A filling of a closed hyperbolic surface is a set of simple closed geodesics whose complement is a disjoint union of hyperbolic polygons. The systolic length is the length of a shortest essential closed geodesic on the surface. A geodesic is called systolic, if the systolic length is realised by its length. For every $g\geq 2$, we construct closed hyperbolic surfaces of genus $g$ whose systolic geodesics fill the surfaces with complements consisting of only two components. Finally, we remark that one can deform the surfaces obtained to increase the systole.

The development of newer, load-independent indices of contractility has not substantially reduced general clinical reliance on ejection fraction and shortening fraction to detect abnormalities of contractility, in spite of common understanding of the preload and afterload dependence of percent fiber shortening. The more widespread application of sensitive indices of contractility has been impeded in part by complex methods of acquisition and analysis of data as well as uncertainty concerning the clinical importance of the additional derived information. Substantial recent experience with analysis of stress-shortening and stress-velocity, nonetheless, demonstrates that physiologically meaningful indices of afterload, preload, and contractility can be obtained noninvasively without hemodynamic interventions. There is extensive theoretical and experimental basis for these methods, and the limitations are similar to other global indices of myocardial mechanics. The superiority of methods which allow distinction between contractile abnormalities and abnormal load are particularly important when altered ventricular loading conditions are a prominent feature of the disease state. Several clinical situations have been identified for which analysis of stress-shortening and stress-velocity demonstrates that assessment by fiber shortening alone has resulted in misrepresentation of myocardial status. The clinical utility of assessment of ventricular function is considerably enhanced when the relative contribution of load and contractile performance is determined.

There has been increasing interest in the study of ventricular function in the patient with congenital heart disease. Numerous indexes have been derived for the assessment of ventricular function, suggesting that none is ideal. While the derivation of some measures of ventricular function have relied on advanced mathematical principles, it is still possible for the non-mathematician to obtain important insights into ventricular function from an assessment of the events which underpin the cardiac cycle. In this review, I use the mechanics of the cardiac cycle to introduce basic concepts of ventricular function for the non-expert. In this way, I analyse ventricular systolic and diastolic performance and describe the contribution of regional variability of function to overall performance. This approach also highlights the role of the ventricle in overall cardiovascular and metabolic homeostasis.