Growth

Overview

FiberVent’s hemi-elliptical ventricle can grow in two modes: concentric (wall thickening / thinning) and eccentric (chamber dilation / constriction).

Concentric growth

Concentric growth mimics myocytes add / removing sarcomeres and mitochondria in parallel by changing the wall thickness $T$. The relevant differential equation is

\[\begin{equation} \frac{dT(t)}{dt} = G_m T(t) g_c(t) \end{equation}\]

where:

• $G_m$ is the master growth rate
• $g_c$ is the concentric growth signal

In turn, $g_c$ is defined by:

\[\begin{equation} \frac{dg_c(t)}{dt} = g_{cp} s_c(t) + g_{cd}\frac{ds_c(t)}{dt} \end{equation}\]

where

• $g_{cp}$ is scaling factor defining proportional feedback
• $g_{cd}$ is scaling factor defining derivative feedback’

and

\[\begin{equation} s_c(t) = \frac{[ATP] - ATP_{set}}{ATP_{set}} \end{equation}\]

where:

• $ATP_{set}$ is a homeostatic set-point

Eccentric growth

Eccentric growth mimics myocytes adding / removing sarcomeres in series by changing the number of half-sarcomeres around the ventricle’s circumference $n$. The relevant differential equation is

\[\begin{equation} \frac{dn(t)}{dt} = G_m n(t) g_e(t) \end{equation}\]

where:

• $G_m$ is the master growth rate
• $g_e$ is the ecceentric growth signal

In turn, $g_e$ is defined by:

\[\begin{equation} \frac{dg_e(t)}{dt} = g_{ep} s_e(t) \end{equation}\]

and

\[\begin{equation} s_e(t) = \frac{F_{titin}(t) - F_{titin\_set}}{F_{titin\_set}} \end{equation}\]

where:

• $F_{titin}$ is the stress in titin molecules
• $F_{titin_set}$ is a homeostatic set-point