Update paper.md

paper.md

@@ -80,9 +80,9 @@ For walking and running, we include a periodicity constraint to the full gait cy
 
 $$ \mathbf{x}(T) = \mathbf{x}(0) + v T \mathbf{x}_{hor} \quad \text{(periodicity)} $$
 
-So far, we have created the problem class "Collocation", which creates a trajectory optimization problem using 
+So far, we have created the problem class 'Collocation', which creates a trajectory optimization problem using 
 direct collocation [@betts:2010]. In direct collocation, the numerical integration of the differential equations that represent 
-the dynamics are solved as equality constraints during the optimization. To do so, collocation nodes, or time nodes 
+the dynamics are solved as equality constraints during the optimization. To do so, collocation nodes, or time nodes, 
 need to be predefined, and the integration method should be selected. We have currently implemented a backward Euler and
 a midpoint Euler integration method. Backward Euler has shown to be most stable and has been used for publications. A 
 direct collocation approach creates a large-scale nonlinear optimization problem, for which the derivatives of the 
@@ -100,15 +100,15 @@ $$ \mathbf{x}(N+1) = \mathbf{x}(0) + v T \mathbf{x}_{hor} \quad \text{(periodici
 
 for $N$ collocation points $i$.
 
-Problems can be solved using the solvers that are implemented in the class "solver". So far, we have implemented IPOPT [@Wachter:2006] to solve the resulting optimization problem. This algorithm can solve optimal control problems transcribed with direct collocation in less than 10 minutes for a 2D model [@koelewijn:2016; @koelewijn:2022] and less than one hour for a 3D model [@nitschke:2020]. Different solvers could easily be integrated into this solver class.
+Problems can be solved using the solvers that are implemented in the class 'solver'. So far, we have implemented IPOPT [@Wachter:2006] to solve the resulting optimization problem. This algorithm can solve optimal control problems transcribed with direct collocation in less than 10 minutes for a 2D model [@koelewijn:2016; @koelewijn:2022] and less than one hour for a 3D model [@nitschke:2020]. Different solvers could easily be integrated into this solver class.
 
-As most analysis is specific to the problem type, most code for analysis can be found in the respective problem class. For example, metabolic cost requires an integration over time, which is dependent on the problem type that is being used. In addition, general methods, e.g., to calculate a correlation or root mean squared error between two variables, or to write results into an OpenSim file format, can be found in the function "HelperFunctions folder". 
+As most analysis is specific to the problem type, most code for analysis can be found in the respective problem class. For example, metabolic cost requires an integration over time, which is dependent on the problem type that is being used. In addition, general methods, e.g., to calculate a correlation or root mean squared error between two variables, or to write results into an OpenSim file format, can be found in the function 'HelperFunctions' folder. 
 
 We have implemented different human dynamics models. All implemented models are musculoskeletal models, but they can 
 also be used as skeletal models, such that the input is generated using joint moments instead of muscle stimulations. 
-We have implemented a 3D model version (gait3d) and two 2D model versions in c, which are compiled as mex functions. The model dynamics can be tested using the test cases coded in the "tests" folder. The 3D model and one 2D model (gait2d_osim) are loaded from OpenSim, but use our own muscle dynamics model, which is described in [@nitschke:2020],
+We have implemented a 3D model version (gait3d) and two 2D model versions in c, which are compiled as mex functions. The model dynamics can be tested using the test cases coded in the 'tests' folder. The 3D model and one 2D model (gait2d_osim) are loaded from OpenSim, but use our own muscle dynamics model, which is described in [@nitschke:2020],
 while the other (gait2dc) is used in our own previous work [@koelewijn:2016; @koelewijn:2022; @dorscky:2019a; @dorschky:2019b].
-The model parameters are defined in the .osim file for the OpenSim models, and defined in an Excel file for model gait2dc (gait2dc_par.xlsx). The models can be personalized by directly adjusting the parameters in the .osim model or Excel file, such that, for example, OpenSim scaling can be used [@seth:2011]. They can also still be adjusted in MATLAB, for example to investigate virtual participants [@dorscky:2019a][@koelewijn:2022]. The model dynamics are explained further for gait2dc [@koelewijn:2022; @dorscky:2019a; @dorschky:2019b], for gait3d [@nitschke:2020]. The gait2d_osim model has not yet been used in publications. It is based on the gait10dof18musc.osim model, and can be loaded in two ways: the original version, called gait10dof18musc, and a version with the lumbar joint locked, called gait2d_osim.
+The model parameters are defined in the .osim file for the OpenSim models, and defined in an Excel file for model gait2dc (gait2dc_par.xlsx). The models can be personalized by directly adjusting the parameters in the .osim model or Excel file, such that, for example, OpenSim scaling can be used [@seth:2011]. They can also still be adjusted in MATLAB, for example to investigate virtual participants [@dorscky:2019a; @koelewijn:2022]. The model dynamics are explained further for gait2dc [@koelewijn:2022; @dorscky:2019a; @dorschky:2019b], for gait3d [@nitschke:2020]. The gait2d_osim model has not yet been used in publications. It is based on the gait10dof18musc.osim model, and can be loaded in two ways: the original version, called gait10dof18musc, and a version with the lumbar joint locked, called gait2d_osim.
 
 We have included several examples in the folder 'ExampleScripts' to highlight the applications of the model and help 
 future users get started with the code. We have added two introduction examples, one for 2D simulations (script2D.m) and one for 
@@ -118,14 +118,14 @@ of the 'gait2d_osim' model, combined with an implementation of a treadmill. Base
 publications, we have added three additional applications. The code in the folder 'IMU2D' shows how simulations can be 
 created that reconstruct inertial sensor movement, and is based on the publications by @dorscky:2019a and @dorschkynitschke:2024.
 The code in the folder 'ExoPaper' shows how simulations can be used to make predictions, in this 
-case of walking with an exoskeleton, based on the paper by @koelewijn:2022. The code in MarkerTracking3D is an 
+case of walking with an exoskeleton, based on the paper by @koelewijn:2022. The code in 'MarkerTracking3D' is an 
 example of how simulations can be created by tracking marker and ground reaction force data, based on the publication by 
 @nitschke:2024.
 
 Currently, the toolbox can be used to solve trajectory optimization problems to solve predictive and reconstructive simulations. We have implemented code to track marker positions, joint angles, translations, ground reaction forces, accelerations, angular velocities, movement duration, and movement speed. We have further implemented objectives to minimize muscular effort, metabolic cost, squared torque, joint accelerations, passive joint moments, ground reaction force impact, and head stability. By combining these different objectives, many different types of simulations can be generated and the movement kinematics and kinetics investigated.
 
 In future, the toolbox can be expanded. New problem classes can be defined, for example for inverse 
-kinematics and inverse dynamics, or to solve muscle activations and stimulations statically or dynamically. Furthermore, a single shooting approach can be implemented, which would allow for models with discontinuous dynamics or control to be investigated, such as a reflex model [@geyer:2010]. 
+kinematics and inverse dynamics, or to solve muscle activations and stimulations statically or dynamically. Furthermore, a single shooting approach can be implemented, which would allow for models with discontinuous dynamics or control to be investigated, such as a reflex model [@Geyer:2010]. 
 
 # Acknowledgements