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Volume measurements are useful in many branches of science and medicine. They are usually accomplished by acquiring a sequence of cross sectional images through the object using an appropriate scanning modality, for example x-ray computed tomography (CT), magnetic resonance (MR) or ultrasound (US). In the cases of CT and MR, a dividing cubes algorithm can be used to describe the surface as a triangle mesh. However, such algorithms are not suitable for US data, especially when the image sequence is multiplanar (as it usually is). This problem may be overcome by manually tracing regions of interest (ROIs) on the registered multiplanar images and connecting the points into a triangular mesh. In this paper we describe and evaluate a new discreet form of Gauss' theorem which enables the calculation of the volume of any enclosed surface described by a triangular mesh. The volume is calculated by summing the vector product of the centroid, area and normal of each surface triangle. The algorithm was tested on computer-generated objects, US-scanned balloons, livers and kidneys and CT-scanned clay rocks. The results, expressed as the mean percentage difference +/- one standard deviation were 1.2 +/- 2.3, 5.5 +/- 4.7, 3.0 +/- 3.2 and -1.2 +/- 3.2% for balloons, livers, kidneys and rocks respectively. The results compare favourably with other volume estimation methods such as planimetry and tetrahedral decomposition.

We are involved in the development of photodynamic therapy (PDT) as a minimally invasive method for treating dysfunctional uterine bleeding, one of the primary clinical indications for hysterectomy. In this paper, we analyse light propagation through the uterus in order to specify the requirements for a light delivery system capable of effectively performing endometrial PDT. Our approach involves developing an analytical model based on diffusion theory to predict optical fluence rate distributions when cylindrical and spherical optical applicators are placed in the uterine cavity. We apply the results of our model calculations to estimate the thermal effects of optical irradiation and the effective photodynamic optical dose. Theoretical fluence rate calculations are compared to fluence rate measurements made in fresh, surgically removed human uteri. Our results show that a trifurcated cylindrical optical applicator inserted into the human uterus can provide a light dose that is sufficient to cause photodynamic destruction of the entire endometrium. When the optical power per unit length of each cylindrical applicator is 100 mW cm-1 (at 630 nm), a fluence rate of 40 mW cm-2 is delivered to the boundary layer between the endometrium and the myometrium (a depth of about 4-6 mm). The optical fluence delivered to the boundary layer after 20 min of exposure is 50 J cm-2, a level that is generally accepted to cause tissue damage throughout the endometrium in most patients.