Quantitative mapping of force–pCa curves to whole-heart contraction and relaxation

Stefano Longobardi, Anna Sher, Steven A. Niederer*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


Abstract: The force–pCa (F–pCa) curve is used to characterize steady-state contractile properties of cardiac muscle cells in different physiological, pathological and pharmacological conditions. This provides a reduced preparation in which to isolate sarcomere mechanisms. However, it is unclear how changes in the F–pCa curve impact emergent whole-heart mechanics quantitatively. We study the link between sarcomere and whole-heart function using a multiscale mathematical model of rat biventricular mechanics that describes sarcomere, tissue, anatomy, preload and afterload properties quantitatively. We first map individual cell-level changes in sarcomere-regulating parameters to organ-level changes in the left ventricular function described by pressure–volume loop characteristics (e.g. end-diastolic and end-systolic volumes, ejection fraction and isovolumetric relaxation time). We next map changes in the sarcomere-regulating parameters to changes in the F–pCa curve. We demonstrate that a change in the F–pCa curve can be caused by multiple different changes in sarcomere properties. We demonstrate that changes in sarcomere properties cause non-linear and, importantly, non-monotonic changes in left ventricular function. As a result, a change in sarcomere properties yielding changes in the F–pCa curve that improve contractility does not guarantee an improvement in whole-heart function. Likewise, a desired change in whole-heart function (i.e. ejection fraction or relaxation time) is not caused by a unique shift in the F–pCa curve. Changes in the F–pCa curve alone cannot be used to predict the impact of a compound on whole-heart function. (Figure presented.). Key points: The force–pCa (F–pCa) curve is used to assess myofilament calcium sensitivity after pharmacological modulation and to infer pharmacological effects on whole-heart function. We demonstrate that there is a non-unique mapping from changes in F–pCa curves to changes in left ventricular (LV) function. The effect of changes in F–pCa on LV function depend on the state of the heart and could be different for different pathological conditions. Screening of compounds to impact whole-heart function by F–pCa should be combined with active tension and calcium transient measurements to predict better how changes in muscle function will impact whole-heart physiology.

Original languageEnglish
Pages (from-to)3497-3516
Number of pages20
JournalJournal of Physiology
Issue number15
Publication statusPublished - 1 Aug 2022


  • force–calcium
  • force–pCa
  • Hill coefficient
  • left ventricular myocyte
  • pCa
  • pCa shift
  • sarcomere modulators
  • steady-state force


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