The design and validation of the musculoskeletal model and controller have been previously published (van der Kruk and Geijtenbeek, 2023a). We employed the H1120 model, featuring 11 degrees of freedom and 20 Hill-type muscles, which was initially developed as an OpenSim3 model and translated into Hyfydy (Figure 1) (van der Kruk and Geijtenbeek, 2023b). Peak isometric forces in this model are based on a lower limb model by (G2392) (Delp et al., 1990). The validation study showed that the simulated joint angles, muscle activation, and joint loading fell within experimental ranges with some limitations. Due to simplified contact geometries of the chair and buttocks, thighs rolling over the chair’s surface is not considered in the simulation which in reality extend the contact period. Ground contact forces for the stance leg’s during the initial step were underestimated due to the simplified foot contact which results in an underestimation of the ankle joint load of the stance leg during this initial step.

Contact forces between the feet and the ground and between the buttocks and the chair were modelled with a Hunt Crossley force spheres and box, respectively. The simulation of the sit-to-walk movement involved the utilization of a standing-up controller (van der Kruk and Geijtenbeek, 2023a) followed by a gait controller (Geyer and Herr, 2010). The standing-up controller operates on a reflex control principle, featuring two distinct states, each with its own set of control parameters. The reflex controller is based on monosynaptic and antagonistic proprioceptive feedback from the muscles and vestibular feedback linked to the pelvis tilt. The timing of the transition between the states is part of the optimization problem. To account for neural latencies, we incorporated data from previous studies.

States calculated from the model were muscle length (L), muscle velocity (v), muscle force (F), and pelvis tilt orientation (θ) and velocity (θ˙). The optimization problem encompassed a total of 551 free parameters, comprising controller gains (KC, KL+, KF±, Kp, and Kv), muscle length feedback offsets (lo), proportional feedback of θ (θo), proportional feedback of the lumbar and thoracic joints, transition times between the controllers, and stance load threshold for the gait state controller.

We used the objective measures from the published sit-to-walk controller (van der Kruk and Geijtenbeek, 2023a). These measures encompassed the following criteria: a gait velocity measure with a minimum threshold of 0.8 m/s, range penalties designed to replicate joint limitations, including lumbar extension (−50°–0°), thorax extension (−15°–15°), pelvis tilt (−50°–30°), and ankle angle (−60°–60°), a constraint on knee limit force (500 N/m) that represents the passive knee properties when the knee exceeds the range of 120° flexion or 10° extension, and minimal head acceleration (threshold of 1 m/s^2). The selected speed was considered the minimum required speed to have a gait pattern that represents gait inside the lab and clinic. In daily life, normal gait speeds for older adults typically range around 0.9 m/s for women and 1.0 m/s for men (Kasović et al., 2021). As such, a speed of 0.8 m/s was considered a realistic minimum for measurements conducted in clinical environments.

Additionally, we included an energy estimate aimed at reducing energy consumption during the stand-up phase and minimizing the cost of transport during gait. The measure consisted of metabolic energy expenditure based on (Wang et al., 2012; Bhargava et al., 2004) ( J m b ), and was complemented by the minimization of cubed muscle activations ( J a c t ), along with torque minimization ( J T ) at the lumbar and thoracic joints to serve as a proxy for the absence of trunk muscles. J m b is a sum of the muscle activation rate ( A ˙ ), the muscle maintenance heat rate ( M ˙ ), the muscle shortening heat rate ( S ˙ ), and the positive mechanical work rate ( W ˙ ). A ˙ and M ˙ depend on the muscle mass, which was estimated by dividing the maximum isometric force over the muscle specific tension (25 N/cm²) multiplied the muscle density (1.0597 g/cm³) and optimal fiber length. Hence, when weakening the VAS muscle in the muscle weakness condition, we reduced the mass accordingly. During the optimization process, the overall energy estimate, a weighted sum between the terms ( J t o t a l = ω m b J m b + ω a c t J a c t + ω T J T ) became the sole non-zero term within the objective function. We empirically set ω m b = 0.01 , ω a c t = 0.1 and ω T = 0.0003 for all conditions.

