Table 2.

Summary of studies reporting on computational techniques to determine muscle forces during strength training of the lower extremities in vivo. Dynamic squat jump was mainly analysed using forward dynamic (FD) simulation, while low-speed ankle, hip, and knee exercises were analysed using quasi-static inverse dynamics (ID) optimisation, electromyography-driven (EMG) modelling, or mixed inverse dynamics/forward dynamics analysis. Different approaches were adopted to distribute the net joint moments from ID across muscles, ranging from simple 1-muscle models to advanced optimization schemes taking muscle force-length-velocity (F-l-v) into account. Data from EMG, optical motion capture (OMC), and ground reaction forces (GRF) were used as input or reference to assess the accuracy of modelling results.

	Exercise	Modelling approach	Subjects	Experi. measure	Reported results	Reference
Low-speed	Foot plantar/dorsi flexion	ID (1-muscle model)	8 M, 8 F (22 y)	EMG, OMC, GRF	Muscle force	Henriksen et al. (2009) [7]
	Deep knee bends	ID (1-muscle model)	3 M (26 y)	OMC, GRF	Muscle and joint forces	Reilly and Martens (1972) [27]
	Squat, leg press, knee extension	ID (F-EMG)	10 M (30 y) experienced	EMG, OMC, GRF	Tibiofem joint kinetics, cruciate ligament force	Wilk et al. (1996) [23], Escamilla et al. (1998, 2001) [21, 22]
	Squat, leg press	ID (optimized F-l-EMG)	10 M (30 y) experienced	EMG, OMC, GRF	Tibiofem joint kinetics, cruciate ligament force	Zheng et al. (1998) [24]
	Squat, leg press, knee extension	ID (optimized F-l-v-EMG)	9 M (29 y), 9 F (25 y), low body fat	EMG, OMC, GRF	Patellofemoral force and stress	Escamilla et al. (2008) [4, 5]
	Squat	EMG-driven/ID/FEM	8 M (29 y), 8 F (29 y)	EMG, OMC, GRF, MRI, open MRI	Knee cartilage stress	Besier et al. (2008) [25] based on Lloyd and Besier (2003) [26]
	Hip extension/flexion	ID (min. stress)	Generic simul.	—	Hip joint forces	Lewis et al. (2009) [13]
	Abdominal crunch	Mixed ID/FD equipment	Generic simul. (three anthropometric cases)	—	Intervertebral joint loading	Nolte et al. (2013) [28]
Dynamic ballistic	Squat jump	FD (activation a_initial or a = 1)	6 M (25 y) well-trained volleyball players	EMG, OMC, GRF	Gastro bioarticularity	van Soest et al. (1993) [20]
			6 M (25 y) well-trained volleyball players	EMG, OMC, GRF	Muscle strengthening	Bobbert and Van Soest (1994) [17]
			6 M (25 y) well-trained volleyball players	EMG, OMC, GRF	Triceps surae series elastic compliance	Bobbert (2001) [14]
			Generic simul.	—	Stimulation onset times	Bobbert and van Zandwijk (1999) [18]
			6 M (26 y)	EMG, OMC, GRF	Fatigue of plantarflexors	Bobbert et al. (2011) [16]
			8 M (20 y) well-trained volleyball and gymnastics	EMG, OMC, GRF	Bilateral deficit	Bobbert et al. (2006) [15]
		FD (activation a = 0, 1)	Generic simul.	—	Optimal controls	Pandy et al. (1990) [12]
			5 M (22 y)	EMG, OMC, GRF	Contribution of muscles to accelerate trunk	Pandy and Zajac (1991) [19]
		FD (n/a)	Generic simul.	—	Bilateral asymmetry	Yoshioka et al. (2011) [29]