View Full Version : Length-Tension Relations for Myocardial Mechanics

Bernard Debono (university Of Malta)
03-12-1998, 06:00 PM
Hello everyone,

I have some questions of a rather basic nature to submit to the Biomch-L
Newsgroup. I
require a manageable muscle model for educational purposes. My first
search through
your archives did not reveal similar discussions on my topic. Further
searches were
stymied due to a misconfiguration on the server. The rest of this e-mail
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[Myocardial Mechanics

I would like to present a tangible conceptual model of the heart as a
hollow muscular
organ to my medical students. My aim is to elucidate the basis of the
equilibrium curves and work diagram (Figure 1) from first principles by
drawing from
Length-Tension relation experiments on skeletal muscle.

Figure 1.

Myocardial preparations, with an almost parallel arrangement of their
muscle fibers,
can be subjected to classical analytic procedures, and model designs
developed for skeletal muscle can be used. My three references on the
topic[1] [2] [3]
support a not-so-robust spring model of muscle tissue depicted in Fig.

Figure 2.

In [1], the cardiac passive tension curve shown in Fig. 3 is attributed
to parallel and
series elastic elements (P.E. and S.E. respectively) under the form of
sheaths, filament components like titin and nebulin, and connective and
tendinous tissue
fibers. It is also claimed that the contractile element (C.E.) is
considered freely
extensible at rest. Thus no tension across the resting C.E. exits.
Cardiac contraction
during systole is an all-or-none phenomenon implying that there is no
partial tonus
activity persisting during diastole.

Figure 3.

There are various points that are, as yet, unclear to me:

1) If C.E.s are freely extensible at rest, then S.E.s cannot contribute
to the passive
tension curve. Wouldn’t this lead to a contradiction of the first
statement in the
paragraph above? If this were so, what would be the shape of the
Length-Tension curve
for S.E.s in isolation? Are the approximate values of the elasticity
modulus of P.E.s and
S.E.s available?

2) [1] [2] and [3] provide no explanation for the isotonic maxima curve
in Fig.3. Why
should a pre-loaded contraction starting at point A (Fig.3) grind to a
halt at point B?
What keeps it from shortening to reach a steady state equilibrium of
forces at C?
Suppose that a pre-loaded contraction starts at D. Wouldn’t the
isometric contraction of
the C.E. be able to ‘relieve’ the P.E.s of some of their tension thus
enabling them to
shorten? Wouldn't this improve actin-myosin overlap and eventually
bring D into the
active increment envelope, leading to F?

3) How was data obtained for isometric contractions starting from a
length shorter than
the resting one. Was the muscle under study already in a state of

Thank you for your time.


[1] Comprehensive Human Physiology, R. Greger U. Windhorst, Springer
[2] Human Physiology, R. Schmidt G. Thews, 2nd ed., Springer-Verlag
[3] Textbook of Medical Physiology, A. Guyton, 9th ed., Saunders

Dr Bernard Debono MD
Department of Physiology and Biochemistry
Biomedical Sciences Building
University of Malta
Tel: +(356) 3290-2286
Fax: +(356) 310577
E-mail: bmds@biomed.um.edu.mt