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