The optimization process was conducted using the open source software SCONE with the Covariance Matrix Adaptation Evolutionary Strategy (CMA-ES) (Geijtenbeek, 2019). Simulations were performed using the Hyfydy simulation engine (Geijtenbeek, 2024). The population size of each generation was 10, and the number of iterations varied depending on the simulation duration. Multiple parallel optimizations were executed with the same initial guesses based on (van der Kruk and Geijtenbeek, 2023a), and the best set was subsequently employed as the starting point for the next set of optimizations, meaning the initial guesses for each condition were based on solution of the previous condition (−30% strength on −20% strength, etc.).

We analysed the trunk flexion, calculated as the angle between the global vertical and the trunk (sum of pelvis tilt, lumbar extension, and thoracic extension). Additionally, we assessed differences in timing, muscle activation, joint loading, and kinematics. The outcomes under various conditions were visualized using the OpenSim software (Delp et al., 2007).

Reducing the maximum isometric strength VAS led to an increased bilateral activation of the Vasti muscle (Figure 2). The simulation compensates with increased hip extensor activity (HAM, GMAX) and increased plantarflexor muscle activity (GAS, SOL) in the stepping leg. This aligns with findings from experimental studies on sit-to-stand movements in older adults (Smith et al., 2020).

We found a bilateral rise increase of ankle joint loading, particularly on the stepping side which doubled in the −50% condition compared to the neutral condition. Reduced VAS muscle strength thus resulted in elevated ankle loads. When VAS strength was further reduced to −60%, the model could not find a solution to rise from the seat unaided.

A minor increase in trunk flexion was observed when VAS strength was reduced (Figure 3). Trunk flexion at seat-off reached 42.8° in the −50% condition versus 38.3° in the −20% condition (40.8° in the neutral condition). The timing of the movement (Figure 3C) showed no noticeable pattern with reduced muscle strength. We hypothesize that in the −20% and 30% condition, there remains sufficient physiological reserve to allow for variations in gait velocity. Consequently, standing up can be slower, as gait velocity can compensate to achieve the desired average speed. Evidently, this compensatory strategy appears to be more efficient in terms of our cost assessment. However, as the strength reduction is further decreased to 40% and 50%, patterns of reduced movement velocity begin to emerge.

In the neutral condition, the peak knee loads (stance leg: 6.8 BW, stepping leg: 5.6 BW) and hip loads (stance leg: 3.6 BW, stepping leg: 3.4 BW) manifest just after seat-off. The peak ankle load in the stepping leg occurs during the rising phase (stepping leg: 1.3 BW), and for stance leg, it arises at the end of the single stance phase (stance leg: 2.4 BW), consistent with experimental data (van der Kruk and Geijtenbeek, 2023a). Unloading of the knee is accomplished by reducing ipsilateral activation of VAS and hamstrings (HAM) (Figure 4). Following Toe-off, there is an increased ipsilateral activation of the tibialis anterior muscle (TA), resulting in increased dorsiflexion, which compensates for reduced foot-ground clearance. Unloading the knee (ranging from −29% to −59%) led to reduced load on the ipsilateral hip (ranging from −23% to −39%) and ankle (ranging from −37% to −40%). However, the ipsilateral ankle did not exhibit proportional unloading, unlike the other joints. Loading on the contralateral knee and hip increased, ranging from +5% to +11% and 0% to +5%, respectively. As for the contralateral ankle, there was a load decrease in the <4BW condition (−4%) and an increase in the other conditions (14% and 29%).

Interestingly, during knee unloading, the simulation yielded a smaller, rather than a greater, trunk angle at seat-off compared to the neutral condition (Figure 4). There was an increase in movement time observed with increased knee unloading (from initiation to heel strike of the first step: 1.1s in the neutral condition up to 1.3s in the <2x BW knee load condition) (Figure 3D).