Modeling control of myocardial wall geometry.

<p>In the CircAdapt model of the whole circulation (left), geometry of the walls determines hemodynamic performance, which in turn determines mechanical load of the wall material (upper right). Local mechano-sensing invokes changes in tissue structure (lower mid) and geometry, by which the control loop for adaptation of wall geometry is closed. A matrix of transfer coefficients (lower right) is used to estimate changes in tissue structure, causing geometry to adapt. Symbols [<i>Sens</i>, <i>M</i>, <i>Geom</i>] are used in Eq. (2–9). Abbreviations are explained in the general list.</p

Quality of reconstruction with combinations of sensed variables.

<p><i>cor_min</i> = minimum correlation coefficient.</p><p><i>EV_max</i> = maximum Eigen value of feedback loop.</p><p><i>svd3</i> = distance to matrix singularity.</p><p><i>ID</i> = evaluated combinations identified by sensor numbers.</p><p><i>S_ecm</i>, <i>S_act</i>, <i>S_int</i>, <i>S_Ztit</i>, <i>L_s,act</i>, <i>L_s,int</i>, <i>e_act</i>, <i>w_stroke</i> are sensed variables (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002369#pcbi-1002369-t002" target="_blank">Table 2</a>).</p

Sensitivity of steady state geometry to changes in target values.

<p>LAW, RAW, LVW, SVW, RVW = myocardial walls.</p><p><i>V_wall</i> = wall volume, <i>A_myom</i> = MyoM area, <i>A_ecm</i> = ECM area.</p

Composition of the heart by 5 walls with MyoM and ECM.

<p>Curved mid-wall surface form the core of macroscopic geometry of atria and ventricles. Left and right atrium (LA, RA) are enclosed by single curved walls (LAW, RAW). The ventricular unit is composed of left, septal and right ventricular wall (LVW, SVW and RVW), enclosing left and right ventricle (LV, RV). Geometry of each wall is deducted from unfolding the wall to a flat surface. Each wall has a volume and a mid-wall area. A wall contains a myocyte matrix (MyoM) intertwined with the extracellular matrix (ECM). Both matrices have their own reference mid-wall area, linking their ultrastructure to the macroscopic geometry of the wall.</p

Transfer coefficients from sensed variable to structural parameter.

<p>Transfer coefficients from sensed variable to structural parameter.</p

Simulation of hypertrophic growth of the five myocardial walls.

<p>The fractional change of wall mass per adaptation step is plotted as a function of the number of steps after 20% increase of cardiac output. The numbers 126, 1346 and 1236 refer to the applied combination of sensed variables, used for mechano-feedback (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002369#pcbi-1002369-t003" target="_blank">Table 3</a>). After fast mass growth during the first 25 cycles, for combination 126 a slow component remains active for a long time. Convergence with 1236 is best. Convergence with 1346 is also fast, but there is more overshoot.</p

Reconstruction of cardiac wall geometry by mechano-sensing.

<p>A large number (10,000) of random increments of structural parameters was induced in all cardiac walls. In each wall, information about mechanical load of the tissue was obtained from 8 locally sensed variables (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002369#pcbi-1002369-t002" target="_blank">Table 2</a>). With this information, best estimates were made of the originally induced increments. For the 3 structural parameters (vertical) and 5 walls (horizontal) reconstructed increment is plotted as a function of original increment. Numbers in the graphs indicate correlation coefficients.</p

Adaptation to a 20% change of pump load and contractility.

<p>Mean volumes of right and left atria (RA, LA) and right and left ventricles (RV, LV), respectively, are indicated by the larger numbers in ml. Mean thicknesses of atrial and ventricular walls are indicated by italic numbers in mm. Drawn changes in geometry are exaggerated for better visibility. End-diastolic pressures are indicated in mmHg. With 20% increase of stroke volume, all volumes and thicknesses increase (eccentric hypertrophy), except for RV volume. With 20% increase of mean aortic pressure, walls thicken, while geometry does not change much. With a 20% decrease of LV and septal contractility, these walls thicken, while further geometry is preserved.</p

Simulation of circulation dynamics and cardiomechanics.

<p>With the CircAdapt model, beat-to-beat circulation dynamics are simulated at moderate exercise (left) and at rest (right). Top: Pressures in left/right ventricle (p_lv/p_rv) and aorta/pulmonary artery (p_ao/p_pa), and flows through aortic/pulmonary (q_ao/q_pa) and mitral/tricuspid valves (q_mitr/q_tric). Lower panels: Stresses in actin and ECM of the 5 cardiac walls and related fiber strains. For exercise and rest, amplitude and time calibrations are the same. Abbreviations LAW, RAW, LVW, SVW, RVW are defined in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002369#pcbi-1002369-g002" target="_blank">Fig. 2</a>.</p

Myocardial wall geometry and hemodynamics.

<p>LAW, RAW, LVW, SVW, RVW: see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002369#pcbi-1002369-g002" target="_blank">Fig. 2</a>.</p><p>*referred to sarcomere length = 2.3 µm.</p