Fig 1.
Flowchart describing the general method to simulate disc adaptation.
To the generic IVD model a general daily loading pattern was applied, mimicking a loading cycle of a healthy generic person. Based on this loading pattern, per integration point (IP) a deviatoric shear strain and fluid velocity was obtained. These serve as input for the mechanoregulation algorithm and based on this algorithm, per IP, a preferred tissue phenotype is determined. The ECM content is adapted to this preferred phenotype with a fixed time step. After this adaptation step, the deviatoric shear strain and fluid velocity are re-determined and the whole cycle is repeated until no changes in ECM content were simulated.
Table 1.
Biochemical input parameters, for the IVD model [22]. The biochemical parameters are only used during the initial simulation of the disc adaptation. Thereafter, the mechanical stimulus determines per integration point what the content is.
Table 2.
Proliferation differentiation and apoptosis rate of fibroblast and chondrocytes chondrocytes were previously calculated in normalized fashion from experimental data collected in an extensive literature review [37].
Table 3.
Production and degradation rates of matrix components by fibroblast and chondrocytes [40,41,42,43].
The represents the preferred matrix content of the fibroblast;
represents the preferred matrix content of chondrocytes.
Fig 2.
Patient-specific disc adaptation implementation.
To make predictions for a patient, first a patient-specific model is generated, including the patient specific composition, geometry and changes in loading conditions. These properties are transferred to the standard model using a mapping procedure. With this procedure, changes in any of the parameters are translated to equivalent changes in parameters used for the standard model. The results of the adaptation simulation are mapped back to the patient model.
Fig 3.
Patient-specific bone adaptation implementation.
From CT scan of a patient, bone density and the geometry are obtained. From the full lumbar model patent-specific boundary conditions and changes in these boundary conditions due to fusion are obtained. The patient-specific FE model is used to determine the organ level load distribution. Using the bone remodelling theory, this is translated to a change in the density distribution.
Table 4.
The bone remodelling parameters as defined in the theory of Colloca et al. [28]. The bone formation rate τ, osteocyte mechanosensitivity μ and resorption volume per cavity vres were fitted, marked with ** see below, other parameters based on Colloca et al. [28].
Fig 4.
An example of a lumbar FE model. The model contains vertebrae, discs and ligaments form L1 till S1.
Fig 5.
Coupling bone and disc adaptation simulation.
In the coupled model, the bone remodelling and the disc adaptation algorithms are combined to represent the bone remodelling and disc adaptation due to intervention. Starting with the bone remodelling, a new density distribution is calculated that is mapped to the disc adaptation model. Changes in disc composition are calculated and are subsequently mapped back to the patient-specific model. Each module is explained in detail above.
Fig 6.
Overview of generating the models for the patient study.
From the lumbar model the two vertebrae neighbouring the degenerated disc and the neighbouring disc are extracted as the ‘patient-specific’ model. Also the boundary conditions representing the pre-operative loading are extracted from the lumbar model. Following, the fusion surgery was simulated and new boundary conditions were calculated. For these new boundary conditions, changes in the disc and the vertebrae neighbouring the operated region were calculated.
Fig 7.
Extra cellular matrix content of a healthy disc.
Cross-sections of a steady state disc with (a) collagen (b) GAG and (c) water (relative amount of content). In the centre of the disc, a region with low collagen (blue) and high GAG (red) and water content is found, similar to cartilage tissue, i.e. NP. Towards the outer shape of the disc, regions with high collagen and low GAG and water content are observed, i.e. AF tissue. In between these regions, a mixture of both tissues is observed, indicating the transition zone between both tissues. The black lines indicate the borders between the original geometrically defined NP and AF region.
Fig 8.
Examples of predicted vs clinical bone changes.
Examples of graphical representation of bone density (BV/TV) as predicted 2 years post-surgery (b, e and h) and measured at the same time point (c, f and i), compared to pre surgery (a, d and g). a, b and c correspond to patient #1, d, e and f to patient #7, g, h and i to patient #10. A black colour indicates a density of 0. Note that the dark-blue appearance at the cortical shell is because the mesh boundaries were taken slightly larger than the vertebral size. As a result, the outer layer of elements can have a very low density.
Table 5.
Correlation between predicted bone density (BV/TV) vs clinical FU bone density. Case #10 was used to fit the remodelling parameters, resulting in a very high correlation.
Fig 9.
Typical extra cellular matrix changes.
a) Start collagen content and predicted collagen content 2 years after fusion (b). c) and d) Change in GAG content for 2 year simulation due to fusion. e) and f) Changes in water content in the disc for 2 year simulation. For visualization purposes, only the disc is shown. Predicted changes are for case #9 and serve as example of the outcome for the other 9 cases.
Fig 10.
Pt-specific results up to 10y post-operative of case #4, visualised on the pt geometry.
Tissue changes in both bone and disc changes simulated up till 10 years post-operative in a combined view. For disc tissue, the ECM components are visualized: collagen, GAG and water content (relative amount). Water content is visualized in black and white, mimicking the water content as could be observed on MRI data. Next to these ECM changes, also bone changes are visualized for the 4 different time points. After 2 years, the clinical FU-data is visualized to show a graphical comparison. Bone density values vary between 0 and 1, relative collagen content between 0.65 and 0.15, GAG between 0.85 and 0.35, water content between 0.81 and 0.75 respectively.
Fig 11.
Pt-specific results up to 10y post-operative of case #6, visualised on the pt geometry.
Tissue changes in both bone and disc changes simulated up till 10 years post-operative in a combined view. For disc tissue, the ECM components are visualized: collagen, GAG and water content (relative amount). Water content is visualized in black and white, mimicking the water content as could be observed on MRI data. Next to these ECM changes, also bone changes are visualized for the 4 different time points. After 2 years, the clinical FU-data is visualized to show a graphical comparison. Bone density values vary between 0 and 1, relative collagen content between 0.65 and 0.15, GAG between 0.85 and 0.35, water content between 0.81 and 0.75 respectively.
Fig 12.
Pt-specific results up to 10y post-operative of case #9, visualised on the pt geometry.
Tissue changes in both bone and disc changes simulated up till 10 years post-operative in a combined view. For disc tissue, the ECM components are visualized: collagen, GAG and water content (relative amount). Water content is visualized in black and white, mimicking the water content as could be observed on MRI data. Next to these ECM changes, also bone changes are visualized for the 4 different time points. After 2 years, the clinical FU-data is visualized to show a graphical comparison. Bone density values vary between 0 and 1, relative collagen content between 0.65 and 0.15, GAG between 0.85 and 0.35, water content between 0.81 and 0.75 respectively.