Ricci-flow based conformal mapping of the proximal femur to identify exercise loading effects

Nathaniel Narra,Shinya Abe,Vassil Dimitrov,Harri Sievänen,Riku Nikander,Reijo Kouhia,Jari Hyttinen

doi:10.1038/s41598-018-23248-y

Abstract

The causal relationship between habitual loading and adaptive response in bone morphology is commonly explored by analysing the spatial distribution of mechanically relevant features. In this study, 3D distribution of features in the proximal femur of 91 female athletes (5 exercise loading groups representing habitual loading) is contrasted with 20 controls. A femur specific Ricci-flow based conformal mapping procedure was developed for establishing correspondence among the periosteal surfaces. The procedure leverages the invariance of the conformal mapping method to isometric shape differences to align surfaces in the 2D parametric domain, to produce dense correspondences across an isotopological set of surfaces. This is implemented through a multi-parametrisation approach to detect surface features and to overcome the issue of inconsistency in the anatomical extent present in the data. Subsequently, the group-wise distribution of two mechanically relevant features was studied – cortical thickness and surface principal strains (simulation results of a sideways fall). Statistical inferences over the surfaces were made by contrasting the athlete groups with the controls through statistical parametric mapping. With the aid of group-wise and composite-group maps, proximal femur regions affected by specific loading groups were identified with a high degree of spatial localisation.

Highlights

Bone is an adaptive hard tissue which, among its other characteristics, is designed to be robust against physiological loads
The data consisted of tomographic Magnetic Resonance (MR) images of the proximal femur of 111 participants - 91 female athletes and 20 physically active women serving as a control group
The cortical thickness distribution in each loading group was contrasted with the control group, and statistical significances inferred by controlling for body weight, femur scale and shape (Fig. 4)

Summary

Introduction

Bone is an adaptive hard tissue which, among its other characteristics, is designed to be robust against physiological loads. Studies have shown that beneficial bone adaptation can be observed through exercise even in older people[8] and can help in arresting the attenuation of bone strength due to age-related bone loss[9] Studying this cause-effect relationship between physical loading and regional adaptation is an area of active pursuit. The method treats the surface as a differentiable manifold and converts the 3D registration problem into 2D This dimension reduction is achieved by a parametrisation procedure where the surface is conformally mapped to the planar domain using discrete surface Ricci-flow[19,20] implemented in MATLAB (Release 2016b, The MathWorks, Inc., Natick, Massachusetts, United States). As a supporting case study, this registration approach was developed into a procedural chain to analyse the spatial distribution of geometric adaptation in the proximal femur in response to long-term habitual physical activity. A geometric adaptation that can improve ‘bone mechanical performance’ at critical fracture sites can help identify beneficial exercises and mobility patterns

Methods

Results

Conclusion