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Subject-specific Musculoskeletal Model for Studying Bone Strain During Dynamic Motion

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Published on: April 11, 2018

Inference in dynamic systems using B-splines and quasilinearized ODE penalties.

Gianluca Frasso¹, Jonathan Jaeger², Philippe Lambert^1,3

¹Faculté des Sciences Sociales, Méthodes Quantitatives en Sciences Sociales, Université de Liège, Boulevard du Rectorat 7, B-4000, Liège, Belgium.

Biometrical Journal. Biometrische Zeitschrift

|November 26, 2015

Summary

This study introduces a new smoothing method for analyzing dynamic systems using ordinary differential equations (ODEs). The approach improves estimation accuracy, especially when initial or boundary conditions are unknown.

Keywords:

Nonlinear ordinary differential equations Penalized splines Quasilinearization

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Area of Science:

Applied Mathematics
Computational Science
Data Analysis

Background:

Nonlinear ordinary differential equations (ODEs) are essential for modeling complex dynamic systems.
Accurate parameter estimation is crucial for reliable system analysis.

Purpose of the Study:

To develop a novel smoothing approach for estimating parameters in nonlinear ODE systems.
To enhance accuracy, particularly when initial or boundary conditions are unknown.

Main Methods:

A smoothing approach regularized by a quasilinearized ODE-based penalty.
Utilizing a quasilinearized spline-based framework for estimation.
Reducing the problem to optimizing spline coefficients within a conditionally linear framework.

Main Results:

The proposed method offers more accurate estimates compared to standard nonlinear least squares.
Performance is validated through both simulated and real-world data.
Applicability of standard ODE compliance parameter selection criteria.

Conclusions:

The quasilinearized spline-based smoothing approach provides a robust method for ODE analysis.
This technique is particularly advantageous when state conditions are not precisely known.
The method integrates seamlessly with existing parameter selection criteria.