# Degeneration-Driven and Load-Modulated Fluid-Driven Viscoelasticity of the Human Intervertebral Disc: A Probabilistic Biphasic Swelling Modeling Study

## TL;DR

This study explores how disc degeneration and compressive loading affect fluid-driven viscoelastic behavior in human intervertebral discs using a probabilistic model.

## Contribution

The novel contribution is a probabilistic biphasic swelling model that systematically examines load-degeneration interactions in disc viscoelasticity.

## Key findings

- Degeneration reduces osmotic pressure and delays fluid equilibration, increasing creep deformation.
- Loading magnitude modulates viscoelastic deformation and reduces degeneration-related differences over time.
- Probabilistic modeling captures disc geometry variability and fluid-driven behavior within experimental ranges.

## Abstract

Intervertebral disc (IVD) viscoelasticity is governed primarily by fluid transport driven by coupled osmotic and mechanical pressure gradients. Disc degeneration disrupts this balance through glycosaminoglycan loss and reduced cartilage endplate permeability. However, how degeneration interacts with compressive loading to regulate fluid-driven viscoelastic behavior at the whole-disc level remains unclear. To address this gap, a probabilistic biphasic swelling finite element framework was employed to simulate fluid-driven viscoelastic behavior of the IVD. Fifty discs were generated by varying anterior–posterior length, lateral width, nucleus pulposus volume ratio, wedge angle, and disc height. These discs were subjected to swelling, creep, and relaxation protocols under multiple compressive magnitudes for both healthy and degenerated conditions. Time-dependent responses were quantified using rheological models comprising two viscoelastic elements and one elastic element. Predicted intradiscal pressure, disc height, and viscoelastic responses fell within reported experimental ranges. Degeneration primarily governed fluid-dependent behavior. It reduced osmotic pressure, limited fluid mobility, and delayed axial equilibration. These changes decreased swelling displacement, increased creep deformation, and prolonged characteristic time constants, while minimally affecting instantaneous elastic response. In contrast, loading magnitude modulated the extent of viscoelastic deformation and progressively reduced degeneration-related differences in long-term creep displacement and long-term relaxation time constant. Collectively, degeneration governs fluid-dependent viscoelastic mechanisms, whereas loading magnitude modulates their expression. This study systematically examines how degeneration and load magnitude interact to regulate fluid-driven viscoelastic behavior of the IVD. By combining probabilistic geometry with biphasic swelling mechanics, it addresses a critical gap in understanding load–degeneration interactions in disc hydration-dependent mechanics.