Unified validation of a refined second-generation HR-pQCT based homogenized finite element method to predict strength of the distal segments in radius and tibia

Introduction: HR-pQCT based micro finite element (pFE) analyses are considered as "gold standard" for virtual biomechanical analyses of peripheral bone sites such as the distal segment of radius and tibia. An attractive alternative for clinical use is a homogenized finite element method (hFE) based on constitutive models, because of its much shorter evaluation times and modest computational resource requirements. Such hFE models have been experimentally validated for the distal segment of the radius, but neither for the distal segments of the tibia nor for both measurement sites together. Accordingly, the aim of the present study was to refine and experimentally validate an hFE processing pipeline for in vivo prediction of bone strength and stiffness at the distal segments of the radius and the tibia, using only one unified set of material properties. Material and methods: An existing hFE analysis procedure was refined in several aspects: 1) to include a faster evaluation of material orientation based on the mean surface length (MSL) method, 2) to distinguish cortical and trabecular bone compartments with distinct material properties and 3) to directly superimpose material properties in mixed phase elements instead of densities. Based on an existing dataset of the distal segment of fresh-frozen radii (double sections 20.4 mm, n = 21) and a newly established dataset of the distal segment of fresh-frozen tibiae (triple sections, 30.6 mm, n = 25), a single set of material properties was calibrated on the radius dataset and validated on the tibia dataset by comparing hFE stiffness and ultimate load with respective experimental results, obtained by compressing the samples on a servo-hydraulic testing machine at a monotonic and quasi-static displacement rate up to failure. Results: Using the identified set of material properties, the hFE-predicted stiffness and failure load were in excellent agreement with respective experimental results at both measurement sites (radius stiffness R-2 = 0.93, slope = 1.00, intercept = 479 N/mm(2)/radius ultimate load: R-2 = 0.97, slope = 1.00, intercept = 679 N; tibia stiffness R-2 = 0.96, slope = 1.01, intercept = -1027 N/mm(2)/tibia ultimate load: R-2 = 0.97, slope = 1.04, intercept = 394 N; combined dataset stiffness R-2 = 0.95, slope = 1.01, intercept = -230 N/mm(2)/combined dataset ultimate load: R-2 = 0.97, slope = 1.03, intercept = 495 N). Discussion and conclusion: In conjunction with unified BV/TV calibration, the established hFE pipeline accurately predicts experimental stiffness and ultimate load of distal multi-sections at the radius and tibia. Processing time for non-linear analysis was substantially reduced compared to previous mu FE and hFE methods but could be further minimized by estimating bone strength based on a fast and linear analysis like as is currently done with mu FE.