Resistance exercises are widely used in training programs and during rehabilitation to enhance performance, health and fitness through strengthening and adaptation of specific soft tissue and musculoskeletal structures. Prevention of muscle atrophy and an increase of lean body mass, together with a decrease of body fat and improvements in bone mineral density, as well as increased insulin sensitivity, have all been demonstrated as positive side effects [1]. To ensure an efficient and targeted adaptation with low injury risk, as well as a safe training design, knowledge of the participant specific loading conditions, but also a clear understanding of the external and internal kinematics and kinetics of the resistance exercises themselves, are essential.

Studies have investigated external (e.g. joint moments) [2–5] as well as internal loading conditions (e.g. patello-femoral joint contact forces or muscle activities based on EMG measurements) [6–10] during training exercises such as deadlifts, goodmornings or split squats, resulting in a variety of training recommendations. However, precise and objective comparisons of the actual muscle forces that act throughout these exercises and provide a more complete understanding of the loading patterns for laying the foundations for evidence-based training recommendations, are clearly missing in the literature. Unfortunately, it is not currently possible to measure muscle forces experimentally in a non-invasive manner during exercise performance in vivo. Moreover, data from alternative measurement techniques are not yet sufficient for deducing internal forces and moments for complex dynamic systems such as the lower limbs, in a straight forward manner [11]. Computational models that are able to provide an insight into the internal loading conditions in the human musculoskeletal system [12] have become available using different software packages (e.g. OpenSim SimTK, LifeModeler™, Anybody Modelling System™, Biomechanics of Bodies). Such models are now widely used in clinical and biomechanical gait analysis for studying lower limb dynamics as well as for investigating loading conditions in strength exercises [13–16]. An improved understanding of these muscle and joint contact forces, including not only the magnitude but also the direction of the forces, is essential for appropriate prescription and modification of training exercises, as well as for improving rehabilitation outcomes [13, 17].

Deadlifts, goodmornings and Split squats are all multi-joint resistance exercises used to enhance athletic performance or for reducing the risk of musculoskeletal injury, but also for specific rehabilitation programmes during recovery from injury through targeted improvement of the dynamic stability of lower limb joints [18–20]. To optimize the training results with a reduced risk of injury, desired trained muscle part should be loaded while all the other parts of the body should be unloaded as much as possible. Deadlifts begin with the lifter in a squat position, with arms straight and directed downwards, with an alternating handgrip on the bar [21]. The movement consists of an extension of the knees and hips until the body reaches an upright standing position. Goodmornings start in an upright standing position and, with the barbell on the shoulders, the hips are progressively flexed until maximum hip flexion is reached where the curvature of the lower spine remains in the lordosis, but the knees remain straight throughout. Similarly, split squats are performed with the barbell on the shoulders, but one foot is placed in an anterior position while the participant flexes the knees as far as possible [22]. Deadlifts, goodmornings and split squats are thought to be comparable in their ability to train strength, speed and power in all sport types [23], as well as for improving joint stability in anterior cruciate ligament (ACL) rehabilitation [24, 25], but also with respect to their potential for injury of the lower limbs and the back while performing the exercises [26]. However, the individual internal loading conditions, and specifically the muscle forces that occur during these different exercises remain unknown.

Therefore, with the goal to improve training and rehabilitation designs with respect to specific joint motion, the aim of this study was to examine and compare the specific muscle forces that occur in the lower limbs’ large muscle groups (Hamstrings, Quadriceps and m gluteus maximus) as well as total knee joint contact forces, during deadlifts, goodmornings and split squats.

