/*
 * Effects of Neuromuscular Strength Training on Vertical Jumping
 * Performance - A Computer Simulation Study
 * 
 * Model Status
 * 
 * This CellML model runs in OpenCell and COR to recreate the published
 * results. The units have been checked and they are consistent.
 * 
 * Model Structure
 * 
 * ABSTRACT: The purpose of this study was twofold: (a) to systematically
 * investigate the effect of altering specific neuromuscular parameters
 * on maximum vertical jump height, and (b) to systematically investigate
 * the effect of strengthening specific muscle groups on maximum
 * vertical jump height. A two-dimensional musculoskeletal model
 * which consisted of four rigid segments, three joints, and six
 * Hill-type muscle models, representing the six major muscles
 * and muscle groups in the lower extremity that contribute to
 * jumping performance, was trained systematically. Maximum isometric
 * muscle force, maximum muscle shortening velocity, and maximum
 * muscle activation, which were manipulated to simulate the effects
 * of strength training, all had substantial effects on jumping
 * performance. Part of the increase in jumping performance could
 * be explained solely by the interaction between the three neuromuscular
 * parameters. It appeared that the most effective way to improve
 * jumping performance was to train the knee extensors among all
 * lower extremity muscles. For the model to fully benefit from
 * any training effects of the neuromuscular system, it was necessary
 * to continue to reoptimize the muscle coordination, in particular
 * after the strength training sessions that focused on increasing
 * maximum isometric muscle force.
 * 
 * The original paper is cited below:
 * 
 * Effects of Neuromuscular Strength Training on Vertical Jumping
 * Performance - A Computer Simulation Study, Akinori Nagano and
 * Karin G.M. Gerritsen, 2001, Journal of Applied Biomechanics,
 * 17, 113-128. (there is no PubMed ID for this article).
 * 
 * [[Image file: nagano_2001.png]]
 * 
 * A two-component of skeletal muscle with the contractile element
 * defined by Hill equations for concentric contraction.
 */

import nsrunit;
unit conversion on;
unit per_newton_second=1 kilogram^(-1)*meter^(-1)*second^1;
unit metre_per_second=1 meter^1*second^(-1);
unit metre2=1 meter^2;
unit per_second=1 second^(-1);
unit newton_per_metre=1 kilogram^1*second^(-2);
unit newton_metre2=1 kilogram^1*meter^3*second^(-2);

math main {
	realDomain time second;
	time.min=0;
	extern time.max;
	extern time.delta;
	real F_isom(time) newton;
	real c newton;
	real L_ce(time) metre;
	when(time=time.min) L_ce=0.05;
	real L_ce_opt metre;
	L_ce_opt=0.055;
	real L(time) metre;
	real width metre;
	width=0.888;
	real Factor per_second;
	Factor=1;
	real A_REL newton;
	A_REL=0.41;
	real B_REL dimensionless;
	B_REL=5.2;
	real v_ce(time) metre_per_second;
	real F(time) newton;
	real F_max newton;
	F_max=3277.4;
	real q dimensionless;
	q=1;
	real c1(time) per_second;
	real c2(time) newton;
	real c3(time) per_newton_second;
	real slope newton;
	slope=2;
	real F_asympt dimensionless;
	F_asympt=1.5;
	real L_see(time) metre;
	real L_slack metre;
	L_slack=0.42;
	real alpha newton_per_metre;
	alpha=1449.027;

	// <component name="environment">

	// <component name="contraction">
	F_isom=(c*(L_ce/L_ce_opt)^2-2*c*L_ce/L_ce_opt+c+(1 newton));
	v_ce=((-1)*Factor*L_ce*((F_isom+A_REL)*B_REL/((1 newton)*(F/(F_max*q))+A_REL)-B_REL));
	L_see=(L-L_ce);
	c=((-1)*(1 newton_metre2)/width^2);
	c2=(F_isom*F_asympt);
	c1=(Factor*B_REL*(F_isom+c2)^2/((F_isom+A_REL)*slope));
	c3=(c1/(F_isom+c2));
	L=(if (time<=(1 second)) (1 metre) else if ((time>(1 second)) and (time<(5 second))) (.92 metre) else (.9 metre));
	L_ce:time=v_ce;
	F=(alpha*(L_see-L_slack));
}