Sphere Under Advection and Mean Curvature Flow

TL;DR

This paper derives a closed-form solution for the advection and mean curvature flow of a sphere, aiding the validation of numerical methods and inverse solvers in modeling bone microarchitecture adaptation.

Contribution

It provides the first explicit solution for sphere evolution under combined advection and mean curvature flow, facilitating numerical validation.

Findings

Closed-form solution for sphere under combined flow

Validation tool for numerical methods

Supports inverse modeling in biological structures

Abstract

Advection and mean curvature flow is used as a model of bone microarchitecture adaptation. It is an equivalent geometric flow to prescribed mean curvature flow with an additional rate term. In order to validate numerical methods for simulating this flow and developing an inverse solver, a closed-form solution for advection and mean curvature flow of a sphere is derived.