Estimation of liver elasticity using the finite element method and four‐dimensional computed tomography images as a biomarker of liver fibrosis

PURPOSE Current radiotherapy planning procedures are generally designed based on anatomical information only and use computed tomography (CT) images that do not incorporate organ-functional information. In this study, we developed a method for estimating liver elasticity using the finite element method (FEM) and four-dimensional CT (4DCT) images acquired during radiotherapy planning, and we subsequently evaluated its feasibility as a biomarker for liver fibrosis. MATERIALS AND METHODS Twenty patients who underwent 4DCT and ultrasound-based transient elastography (UTE) were enrolled. All patients had chronic liver disease or cirrhosis. Liver elasticity measurements of the UTE were performed on the right lobe of the patient's liver in 20 patients. The serum biomarkers of the aspartate aminotransferase (AST)-to-platelet ratio index (APRI) and fibrosis-4 index (FIB-4) were available in 18 of the 20 total patients, which were measured within 1 week after undergoing 4DCT. The displacement between the 4DCT images obtained at the endpoints of exhalation and inspiration was determined using the actual (via deformable image registration) and simulated (via FEM) respiration-induced displacement. The elasticity of each element of the liver model was optimized by minimizing the error between the actual and simulated respiration-induced displacement. Then, each patient's estimated liver elasticity was defined as the mean Young's modulus of the liver's right lobe and that of the whole liver using the estimated elasticity map. The estimated liver elasticity was evaluated for correlations with the elasticity obtained via UTE and with two serum biomarkers (APRI and FIB-4). RESULTS The mean ± standard deviation (SD) of the errors between the actual and simulated respiration-induced displacement in the liver model was 0.54 ± 0.33 mm. The estimated liver's right lobe elasticity was statistically significantly correlated with the UTE (r = 0.87, P