
Li Tao ◽  
Ingrid Brust-Mascher ◽  
Roy Wollman ◽  
Jonathan M. Scholey
Keyword(s):  
Narrow Range ◽  
Force Balance ◽  
Balance Model ◽  
Power Stroke ◽  
Mitotic Spindles ◽  
Stochastic Force ◽  
Lamin B ◽  
Spindle Poles

We tested the classical hypothesis that astral, prometaphase bipolar mitotic spindles are maintained by balanced outward and inward forces exerted on spindle poles by kinesin-5 and -14 using modeling of in vitro and in vivo data from Drosophila melanogaster embryos. Throughout prometaphase, puncta of both motors aligned on interpolar microtubules (MTs [ipMTs]), and motor perturbation changed spindle length, as predicted. Competitive motility of purified kinesin-5 and -14 was well described by a stochastic, opposing power stroke model incorporating motor kinetics and load-dependent detachment. Motor parameters from this model were applied to a new stochastic force-balance model for prometaphase spindles, providing a good fit to data from embryos. Maintenance of virtual spindles required dynamic ipMTs and a narrow range of kinesin-5 to kinesin-14 ratios matching that found in embryos. Functional perturbation and modeling suggest that this range can be extended significantly by a disassembling lamin-B envelope that surrounds the prometaphase spindle and augments the finely tuned, antagonistic kinesin force balance to maintain robust prometaphase spindles as MTs assemble and chromosomes are pushed to the equator.

Abstract 649: Increased Left Ventricular Filling Pressure is Associated with Left Atrial Thrombus in Patients with Atrial Fibrillation.

Circulation ◽  
2008 ◽  
Vol 118 (suppl_18) ◽  
Author(s):  
Katsuomi Iwakura ◽  
Hiroshi Ito ◽  
Atsunori Okamura ◽  
Yasushi Koyama ◽  
Motoo Date ◽  
...  
Keyword(s):  
Atrial Fibrillation ◽  
Diastolic Function ◽  
Left Atrial ◽  
Multivariate Logistic Regression Analysis ◽  
Left Ventricular ◽  
Filling Pressure ◽  
Diastolic Filling ◽  
Ventricular Filling Pressure ◽  
Lv Diastolic Dysfunction ◽  
Ventricular Filling

Patients with atrial fibrillation (AF) are frequently associated with reduced left ventricular (LV) diastolic dysfunction. It is still unclear whether reduced diastolic function is associated with the risk of left atrial (LA) thrombus in AF. The ratio of transmitral E velocity to mitral annular velocity (e′) is an echocardiographic estimate of diastolic LV filling pressure even under AF rhythm. We investigated whether reduced LV diastolic function is associated with the risk of LA thrombus in AF patients, using E/e′ ratio as an index. We enrolled consecutive 405 patients with non-valvular, paroxysmal or chronic AF, who underwent both transthoracic- (TTE) and transesophagial echocardiography (TEE) examination within a month. We measured LA and LV dimensions, LV ejection fraction (%EF), wall thickness, E and e′ velocities on TTE, and determined E/e′ ratio. LA appendage thrombus was found in 33 patients (8.1%). Patients with LA thrombus showed lower e′ velocity (5.3±1.8 vs. 7.0±2.2 cm/s, p<.0001) and higher E/e′ ratio (17.2±9.2 vs. 11.5±5.9, p<.0001) than those without it. Using 12.4 as an optimal cutoff point, E/e′ predicted LA thrombus with 70% sensitivity and 70% specificity (AUC=0.72). Odds ratio for LA thrombus in patients in the highest quartile of E/e′ was 6.38 (3.06–13.9). Multivariate logistic regression analysis indicated that the highest quartiles of E/e′ ratio was an independent predictor of LA thrombus among echocardiographic parameters, along with LA dimension and %EF, whereas e′ was not. LA appendage flow velocity was significantly correlated with E/e′ ratio (p<.0001), implying that increased diastolic filling pressure could be associated with impaired blood flow within LA. Increased LV filling pressure increased the risk of LA thrombus in patients with AF, partially through impaired LA hemodynamics. E/e′ ratio on TTE could be useful for detecting high-risk patients for LA thrombus.

scholarly journals A force balance model for the motion, impact, and bounce of bubbles

2014 ◽  
Vol 26 (9) ◽  
pp. 092101 ◽  
Author(s):  
Evert Klaseboer ◽  
Rogerio Manica ◽  
Maurice H. W. Hendrix ◽  
Claus-Dieter Ohl ◽  
Derek Y. C. Chan
Keyword(s):  
Force Balance ◽  
Balance Model

scholarly journals Glaciological studies on Nelson Island, South Shetland Islands, Antarctica

1995 ◽  
Vol 41 (138) ◽  
pp. 408-412 ◽  
Author(s):  
Ren Jiawen ◽  
Qin Dahe ◽  
J. R. Petit ◽  
J. Jouzel ◽  
Wang Wenti ◽  
...  
Keyword(s):  
Accumulation Rate ◽  
Local Environment ◽  
High Viscosity ◽  
Force Balance ◽  
South Shetland Islands ◽  
Balance Model ◽  
Shetland Islands ◽  
Ice Cap ◽  
Basal Sliding ◽  
Marine Air

AbstractThe ice cap on Nelson Island in the South Shetland Islands, West Antarctica, was studied between 1985 and 1989. The ice cap has an average thickness of 120 m. it is temperate, exists under the sub-Antarctic maritime climate and almost completely covers the island. Owing to intense percolation of meltwater (and, to some extent, liquid precipitation), the snow-firn layer is in the soaked facies, with a firn-ice transition at a depth of 25-26 m at the summit. A force-balance model suggests that the ice is almost linearly viscous but has a high viscosity. The model further suggests that basal sliding makes a larger contribution to the ice movement than does ice deformation. From 1970 to 1988. the average accumulation rate was 120 kg m−2a−1at the centre, and between 1985 and 1989 the equilibrium-line elevation averaged 110m a.s.l. Analysis of chemical impurities in the surface snow suggests that the precipitation source is mainly local marine air masses and that human activity has already exerted a detectable influence on the local environment.

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