The input data used to feed the computational models in this study were published in previous studies examining external loading conditions and joint angles [2, 3]. Two different groups were measured, either performing deadlifts and goodmornings, or split squats. All participants of both groups were sports students and experienced in resistance training (performing strength training two or more times a week). For the deadlifts and goodmornings, 13 participants (4 female, 9 male; 25 ± 4 years, 74 ± 11 kg, 1.80 ± 0.07 m) were observed [2], while five female and six male participants (25 ± 3 years, 68 ± 9 kg, 1.76 ± 0.07 m) were analysed while undertaking split squats [3]. The local ethics committee (Ethics Committee, ETH Zurich, Switzerland) approved both studies (EK2012-N-57 and EK2010-N-24), and participants each provided written informed consent before commencing the testing. To analyse the motion of the body, an opto-electronic system (Vicon, Oxford Metrics Group, UK), recording at 100 Hz with twelve cameras (MX40) was used. Ground reaction forces under each foot were measured using two 400 × 600 mm force plates (type 9281B Kistler, Winterthur, Switzerland) at a frequency of 2 kHz and time synchronised. Additionally, the force plates were calibrated to accurately determine the centre of pressure [27]. The IfB Marker Set consisting of 55 skin markers [28], applied mainly on the lower extremities of the participants was attached by trained personnel. Participants wore their normal training shoes throughout the exercise testing.

After an appropriate warm up of at least 5 Minutes on a stationary bike or a stepper, all participants performed standardised basic motion tasks to functionally determine the centres of rotation (fCoR) and axes in the hips, knees and ankle joints according to List and co-workers [28]. To normalize external and internal loading conditions and be able to compare values across subjects, standardized loads based on subject’s bodyweight (BW) were attached to the barbell rather than loads based on each subject’s repetition maximum one (RM1). An additional load of 25% of each participant’s BW was added to the barbell (deadlifts, goodmornings and split squats) as well as 50% of the participant’s BW for deadlifts only. For the split squats, the step length as well as the frontal tibial angle of the split squats were varied. These variations led to 10 different variations of split squats performed by each subject [3]. For each exercise and exercise variation, more than six repetitions were performed by each participant to be averaged for each subject and each exercise later on. In this study, data from two different studies were used [2, 3] which lead to different subjects performing different strength exercises. Beside the limitation of two different subject cohorts, the population measured in both studies is comparable in respect to gender distribution, age, height, weight, and resistance training experience. Furthermore, in both studies the same relative additional load on the barbell as well as the same data acquisition and processing were used. In order to minimize the influence of the two different groups, all the calculations were performed subject-specific including a functional approach to determine the joint centres (and therefore the length of the segments), gender specific anthropometric data, musculo-skeletal modelling and normalized to body weight.

Captured data were further processed in Matlab (R2014a, MathWorks, Natick, MA, United States) to extract skin marker and joint centre locations in space for each time frame, as well as joint angles and ground reaction forces. Velocity of the barbell markers was used to define the start- and end-point of the strength exercise cycle (v_barbell > 40 mm/s respectively <40 mm/s), while the total time of each cycle, also known as lifting time, was normalized to 100%. Using OpenSim (SimTK, Stanford, CA, United States [29]), the extracted data were used to calculate muscle forces in the lower extremities [30]. Here, an adapted standard and widely used musculoskeletal model (‘Gait2392_simbody’ [31–34]) including 14 body segments, 29 degrees of freedom (including 3 DoFs in each knee and ankle joint) and 92 muscles [35] was scaled to each participant’s individual segment length using the fCoRs of the hip, knee and ankle joints, as well as all the skin markers and pre-calculated joint angles. Using the participant’s specific models, the kinematics (in OpenSim termed: inverse kinematics) were calculated as recommended by Schellenberg and co-workers [30], where the fCoRs of the hips, knees and ankles were weighted with a factor of 100, 100 and 60 respectively. Furthermore, all attached skin markers were automatically weighted based on soft tissue artefact [30, 36], with a total weighting of 10 for each segment; pre-calculated joint angles were weighted with 0.02 to avoid flipping of the segments. A standardised OpenSim static optimization, using a cost function that minimised the sum of the squared muscle activation at each time frame, was performed using 6 Hz low pass filtered resultant kinematic data and the measured ground reaction force.

Quadriceps, Hamstrings, m gluteus maximus muscle groups and absolute total knee joint contact forces were evaluated. Quadriceps consisted of M. rectus femoris, m. vastus lateralis, m. vastus medialis, and m. vastus intermedius, while the Hamstrings consisted of m. biceps femoris long and short head, m. semitendinosus and m. semimembranosus. The m gluteus maximus muscle was considered to consist of three different parts, the lateral, the intermedial, and the medial part (Fig. 1).

