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Figure 9 | BioMedical Engineering OnLine

Figure 9

From: A new electric method for non-invasive continuous monitoring of stroke volume and ventricular volume-time curves

Figure 9

Schematics representing various anatomical and cardiological features that contribute to the non-linearity in the relation between voltage change and volume change. a: The non-spherical shape of the ventricles (feature (a) in the appendix) corresponds to an assembly of multiple spheres. In this figure, a simple representation of a ventricle, using only two spheres (indicated by S and S’), is depicted. During ventricular systole, the volume of each sphere decreases. The voltage increase, due to the volume decrease of the combination of the two spheres in close proximity, is less than the sum of the effects would have been when the effects of both spheres would have been calculated separately, without taking into account the close proximity of the two spheres. For instance, if the volume change of S’ increases (i.e., S’ becomes extra small near the end of the ventricular systole), then the strength of the incident field on S decreases during ventricular systole, thus diminishing the effect of the decrease of the volume of S on the measured voltage. Therefore, the non-linearity due to this “shadow effect” of S’ on S (and vice versa) yields a negative η value, viz. η=−0.033. b: The proximity of the heart to a boundary surface (skin-air), viz. the frontal surface of the thoracic skin. The non-linear effect due to the proximity to this boundary surface has been calculated using the Method of Image Charges [21], resulting in η=0.035. A decrease of S would entail a decrease of the mirror sphere S’ as well. A decrease of the volume of S’ would cause an increase of the strength of the incident field on S, thus increasing the effect that the decrease of S would have on the measured voltage. Hence the value of η is positive in this case. c: The cardiological phenomenon that a decrease of ventricular volume is generally accompanied by a simultaneous increase in atrial volume, and vice versa. In this schematic, the continuous lines represent the end-systolic situation, whereas the dotted lines refer to the end of the diastole. d: The same as in c, but now depicted using spheres, yielding η=0.107. The combined effect of the phenomena depicted in b and c yields a “worst case” of η=0.142. The “atrial” spheres are depicted in opaque grey.

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