A bond graph model of chemo-mechanical transduction in the mammalian left ventricle

Abstract

We present a new lumped model of the pump behaviour of the mammalian left ventricle based on simple but physiologically plausible sub-models of chemo-mechanical energy transduction in muscle, mechano-hydraulic energy transduction in the ventricular wall and hemodynamical coupling of the ventricle and its arterial load. The model builds upon the foundation of classical analog ventricular models (dynamic compliance and visco-elastic models). However, we show that these classical models are not coherent from an energy viewpoint. To insure this coherency, we introduce explicit cross-bridge mechanisms linked to the mechano-hydraulical part of the model by a two-port capacitive (2PC) transducer representing chemo-mechanical coupling. We show that this 2PC is thermodynamically plausible and, when coupled to dissipative models of chemical energy generation and transfer, provides a novel and consistent characterisation of cardiac energetics at the global pump level. Finally, we briefly discuss some generalisations using nonlinear elements described by functional equations to represent muscle memory and sur-activation. It is a well-known fact that languages shape perception. Of all the lumped modelling languages, the bond graph (BG) method is the only one to use the notion of a 2PC as a primitive modelling concept. Our hypothesis (mental model) is thus directly inspired by the fact that we use the BG language. Our claim is thus that our work demonstrates very clearly the heuristic and descriptive power of BGs in shaping new ideas about multi-energy and nonlinear physiological applications.