Stochastic modeling of the tumor volume assessment and growth patterns in hepatocellular carcinoma

The growth pattern of hepatocellular carcinoma (HCC) arising from cirrhosis is variable and depends on the degree of differentiation and vascularization. Because growth is not constant in the natural history of HCC, prediction of subsequent growth rate based on tumor volume doubling time and correlation with histological and ultrasonographical characteristics at the moment of initial diagnosis are usually unreliable. The aim of our study was to assess the growth patterns of HCC with the aid of stochastic modeling. Thus, we included in our study 27 patients with histologically proven HCC, which had multiple (more than three)follow-up ultrasound studies in a six months interval. The patients did not receive any treatment during the observation period. HCC was visualized by computer aided ultrasound imaging, obtaining both the primary size quantification and the edge-detection enhancement. By a bi-cubic B-spline interpolation of points on the edges (3-D Bezier approximation) we approximated the surfaces shapes, and using the hit or miss Monte Carlo method we accurately estimate the tumor volume. Starting from the previous tumor volumes time series recorded during the first six months of evolution we applied both a linear, exponential and logarithmic smoothing to forecast the future size of the HCC tumor in the next six months. Our conclusion was that a dynamic forecasting model of HCC volumes could be very accurate for the assessment of tumor volume doubling time usually obtained by two discrete volume measurements of the tumor.