Muscle forces relative to the joint angles and maximal muscle forces during all examined exercises were calculated in each repetition. All muscle forces were then normalised to the participant’s BW and are thus presented in the unit N/kg (i.e. force per kg of bodyweight). Normalized maximal muscle forces are presented for all exercises and all variations. To compare muscle forces and ranges of motion between the different strength exercises, normalized muscle forces were averaged over all participants and plotted as a function of knee and hip flexion angle for deadlifts, goodmornings, and one typical split squats variation. The typical split squat variation was stated using a step length of 70% of the participant’s leg length and a maximal tibial angle of 90°.

For each individual and exercise, maximal muscle forces in all repetitions of an exercise were calculated and averaged over all repetitions. Using this parameter, two statistical tests were performed: First to compare the results between the exercise types and second to compare the results between the different split squat variations. For the first test (comparing between the exercise types), participants’ maximal muscle forces from the deadlifts (25% and 50% additional load), goodmornings (25% additional load), as well as from the typically performed split squat variation (for both the front and rear limbs and using 25% additional load) were used and compared against each other. A linear mixed model with maximal muscle forces and exercise variation as fixed effects and participants as random effects was used to test the influence of the different exercises on each muscle force of the three different muscle groups. For the second test (comparing between the different split squat variations), a linear mixed model with step length and tibial angle as fixed effects and participants as random effects was used to examine maximal muscle forces between the 10 different split squats execution forms. For both investigations, a Bonferroni post-hoc test was conducted and adjusted by means of a Bonferroni correction in all aforementioned cases, if significant differences (p < 0.05) were detected. Statistical tests were performed using IBM SPSS (version 22, SPSS AG, Zürich, Switzerland).

All trials of all participants could be successfully simulated. There was no difference between the two cohorts regarding age, weight and height.

Absolute total knee joint contact forces averaged over all participants ranged from 9 to 111 N/kg for deadlifts with 25%; 12-127 N/kg for deadlifts with 50%; 14-47 N/kg for goodmornings; 14-120 N/kg for all types of split squats in the front limb; 17-65 N/kg for all types of split squats in the rear limb.

Quadriceps muscles

Different exercises and the different execution form influenced the Quadriceps muscle forces. During goodmornings, almost no forces in the Quadriceps muscles were observed (Table 1, Fig. 2). For deadlifts and the front limb of split squats, forces were similar, and significantly higher (m. vastus lateralis and m. vastus intermedius) compared to the rear limb of split squats (Table 2). For both exercises, m. vastus lateralis showed the highest forces followed by m. vastus medialis, m. vastus intermedius and M. rectus femoris (Table 1). During deadlifts, at knee angles of 40° and above, highly loaded Vasti muscles were observed (Fig. 2). The M. rectus femoris force of the rear leg showed a rather constant muscle force (>7 N/kg) over the whole range of motion (RoM, Fig. 1) of the split squats while the vasti forces were significantly lower (Table 1).

