Research Article

Simulation of the Frank-Starling Law of the Heart

Figure 5

Sample values of cardiovascular variables in a single cardiac cycle during initial conditions (column a), maximal preload (column b), or maximal afterload (column c) when atrium is contracting. Each column is subdivided in four blocks. Upper two blocks: AP, VP, AtP, and CO (VP and AtP also at an enlarged pressure scale). Middle block: mitral flow and aortic flow. Bottom block: EDVV, ESVV, and SV. Note the “hump” in AtP in late diastole. Note also that the early mitral flow commences when AtP = VP. The higher is this pressure, the higher is peak early mitral flow. (a) Initial conditions (57.6 s–58.4 s of simulation time). Note that atrial contraction (immediately prior to the ventricular contraction) results in a late mitral flow, increasing EDVV by about 20 mL. Aortic flow is synchronous with ventricular contraction; this flow is stopped abruptly as soon as VP is lower than AP. Early mitral flow starts as soon as VP is lower than AtP. (b) Preload increased to 8 mm Hg (177.6 s–178.4 s of simulation time). Note that AP and VP are strongly increased. Similarly, both mitral flows and aortic flow are increased, and consequently EDVV, SV, and CO are strongly increased. Almost no change in ESVV, in ICT, and in IRT. dp/dt is increased from the resting value 1886 mm Hg/s to 3125 mm Hg/s; consequently, TtP is decreased from its resting value 72 ms to 63.6 ms. (c) Afterload increased to 10 U (177.6 s–178.4 s of simulation time). Note that both AP and VP are strongly increased. However, both mitral flows and aortic flow are decreased. Consequently EDVV and ESVV increase in an unequal extent, so that SV and consequently CO are slightly decreased. Note also that both ICT and IRT are increased. dp/dt is slightly increased from the resting value 1886 mm Hg/s to 2127 mm Hg/s; consequently TtP is increased from its resting value 72 ms to 90 ms. (d) The P-V loop diagram of the conditions above. If preload is increased, the loop diagram becomes broader. Both ventricular pressure and SV are increased. If afterload is increased, the loop diagram becomes narrower. Ventricular pressure is increased, but SV is slightly decreased. Ventricular work is given in mm Hg·mL and in J.
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(a) Initial conditions
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(b) Maximum preload
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(c) Maximum afterload
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