Ventricle

Dimensions

FiberVent assumes the left-ventricle is a hemi-ellipse with internal radius $r$ and height $z$.

The chamber volume is given by

\[\begin{equation} V = \frac{2}{3} \pi r^2 z \end{equation}\]

where

\[\begin{equation} z = z_{scale} (\frac{l}{l_0})^{z_{exp}} \end{equation}\]

and

• $z_{scale}$ is a scaling factor
• $l$ and $l_0$ are the current and reference half-sarcomere lengths respectively
• $z_{exp}$ is an exponent

If $z_{scale}$ is greater than 1, the ventricle is longer than it is wide.

The $(\frac{l}{l_0})^{z_{exp}}$ term allows the ventricle to shorten as it contracts mimicking some of the geometrical advantages provided by the helical array of sheet angles found in normal hearts.

Pressure

FiberVent calculates the intraventricular pressure $P$ using the thick-wall approximation of Laplace’s law.

\[\begin{equation} P = \frac {\sigma T \left(2 + \frac{T}{r} \right) } { r } \end{equation}\]

where:

• $\sigma$ is wall stress
• $T$ is the wall thickness
• $r$ is the internal radius.