| Objective: Calculating centroids or barycenters of tumors in vivo andcalculating the relative location in space between centroids or barycentersand puncturing points of body surface in order to afford exact location onthe puncturing pathway for percutaneous microwave coagulationtherapy(PMCT) for hepatocellular carcinoma(HCC), so that tumors ofless than 5 centimeter could be covered conformally treated by singleelectrode and excessive normal liver tissue could be avoided to damage.Materials and Methods(1) CT images of 15 patients with HCC were collected, and areas,CTvalues and largest diameters were measured and coordinates of any pointwere marked on CT images by tools of eFilm software.(2)Following X, Y and Z axials, areas and weights of every layer oftumors were calculated by area-drawing method and elliptic area formula.Using direct comparison method, the largest area or weight layer werefound along X, Y and Z axials and three largest layers passed across atone point that is the centroid(C0,C0') or barycenter(C1) of tumors in vivo.(3) Mathematical modeling with the centroid or barycenter formula of theobject: on account of area-drawing method, centroids C2 and barycentersC3 of tumors were calculated by the centroid formula or the barycenterformula; on account of elliptic area formula, the centroids C4 were calculated by the centroid formula, then the calculating course werecarried with MATLAB programming and centroids and barycenters werecompared with centroids C0.(4) Intercostals sites of tumors were definited and puncturing points onbody surface were signed, then distances and angles between puncturingpoints and centroids were calculated using relative distance in spaceformula and direction angle formula of the vector.Results:(1) Significant difference were found in area values by area-drawingmethod and elliptic area formula (P＜0.05). but centroids C0(7.63±2.61,12.36±3.53, 8.55±2.70) and C0' (7.63±2.61, 12.36±3.53, 8.55±2.70) byboth methods were on the same layer; barycenters C1(7.63±2.61,12.36±3.53, 8.55±2.70) were centroided with centroids Co.(2)Centroids C2 and C4, C2 and Co, C4 and Co were compared, nosignificant difference were found(P＞0.05).(3)The computation of distances between puncturing points and centroidsor barycenters, as well as the computation of direction angles wereviewed in attached table 7.Conclusion:(1) It's feasible to calculate the area value of the tumor layers witharea-drawing methods or elliptic area formula.(2) Through direct comparison method and the centroid or barycenter formula, the centroid coordinate coincide with the barycenter coordinateon the whole, that indicate it's reasonable of the diagnosis in CT that thetumor of less than 5cm be regarded as the homogeneous object,meantimes it's easy that only centroid of the tumor is calculated inclinical location.(3)For HCC, it's suggested to calculate the centroid of the tumor by theelliptic area formula and the centroid formaula.(4)In this study of computer-assistant calculation, the accuracy of thedistance between the puncturing point on surface and the centroid in thetumor is 10-4cm, and the accuracy of the azimuthal angle is 0.1°.
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