Predicting longitudinal changes in joint contact forces in a juvenile population: scaled generic versus subject-specific musculoskeletal models

Figures & data

Figure 1. Comparison between Gen (red) and SubS (blue) model estimations of joint contact forces at observations M0 and M12. Black bars indicate region of gait cycle with significant statistical difference between the two models at P < 0.01.

Table 1. Inter-model analysis of gait waveform profile at M0 and M12.

	M0			M12
	RMSD (IQR)	%Diff (SD)	$R^2$(range)	RMSD (IQR)	%Diff (SD)	$R^2$(range)
Hip	0.38 (0.17)	11 (3)	0.87 - 0.97	0.40 (0.18)	10 (2)	0.77 - 0.98
Knee	0.43 (0.27)	17 (6)	0.74 - 0.98	0.63 (0.41)	17 (7)	0.71 - 0.98
Ankle	0.32 (0.15)	8 (3)	0.93 - 0.99	0.29 (0.22)	8 (5)	0.95 - 0.99

Median RMSD, interquartile range (IQR) and range of JCF curve similarity (correlation) between Gen and SubS model estimates for the hip, knee and ankle joints of 11 participants. %Diff is the mean RMSD expressed as a percentage of the range of normalised JCF estimated by SubS.

Figure 2. Boxplot distribution of P1 and P2 JCF estimates for scaled generic and subject-specific models at two observations, M0 and M12. * indicates significant difference at P < 0.05.

Figure 3. Boxplot distribution of overall joint loading estimates calculated as area under BW-normalised JCF curve. AUC expressed as BW*%Gait Cycle (BW.%c).

Table 2. Inter-model differences in participant estimates at M0.

	|Δm(AUC)|[BW.%c]			|Δm(Peak)|[BW]					$R^2$[Δm(JCF)]
	H	K	A	P1H	P2H	P1K	P2K	P2A	H	K	A
S1	9.1	14.1	11.0	0.4	0.3	0.8	0.6	0.5	0.94	0.75	0.96
S2	0.1	13.6	0.8	0.3	0.2	0.2	0.6	0.9	0.93	0.90	0.93
S3	3.2	15.7	10.5	0.9	0.1	0.5	0.7	0.6	0.89	0.85	0.99
S4	6.9	39.5	0.7	1.2	0.1	0.5	1.6	0.6	0.92	0.94	0.98
S5	7.7	42.2	16.4	0.4	0.6	0.7	1.7	0.3	0.94	0.94	0.99
S6	9.0	22.4	1.0	0.8	0.7	0.3	1.2	0.9	0.87	0.74	0.93
S7	21.5	12.1	17.9	1.2	0.5	0.4	0.7	0.4	0.96	0.88	0.96
S8	12.1	20.1	13.3	0.5	0.2	0.8	0.4	0.6	0.92	0.98	0.98
S9	6.2	14.4	30.3	0.1	0.5	0.3	0.3	0.6	0.97	0.92	0.98
S10	17.5	15.4	29.9	1.0	0.2	0.2	0.5	0.6	0.95	0.89	0.99
S11	37.3	91.5	0.3	1.5	1.0	1.1	4.9	0.0	0.91	0.86	0.99
n	10	0	4	4	11	5	5	10	11	11	11

Absolute values of inter-model differences (Δ_m) at M0. Values in bold indicate greater than applied thresholds. [n] is the number of participants for which Gen and SubS were considered to be in agreement based on Δ_m. AUC expressed as BW*%Gait Cycle (BW.%c).

Table 3. Inter-model differences in participant estimates at M12.

	|Δm(AUC)|[BW.%c]			|Δm(Peak)|[BW]					$R^2$ [Δm(JCF)]
	H	K	A	P1H	P2H	P1K	P2K	P2A	H	K	A
S1	19.5	41.6	75.1	0.4	0.4	0.2	1.8	1.3	0.91	0.78	0.95
S2	9.5	29.6	27.0	0.0	0.4	0.3	1.3	0.1	0.95	0.91	0.96
S3	11.3	25.2	7.3	0.6	0.9	0.6	1.6	0.9	0.90	0.81	0.98
S4	4.8	38.7	26.0	1.4	0.5	0.1	1.7	1.9	0.90	0.95	0.98
S5	1.9	34.3	3.1	1.1	0.4	0.3	1.4	0.1	0.92	0.95	0.99
S6	1.1	26.3	9.9	1.3	0.6	0.9	1.6	0.6	0.77	0.71	0.95
S7	0.1	16.2	2.0	0.9	0.2	0.7	1.1	0.2	0.95	0.82	0.97
S8	12.4	16.9	24.5	0.3	0.5	0.2	0.4	0.7	0.98	0.98	0.99
S9	5.4	10.0	18.7	0.6	0.0	0.1	0.6	0.1	0.98	0.92	0.98
S10	9.8	10.4	5.4	0.6	0.5	0.4	0.5	0.5	0.98	0.88	0.97
S11	20.3	41.9	5.1	1.5	0.6	1.0	3.1	0.1	0.95	0.85	0.99
n	11	0	2	3	11	7	3	9	11	11	11

