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

https://doi.org/10.1016/S0928-4869(99)00023-3Get rights and content

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.

Section snippets

Introduction: current status of bond graphs in life sciences

As demonstrated by other papers in this special issue of SIMPRA, bond graphs (denoted frequently hereafter by the notation BG) are ideally suited to the modelling of nonlinear, multi-energy systems. Biophysical and physiological systems belong to this category. We should thus expect a wide use of BGs in these fields but this is clearly not the case. After an initial surge of interest in the early 1970s [1], the use of BGs in life science modelling has become quite uncommon. In our opinion, this

A primer on analog models in cardiac dynamics

Many experiments (see [10]) have suggested that, in normal conditions, the time-dependent values of the pressure and volume generated by the left ventricle (LV) are approximately related by:plv(t)=α(t)pa(Qlv)+(1−α(t))pr(Qlv),where plv and Qlv are respectively the left ventricular pressure and volume: pr and pa are nonlinear functions of Qlv describing the experimentally measured pressure–volume curves characterising the ventricle in completely relaxed (r) and active (a) conditions. Finally, α(t

Informal description of the mechanisms incorporated in the model

Fig. 3 illustrates a physiological preparation in which a canine left ventricle is isolated from the body and attached to glass pipes in a glass box B providing adequate external conditions and coronary metabolic support from a support dog [6], [8]. The ventricle is represented by a variable compliance (LVC) which, due to the muscle in its wall, alternates between soft and stiff values. This LVC is attached to glass tubes connected to its valves (MIV = mitral = input and AOV = aortic = output).

The 2PC model of chemo-mechanical transduction

To the best of our knowledge, it is the first time that a chemo-mechanical 2PC is proposed as a modelling element not only in physiology but also in the entire BG literature. Its definition, its conditions of validity and the derivation of its constitutive equations will therefore be completely detailed in this section. We will proceed by analogy with a similar transducer, a moving plate electrical capacitor which has a well-known elementary theory [11]. However, the reader should realise that

Implementation and preliminary results

We have implemented our model using 20-SIM (a trademark of CONTROL-LAB, The Netherlands). Since most of our BG elements are not classical, sub-models had to be defined for some elements using SIDOPS, the object-oriented language underlying the graphical definition of BGs in 20-SIM. The full model is given in Fig. 5. At first sight, it is complex and a far cry from an intuitive description close to the mental models of the physiologists. However, by isolating mentally the BG part from the block

Conclusion

This paper has introduced a model of the left ventricle which implements what is essentially a new “macro-interpretation” of the ventricular capacity for generating elastic potential energy. Instead of being unidirectional like in all previous models, the chemo-mechanical coupling is seen as reversible, storing potential energy and closely linked to the contractile chemical events. However the generation of chemical energy itself remains obviously irreversible and heat generating. Although heat

Acknowledgments

This work was done while the first author was based at the Sherrington School of Physiology (now part of King's College Medical School), St. Thomas's Campus, University of London.

References (14)

  • J. Montbrun-Di Filippo et al.

    A survey of bond graphs: theory, applications and programs

    J. Franklin Inst.

    (1991)
  • M.A. Savageau

    Biochemical System Analysis

    (1976)
  • B. Hannon et al.

    Modeling Dynamic Biological Systems

    (1997)
  • V.C. Rideout

    Physiological Systems Modeling

    (1989)
  • J. LeFèvre, P. Weller, Genetic optimisation of fuzzy policies in models of managed systems: a keynote lecture, in:...
  • K. Sagawa et al.

    Cardiac Contraction and the Pressure–Volume Relationship

    (1988)
  • C.L. Gibbs et al.

    Cardiac mechanics and energetics: chemomechanical transduction in cardiac muscle

    Am. J. Physiol.

    (1985)
There are more references available in the full text version of this article.

Cited by (0)

View full text