A hybrid statistical morphometry free-form deformation approach to 3D personalized foot-ankle models

The foot contains 26 bones, which are interconnected by 33 joints, and supported by a network of more than 100 muscles, tendons, and ligaments. Personalized biomechanical models of the foot may assist in understanding form function relationships (Xiang et al., 2023) through techniques such as finite element (FE) analysis (Xiang et al., 2022). Foot geometric characteristics are typically obtained from medical images, considered the gold standard, primarily computed tomography (CT) and magnetic resonance imaging (MRI). Foot surface scanning is less expensive and time-saving, and it can also be used conveniently outside the gait laboratory and hospital (Telfer and Woodburn, 2010). It has been widely used in gait labs and footwear manufacturing. However, data from foot scanning is limited to foot surfaces and neglects the inner anatomical structure.

Statistical shape modeling (SSM) is a statistical method in bioengineering and biomechanics for anatomical shape reconstruction based on methodologies incorporating point coordinate registration, shape morphing and fitting, and dimensionality reduction (Saxby et al., 2020, Zhang et al., 2016). SSM can capture a spectrum of expected, evidence-based variations within a population, allowing for the anatomical scaling of a model to an individual subject based on a limited set of data points.

A common approach for lower limb biomechanical analysis is to scale and build a musculoskeletal model from a generic one (Bahl et al., 2019). However, the results may not be accurate enough due to personal variations. In recent years, there has been a surge of interest in the biomechanical field for SSM-based person-specific musculoskeletal models (Modenese and Renault, 2021, Saxby et al., 2020). SSM has been used on the foot, including the foot surface (Boppana and Anderson, 2021, Kobayashi et al., 2018, Schuster et al., 2021, Stanković et al., 2020) and internal bones (Grant et al., 2020), but not all together. It aids in understanding foot shape disparities across populations and allows for foot model reconstruction using sparse anatomical data. Free-form deformation (FFD) is a geometric morphing technique used to deform rigid objects by deforming the lattice grids that enclose the object and then transforming the object within the hull. Based on the FFD technique, the host-mesh fitting variant is used to customize geometric transformations, including Euclidean and Affine operations (Fernandez et al., 2004).

Personalizing a foot and ankle joint model is highly time-consuming in terms of medical image collection and data processing. Grant et al. (2020) developed SSM from MRI data for reconstructing foot bones and showed promising results. The 3D optical foot scan technique has been shown to be reliable for analyzing 3D foot shape deviations and deformation (Schuster et al., 2021). However, generating inter-bony relationships is still quite challenging in the field. A comprehensive foot model generally requires foot tissue and bone geometric information from the CT or MRI scan to be fed into SSM.

To the best of our knowledge, no existing approach in the literature has achieved the generation of a complete foot model (encompassing both the skin surface and all underlying bones) solely from surface-based foot scans. In this novel framework, the integration of SSM with FFD enables the precise alignment of internal bone structures to personalized external foot geometries, leveraging only skin measurements for the SSM. This approach allows for detailed surface modeling through SSM and adaptable internal bone reconstruction through FFD, ensuring a harmonized and individualized representation of the foot's surface and its skeletal architecture. Consequently, this study aims to develop and evaluate a framework for reconstructing comprehensive 3D foot–ankle models, including internal bones, based solely on SSM derived from skin measurements.

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