Anatomy Approximation Analysis

MATLAB class for multi-sphere approximation of complex geometries and comparison of multi-sphere models

The MATLAB class Approxi provides a framework for approximating anatomical volume models using clumped-sphere models with iterative scaling to adapt to target volumes and model comparison. Developed for applications in orthopaedics, biomechanics, and computational geometry.

Key Features:

Sphere Model Generation

1. Mulit-Sphere Model Generation: Interface with Sihaeri's clumped sphere algorithm

2. Volume Scaling

• Voxel-based intersection of sphere models and reference geometries.
• Iterative scaling of sphere models to match target volumes.

3. Model Comparison: Frequency analysis of voxel occupancy across different models (multiple scoring metrics)

4. Geometric Analysis: Vertex-to-nearest-neighbour distance mapping between original surface models and sphere models (with color-coded results).

How to Use:

1. Code structure: The Approxi Class can be integrated into a corresponding main script. The key parts of the code are extracted into individual functions for reuse.

2. Import: Import your STL (or mesh) into MATLAB and make sure required functions like DEM-clumpedSphere (populateSpheres) and inpolyhedron are added to your MATLAB path

3. Generate Multi-sphere Models: Create multi-sphere models from input meshes using the DEM-clumpedSphere method

4. Run Volume Intersection: Compute voxel-based intersections between multi-sphere models and a reference geometry and adjust multi-sphere models to match target volumes

5. Compare and visualize Models: Compare the voxel frequency across multiple multi-sphere models and calculate the distances between the multi-sphere models and the original surface model for 2D/3D visualisation

Use Cases:

• Orthopaedic and biomechanical volume modelling
• Shape approximation of complex structures with multi-sphere models
• Model selection based on voxel-based fit metrics
• Distance-based analysis between patient-specific geometries and approximations

Benefits:

• Mulit-Sphere Model for complex geometries
• Scalable models (voxel-based) – automatically adjusted to target volumes
• Visualization-ready outputs (distance maps)

Keywords:

sphere approximation, clumped spheres, volume intersection, voxel grid, biomechanics, orthopaedics, mesh analysis, distance mapping

Compatibility:

These class is compatible with MATLAB and can be easily integrated into existing workflows to generate multi-sphere models from anatomical models. It is optimised for MATLAB 2024a but should be compatible with the most recent versions of MATLAB.

Disclaimer:

This MATLAB class is provided on the MATLAB File Exchange for educational and research purposes. Users should ensure that the class meets their specific analysis requirements and may need to adapt it accordingly. The code is provided "as-is," and the author assumes no responsibility for its use or any consequences thereof.

References:

• S. Haeri, ‘‘Optimisation of blade type spreaders for powder bed preparation in Additive Manufacturing using DEM simulations,’’ Powder Technology, vol. 321, pp. 94–104, 2017. [Online]. Available: http://dx.doi.org/10.1016/j.powtec.2017.08.011
• S. Haeri, ‘‘sihaeri/DEM-ClumpedSphere,’’ MATLAB Central File Exchange, 2025. [Online]. Available: https://de.mathworks.com/matlabcentral/fileexchange/67754-sihaeri-dem-clumpedsphere