The Geometric Model

Abstract

As mentioned in section II-1, the X-ray installation as a measurement tool was already made use of in the beginning of this century. Some methods in use nowadays for the determination of intraventricular volume originate from those applied to total heart volume measurement. Since the introduction of the orthodiagraphic projection method by MORITZ (1900), clinicians have looked for a basis to compare the size of hearts in a quantitative way. GEIGEL (1914) has often been criticized for the simplicity of the ball model he suggested, although in his article he admits several times that this is not a geometrical approximation but only a measure to be used in comparative studies. From the volume \(V = 4F^{\frac{3}{2}} /3\sqrt \pi\) , in which formula F equals the planimetered area of the heart shadow, he derived a “reduced heart quotient” by omitting the numerical factor and dividing by body weight (normal values are 15–23). Basing himself on dimensional considerations, ROHRER (1916) gave several formulae for the determination of body cavity volumes from linear or area measurements. Depending on the choice, different numerical constants were applied; these factors are the least dependent on shape if as many area measures as possible are used. From parallel projections in two perpendicular directions (sagittal and transversal) the shadow area F and largest diameter L were determined respectively, and next the cardiac volume was calculated with V = 0.63 F.L. The constant chosen was the average value of the factor which may be calculated in similar expressions for a sphere (0.66) and a paraboloid (0.59); it proved to correspond excellently with experiments with a heart model which gave the value 0.62.