Fig 1.
Examples of GRFs vs. tibial bone loading.
(A) Tibial bone compression force (green) is much larger than GRF (blue) during running due to forces from muscle contractions (red); adapted from [21]. Forces are reported in body weights (BWs). (B) Peaks in tibial force (at the ankle joint, green) do not temporally coincide with peaks in GRF (blue) during the triple jump; adapted from [25]. Note, the GRF impact peak is not depicted here because it was not reported in this prior study, but it would have occurred at 0% of the cycle. (C) Standing flat footed vs. standing on one's toes results in the same GRF (blue), but different tibial forces, due to calf muscle contraction force (red) [26].
Fig 2.
(A) Each subject performed 30 running trials at a combination of speeds and slopes. (B) Experimental protocol involved subjects running on a force-instrumented treadmill while GRFs (blue vector) and lower-limb kinematics were recorded (white circles represent motion capture markers).
Fig 3.
(A) Four commonly-used vertical GRF metrics: Fvgrf,impact: impact peak; VALR: vertical average loading rate; Fvgrf,active: active peak; Jvgrf: total vertical impulse. (B) Two tibial bone force metrics: Ftibia,max: maximum tibial compression force; Jtibia: tibial compression force impulse. Two additional force estimates are shown for reference: Fext: the contribution of the external GRF to tibial compression; Fint: the contribution of internal muscle force to tibial compression.
Fig 4.
Regression results for GRF metrics vs. tibial bone load metrics across 30 running trials, for a single subject (Subject 1).
Each gray dot represents a single condition (i.e., a given speed and slope from Fig 2), and n indicates number of running conditions that exhibited a measurable GRF impact peak for Subject 1. The correlation coefficient (r) was computed for Subject 1 across all running speeds and slopes. Note that no single subject should be considered representative given the large inter-subject variability observed. For instance, the one strong correlation shown for this subject (r = 0.89) was as low as r = 0.16 for another subject. The correlation coefficients for each individual subject are reported in Table 1.
Table 1.
Correlation coefficients (r) between GRF metrics and tibial bone load metrics across all trials within a subject.
Ten rows represent the 10 subjects (F = female, M = male). Within a subject, (n) indicates the number of running conditions (of 30 total conditions) that exhibited a measurable GRF impact peak (i.e., evident in more than half the gait cycles). Mean and standard deviation (std) were computed using Fisher’s z transformation.
Fig 5.
Force trends due to changing speed vs. changing slope for a single subject (Subject 1).
Lines represent regression results for GRF metrics vs. tibial bone load metrics when only speed or slope was varied. Dark orange dots represent conditions when speed was varied while running on a fixed slope (level ground). Light blue dots represent conditions when ground slope was varied while speed is held constant (at 2.6 m/s). Small gray dots are all remaining parameter sweep conditions.