				Quadriceps				Hamstrings				m. gluteus maximus
				rf	vi	vl	vm	bl	bs	sm	st	lp	ip	mp
		LL	TA	[N/kg]	[N/kg]	[N/kg]	[N/kg]	[N/kg]	[N/kg]	[N/kg]	[N/kg]	[N/kg]	[N/kg]	[N/kg]
GM 25				1 ± 2	0 ± 1	0 ± 1	0 ± 1	10 ± 3	15 ± 6	14 ± 5	1 ± 1	3 ± 1	12 ± 5	3 ± 2
DL 25				8 ± 5	18 ± 4	30 ± 4	21 ± 5	13 ± 3	6 ± 5	28 ± 5	3 ± 2	6 ± 3	20 ± 4	8 ± 2
DL 50				10 ± 6	22 ± 4	34 ± 6	25 ± 6	15 ± 4	8 ± 5	30 ± 5	5 ± 3	8 ± 3	21 ± 3	11 ± 2
Split Squat 25	front	55%	60°	5 ± 8	22 ± 3	33 ± 3	26 ± 5	12 ± 8	3 ± 2	22 ± 7	2 ± 0	10 ± 3	24 ± 3	4 ± 2
		55%	75°	1 ± 1	21 ± 4	31 ± 4	24 ± 7	12 ± 6	4 ± 2	19 ± 7	2 ± 1	10 ± 4	24 ± 5	3 ± 1
		55%	90°	2 ± 3	19 ± 5	28 ± 7	22 ± 7	12 ± 6	5 ± 3	19 ± 8	1 ± 1	9 ± 5	23 ± 5	3 ± 1
		70%	60°	6 ± 10	22 ± 3	31 ± 5	28 ± 4	17 ± 7	3 ± 2	26 ± 7	2 ± 0	12 ± 3	25 ± 3	4 ± 2
		70%	75°	2 ± 4	21 ± 4	32 ± 4	25 ± 6	14 ± 7	4 ± 2	22 ± 7	2 ± 1	11 ± 3	25 ± 4	3 ± 2
		70%	90°	6 ± 10	20 ± 5	30 ± 6	25 ± 7	16 ± 6	5 ± 2	24 ± 10	2 ± 1	10 ± 4	25 ± 4	4 ± 2
		85%	60°	6 ± 12	22 ± 2	33 ± 4	29 ± 3	21 ± 5	3 ± 2	34 ± 8	3 ± 1	11 ± 4	25 ± 3	7 ± 4
		85%	75°	4 ± 9	21 ± 3	33 ± 5	26 ± 5	16 ± 7	3 ± 2	27 ± 8	2 ± 1	10 ± 3	24 ± 3	4 ± 2
		85%	90°	1 ± 2	20 ± 4	32 ± 6	24 ± 7	16 ± 6	4 ± 3	26 ± 9	2 ± 2	11 ± 3	25 ± 3	4 ± 2
		85%	105°	5 ± 7	17 ± 6	22 ± 8	20 ± 8	16 ± 6	5 ± 3	22 ± 10	1 ± 1	10 ± 4	25 ± 4	4 ± 2
	rear	55%	60°	15 ± 3	11 ± 2	18 ± 3	17 ± 3	0 ± 0	4 ± 2	0 ± 0	0 ± 0	0 ± 0	0 ± 0	1 ± 1
		55%	75°	15 ± 2	12 ± 2	21 ± 5	20 ± 4	0 ± 0	4 ± 2	0 ± 0	0 ± 0	0 ± 0	0 ± 1	1 ± 1
		55%	90°	13 ± 3	14 ± 1	26 ± 6	21 ± 5	0 ± 0	4 ± 2	1 ± 2	1 ± 1	1 ± 0	2 ± 1	2 ± 1
		70%	60°	20 ± 5	8 ± 2	11 ± 4	12 ± 3	0 ± 0	6 ± 3	0 ± 0	0 ± 0	0 ± 0	0 ± 0	0 ± 0
		70%	75°	18 ± 5	10 ± 2	15 ± 5	15 ± 4	0 ± 0	5 ± 3	0 ± 0	0 ± 0	0 ± 0	0 ± 0	0 ± 0
		70%	90°	14 ± 3	12 ± 2	22 ± 5	19 ± 5	0 ± 0	5 ± 2	0 ± 0	0 ± 0	0 ± 0	0 ± 1	1 ± 1
		85%	60°	27 ± 4	5 ± 3	5 ± 5	7 ± 3	0 ± 0	7 ± 5	0 ± 1	0 ± 0	0 ± 0	0 ± 0	0 ± 0
		85%	75°	26 ± 4	7 ± 3	8 ± 6	9 ± 5	0 ± 0	7 ± 4	0 ± 1	0 ± 0	0 ± 0	0 ± 0	0 ± 0
		85%	90°	22 ± 6	11 ± 2	17 ± 5	16 ± 5	0 ± 0	6 ± 3	0 ± 0	0 ± 0	0 ± 0	0 ± 0	0 ± 0
		85%	105°	18 ± 6	12 ± 2	20 ± 6	17 ± 4	0 ± 0	6 ± 3	0 ± 0	0 ± 0	0 ± 0	0 ± 0	0 ± 0

GM goodmorning, DL deadlifts, LL % of participants’ leg length, TA tibia angle relative to the ground, Added weight additional weight on the barbell as % of participant’s bodyweight. Quadriceps, including m. vastus lateralis (vl), m vastus intermedius (vi), m. vastus medialis (vm) and M. rectus femoris (rf); Hamstrings including m. biceps femoris short head (bs), m. biceps femoris long head (bl), m. semimembranosus (sm) and m. semitendinosus (st); m. gluteus maximus muscles, including three different parts, the lateral part (lp), the intermedial part (ip), and the medial part (mp) were examined