Absolute values of inter-model differences (Δ_m) at M12. Values in bold indicate greater than applied thresholds. [n] is the number of participants for which Gen and SubS were considered to be in agreement based on Δm. AUC expressed as BW*%Gait Cycle (BW.%c).

Table 4. Agreement in longitudinal changes (M12 - M0) in selected metrics between Gen and SubS predictions of JCF for each of 11 participants.

	Δt(AUC)			Δt(Peak)[BW]					$R^2$[Δt(JCF)]
	H	K	A	P1H	P2H	P1K	P2K	P2A	H	K	A	Tots
S1	✓	✓	×	✓	✓	×	✓	×	✓	✓	×	7
S2	✓	✓	✓	✓	✓	✓	✓	×	✓	✓	×	9
S3	✓	×	×	×	✓	✓	×	✓	✓	×	✓	6
S4	✓	✓	✓	×	✓	✓	✓	✓	✓	✓	✓	10
S5	✓	✓	×	×	✓	✓	✓	✓	✓	✓	×	8
S6	✓	✓	✓	✓	✓	✓	✓	✓	×	×	✓	9
S7	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	×	10
S8	✓	×	✓	✓	✓	×	✓	✓	✓	✓	✓	9
S9	✓	✓	✓	✓	✓	✓	✓	✓	✓	×	✓	10
S10	✓	✓	×	×	✓	✓	✓	✓	×	✓	×	7
S11	×	✓	✓	✓	✓	✓	✓	✓	×	×	×	7
Totg	10	9	7	7	11	9	10	9	8	7	5

Change (Δ_t) in area under JCF curve (AUC), peak 1 (P1) and peak 2 (P2) and coefficient of determination for Gen against SubS ΔJCF. Subscripts represent hip (H), knee (K) and ankle (A). (✓) agreement, (×) disagreement. Tot_g and Tot_s refer to the number of participants with agreement for a particular metric and number of metrics in agreement per participant, respectively.

Figure A1 Different indices for the description and analysis of the simulation results. A: Goodness of fit was assessed with the RMSD. B: Joint loading during the loading response (P1) and push off (P2) phases were analysed using the peak values and overall joint loading by the area under JCF/BW curve.

Figure A2 Comparison between Gen (red) and SubS (blue) model estimations of sagittal plane joint angles, moments and powers at all observations for 11 juvenile participants. Joint moments and powers normalised by body mass. Black bars indicate significance at P < 0.05 according to the non-parametric one-sample paired t-test. Extension/Flexion (Ext/Flex), Plantarflexion/Dorsiflexion (PF/DF) and Absorption/Generation (Abs/Gen).

Figure A3. Muscle forces estimated by the Gen (red) and SubS (blue) models for 12 selected muscles at M0 and M12. Black bars indicate statistical significance at P < 0.05 between models. Selected muscles are biceps femoris long head, biceps femoris short head, gastrocnemius lateralis, gastrocnemius medialis, rectus femoris, semimembranosus, soleus, tibialis anterior, tibialis posterior, vastus intermedius, vastus lateralis and vastus medialis.

Table A1. p-values for Wilcoxon sign ranked test between M0 and M12 for Δ_m(RMSD).

	Hip	Knee	Ankle
p-value	0.929	0.285	0.959
Effect size (Cohen’s d)	0.069	−0.037	−0.302

Table A2. P-values for Wilcoxon sign ranked test between Gen and SubS for Δ_t(RMSD).

	Hip	Knee	Ankle
p-value	0.965	0.779	0.859
Effect size (Cohen’s d)	−0.043	−0.156	0.092

Table A3. p-values for Wilcoxon sign ranked test between Gen and SubS estimates of AUC(JCF).

	M0			M12
	Hip	Knee	Ankle	Hip	Knee	Ankle
p-value	0.286	0.050	0.182	0.424	0.050	0.091
Effect size (Cohen’s d)	−0.320	0.454	0.541	−0.072	1.009	0.648