# Reducing the Complexity of Musculoskeletal Models Using Gaussian Process Emulators
## 2 Materials and Methods
### Mechanistic Modelling  
#### 2.1.1 Input Data and Baseline Musculoskeletal Models  
This study used legacy data collected from post-menopausal women (UK EPSRC Multisim Study approved by the Health Research Authority of East of England and Cambridgeshire and Hertfordshire Research Ethics Committee, reference 16/EE/0049) [23; 32]. We selected a representative participant (74.6 y, 56.8 kg, 163.5 cm, BMI = 21.2) for whom 3D gait analysis data (marker trajectories and ground reaction forces) and MRI were available (full details of experimental data are described in [23]. Two different baseline monolateral MSKMs were built, one scaled-generic and one subject-specific. Each model included four body segments (pelvis, femur, tibia, foot) articulated by an ideal ball-and-socket joint for the hip, and two ideal hinges: one for the knee and one for the ankle and 43 lower-limb muscles. However, they differed for how the joint axes were defined and for the values of F\({}_{\text{max}}\) assigned to the individual muscles. The details of the two models are as follows:  
* Scaled-generic model (SGM). Marker-based scaling of a literature model (Gait2392, [1]) allowed to obtain a scaled generic model of the participant's limb. Scaling was  
Figure 1: Workflow of the study. From top left clockwise, (**A1**) literature Gait2392 model is scaled in OpenSim using a static standing trial to obtain a scaled-generic model (SGM) while (**A2**) MRI segmentation is used to generate a subject-specific model; (**B**) literature F\({}_{\text{max}}\) values from 29 lower-limb muscles are used to estimate distributions of F\({}_{\text{max}}\) across a virtual population (\(n=200\)); (**C**) joint contact forces (JCF) are estimated for hip, knee and ankle and input to the Gaussian Process emulator (GP) together with associated F\({}_{\text{max}}\) values for training and validation; (**D**) JCF waveforms are emulated (\(n=30\) K) to conduct (**E**) a [PERSON]’s sensitivity analysis, whose results are then used to inform model reduction strategy; (**F**) [PERSON]’s correlation between JCF and F\({}_{\text{max}}\) of most influential muscles is assessed; (**G**) the reduced model is compared, through RMSD and absolute maximum difference, to the nominal, fully personalised model.  
performed according to best practice recommendation [33] using a static standing trial and the OpenSim Scaling Tool [34]. Muscle F\({}_{\text{max}}\) was linearly scaled [34] from Gait2392 default values based on participant's body mass.
* Subject-specific model (SSM). MRI segmentation enabled the generation of a subject-specific model with personalised bone geometries and segment inertia [7] and joint axes determined via morphological fitting to the articular surface of the segmented bone geometries. The same set of muscles included in SGM was included in SSM but their origin, insertion and via points were personalised based on the MRI. In SSM, muscle length parameters were linearly scaled from Gait2392 values in order to maintain their ratio to musculotendon length. F\({}_{\text{max}}\) of 29 lower-limb muscles was personalised using MRI-segmented muscle volume available from the online free repository associated with a study by [PERSON] and colleagues [23], comprising of eleven older women (including the participant used in this study) enrolled as part of the above-mentioned Multisim project [35]. F\({}_{\text{max}}\) of the remaining 14 muscles (not available in the above-mentioned repository as deemed as not-repeatably measurable) were linearly scaled from Gait2392 values based on body mass of the participant.