DL25	DL50	70% 90° front	70% 90° rear
rf, vi, vl, vm	rf, vi, vl, vm	vi, vl, vm	rf, vi, vl, vm	quad	GM25
bs, sm, st	bl, bs, sm, st	bl, bs, sm	bl, bs, sm	ham
lp, ip, mp	lp, ip, mp	lp, ip	ip	glut
			vi, vl	quad	DL25
	st		bl, sm, st	ham
	mp	lp, mp	lp, ip, mp	glut
			vi, vl	quad	DL50
		st	bl, sm, st	ham
		mp	lp, ip, mp	glut
			rf, vi, vl, vm	quad	70% 90° front
			bl, sm	ham
			lp, ip, mp	glut

Quadriceps (quad), including m. vastus lateralis (vl), m vastus intermedius (vi), m. vastus medialis (vm) and M. rectus femoris (rf); Hamstrings (ham) including m. biceps femoris short head (bs), m. biceps femoris long head (bl), m. semimembranosus (sm) and m. semitendinosus (st); m. gluteus maximus muscles (glut), including three different parts, the lateral part (lp), the intermedial part (ip), and the medial part (mp) were examined

For the different split squats, vasti muscle forces of the front limb significantly decreased with increasing tibial angle (Tables 1 and 3), while they increased with increasing tibial angle in the rear limb. Additionally, the m. vastus medialis force of the front limb increased significantly with step lengths above 55% of leg length. A large step length with a small tibial angle (60°/75°) resulted in a significantly higher M. rectus femoris muscle force (Tables 1 and 3). Contrary to the front limb, m. vastus lateralis and m. vastus medialis of the rear limb increased significantly with an increasing tibial angle and decreased with a larger step.

Front Limb: Step Length				Rear Limb: Step Length
70%	85%			70%	85%
vm	vm	quad	55%	rf, vl, vm	rf, vl, vm	quad	55%
bl, sm	bl, sm, st	ham		bl, bs	bl, bs	ham
Ip	ip	glut		-	-	glut
	-	quad	70%		rf, vl, vm	quad	70%
	sm, st	ham			bs	ham
	-	glut			-	glut
Front Limb: Tibia Angle				Rear Limb: Tibia Angle
75°	90°			75°	90°
vi, vm	vi, vl, vm	quad	60°	vl, vm	rf, vl, vm	quad	60°
bl, sm	bs, sm	ham		-	bl	ham
-	-	glut		-	-	glut
	-	quad	75°		rf, vl, vm	quad	75°
	-	ham			-	ham
	-	glut			-	glut

Quadriceps (quad), including m. vastus lateralis (vl), m vastus intermedius (vi), m. vastus medialis (vm) and M. rectus femoris (rf); Hamstrings (ham) including m. biceps femoris short head (bs), m. biceps femoris long head (bl), m. semimembranosus (sm) and m. semitendinosus (st); m. gluteus maximus muscles (glut), including three different parts, the lateral part (lp), the intermedial part (ip), and the medial part (mp) were examined. Interactions were observed between mp of the front limb and vi, sm, st, lp, ip and mp of the rear limb

In this study, three different strength exercises, deadlifts, goodmornings and split squats, with a total of 23 different variations were analysed using musculoskeletal simulation software with the aim to compute internal loading conditions and specifically forces in the muscles. These insights are now able to form the basis for providing evidence-based recommendations for efficient training and rehabilitation.

Since specific muscle forces that act during strength exercises were, until now, almost unknown, the results of this study therefore provide coaches and physiotherapists the ability to choose a minimal risk and performance targeted strength-training design for athletes or patients. To reduce the risk of injury of an ACL rupture, performing goodmornings is suggested to shift the H:Q-Ratio towards Hamstrings. Deadlifts produce considerable loading over large ranges of motion in all examined muscles, while only split squats (rear leg) seem to activate the rectus femoris in a substantial manner, but the loading conditions of the exercise itself are highly dependent upon the step lengths and the frontal tibia angle.