Geometry Dash Optimizer

[Fidel Genereux]

Touse this feature, create a text file to specify the constraint and pass it to geometric-optimize after the input file.As noted in Options, this file may also contain other command line options and arguments before the constraint specifications.

For $scan, starting and ending values plus a whole number (# of steps) must follow the atom selection.These jobs are also called potential energy scanning or coordinate driving.In order to scan the dihedral angle from 0 degrees to 180 degrees in 15 degree increments:

dihedral : The dihedral angle defined by four atoms A-B-C-D is constrained.Provide four numbers for the atomic indices of A, B, and C, and D in that order.Values provided to $set and $scan are in degrees.

Values provided to $set or $scan are in Angstrom. The number of values required depends on how many dimensions are constrained:for example, to use xz or trans-xz two numbers are required for $set and five numbers are required for $scan for the initial value, final value and number of steps.

To use $set, provide four total numbers: three numbers for the rotation axis, which is automatically normalized,plus a single number for the rotation angle (in degrees) to indicate that the final structure shouldbe rotated by this amount from the initial angle along the provided axis.

To use $scan, provide six total numbers: three numbers for the rotation axis, which is automatically normalized,then three numbers for the initial and final values of the rotation angle (in degrees) and the number of steps.

centroid_distance : The distance between centroids of two molecules or fragments is constrained.Two atom selections should be used to define the fragments, using the comma and dash syntax.Values provided to $set and $scan are in Angstrom.

In the default constrained optimization algorithm, the constrained degrees of freedom converge to their target values rather slowly if the starting and target values are not the same.This behavior can be adjusted using the --enforce command line option.By passing a parameter such as --enforce 0.1 (for example), the optimizer will switch to an algorithm that exactly enforces constraint satisfaction once the current values are within 0.1 of the target.The units are in bohr/radians, so exact constraint enforcement is turned on when bond length constraints are within 0.1 bohr (about 0.529 Angstrom) and angle/dihedral constraints are within 0.1 rad (about 6.28 degrees) of the target values.

GeomeTRIC supports rigid-body optimizations in which the intermolecular positions and orientations of rigid molecules or fragments are optimized.Together with the centroid distance constraint, this may be used for calculating interaction energy curves of molecular dimers while excluding the effects of intramolecular deformations.

To enable this feature, use the command line option --rigid yes. When this option is turned on, molecular net forces and torques will be used instead of atomistic gradients for the convergence criteria.The net force and torque vectors for each molecule are concatenated into an array, then the RMS and maximum norms are computed (the unit of torque is Hartree/bohr * bohr).

It is highly recommended that the revised constraint algorithm is also activated by passing --conmethod 1, as this may improve convergence for structures in the repulsive region of the interaction energy curve.

Musculoskeletal geometry and muscle volumes vary widely in the population and are intricately linked to the performance of tasks ranging from walking and running to jumping and sprinting. As an alternative to experimental approaches, where it is difficult to isolate factors and establish causal relationships, simulations can be used to independently vary musculoskeletal geometry and muscle volumes, and develop a fundamental understanding. However, our ability to understand how these parameters affect task performance has been limited due to the high computational cost of modelling the necessary complexity of the musculoskeletal system and solving the requisite multi-dimensional optimization problem. For example, sprinting and running are fundamental to many forms of sport, but past research on the relationships between musculoskeletal geometry, muscle volumes, and running performance has been limited to observational studies, which have not established cause-effect relationships, and simulation studies with simplified representations of musculoskeletal geometry. In this study, we developed a novel musculoskeletal simulator that is differentiable with respect to musculoskeletal geometry and muscle volumes. This simulator enabled us to find the optimal body segment dimensions and optimal distribution of added muscle volume for sprinting and marathon running. Our simulation results replicate experimental observations, such as increased muscle mass in sprinters, as well as a mass in the lower end of the healthy BMI range and a higher leg-length-to-height ratio in marathon runners. The simulations also reveal new relationships, for example showing that hip musculature is vital to both sprinting and marathon running. We found hip flexor and extensor moment arms were maximized to optimize sprint and marathon running performance, and hip muscles the main target when we simulated strength training for sprinters. Our simulation results provide insight to inspire future studies to examine optimal strength training. Our simulator can be extended to other athletic tasks, such as jumping, or to non-athletic applications, such as designing interventions to improve mobility in older adults or individuals with movement disorders.

Our study addresses the challenge of determining optimal musculoskeletal parameters for tasks like sprinting and marathon running. Existing research has been limited to observational studies and simplified simulations. To overcome these limitations, we developed a differentiable musculoskeletal simulator to optimize running performance. We replicated past findings and uncovered new insights. We confirmed the benefits of increased muscle mass for sprinters and identified key factors for marathon runners, such a mass in the lower end of the healthy BMI range and an increased leg-length-to-height ratio. Hip musculature was found to be critical for both sprinting and marathon running. Our simulation results have practical implications. They can inform customized strength training for sprinters and marathon runners. Additionally, the simulator can be extended to other athletic tasks, benefiting various sporting events. Beyond athletics, our open-source simulator has broader applications. It can determine minimal strength requirements for daily activities, guide strength training in the elderly, and estimate the effects of simulated musculoskeletal surgery.

Copyright: 2024 Van Wouwe et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Funding: TVW was supported to perform this work by the Joe and Clara Wu Tsai Foundation through the Wu Tsai Human Performance Alliance. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

The 100m dash is arguably the most prestigious event in track-and-field [12,13], and marathon running serves as a frontier of human endurance [14,15]. Success in these two events has been associated with different skeletal and muscular features, largely through observational studies. For example, Sedeaud et al. [1] found that mean height, mean body mass index (BMI), and variability in BMI decreased with increasing distance of the event in which male runners specialized. Size, proportions, and other aspects of musculoskeletal geometry have also been associated with an advantage in sports such as speed skating and swimming [2], and cycling [3].

Compared to the general population, distance runners are shorter, have lower BMIs [20,24] and have a greater tibia-to-femur length ratio [25,26]. In trained distance runners, a greater relative tibia-to-femur length ratio is also associated with better running performance [26], as is a greater relative lower limb length [25,27]. Distance runners, compared to sprinters, have lower maximal isometric knee flexor and extensor torques, in absolute terms and when normalized by body weight [28].

While the observational studies described above reveal associations between performance and musculoskeletal features, they are limited in their ability to identify cause-effect relationships. To overcome this, Deane et al. [29] conducted an interventional experiment, which revealed that hip flexor training significantly improves 40-yd dash times. However, such interventional studies are rare, costly, and difficult to control (e.g., hip flexor training might increase strength of additional muscle groups).

In this study, we developed a three-dimensional musculoskeletal simulator that is fully differentiable with respect to both body-segment dimensions and muscle properties to analyze the effects of body-segment dimensions, muscle volume, and distribution of muscle volume on sprinting and marathon running performance. We sought to determine how body-segment dimensions affect maximal sprinting speed and the metabolic cost of running a marathon at moderate speed. We also simulated how optimized, targeted strength training improves sprinting and marathon running performance. Understanding the influence of body segment dimensions and muscle volume distribution on performance can inform the selection of sports in which to compete and personalize training to help maximize performance. Our simulator is open source and enables researchers to conduct additional studies investigating the relationships between musculoskeletal parameters and increased performance, as in sport, or reduced performance, as can result from injuries, diseases, and disorders.

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