USE OF 2-DIMENSIONAL SAGITTAL KINEMATIC VARIABLES TO ESTIMATE GROUND REACTION FORCE DURING RUNNING

Abstract

Background

Variations in vertical loading rates have been associated with overuse injuries of the lower extremity; however, they are typically collected using 3-dimensional motion capture systems and in-ground force plates not available to most clinicians because of cost and space constraints.

Purpose

The purpose of this study was to determine if kinetic measures commonly used to describe lower extremity loading characteristics could be estimated from step rate and specific sagittal plane kinematic variables captured using 2-dimensional motion analysis during treadmill running.

Study Design

Observational Study

Methods

Ten high school cross-country runners (4 men and 6 women) voluntarily consented to participate in this study. Reflective markers were placed on each lower extremity over multiple anatomical landmarks. Participants were then asked to run on the instrumented treadmill at their preferred running speed. When the participants indicated they were in their typical running pattern, they continued to run at their preferred speed for a minimum of five minutes. After three minutes of running at their preferred running speed, the participant's step rate was counted and after running for four minutes, video and ground reaction force data were recorded for 60 sec. All running motion data were recorded using a single high-speed camera at 240 frames per second and ground reaction force data were sampled at 1000 Hz.

Results

Mean kinematic values between the left and right extremities for all 10 participants were not significantly different. Consequently, data for the left and right extremities were grouped for all further analyses. The stepwise forward regression to predict vertical ground reaction force resulted in a five-variable model (step rate and four kinematic variables) with R² = 0.56. The stepwise forward regression to predict average loading rate also resulted in a five kinematic variable model with R² = 0.51.

Conclusions

Step rate and sagittal plane kinematic variables measured using a simplified 2-dimensional motion analysis approach with a single high-speed camera can provide the clinician with a reasonable estimate of ground reaction force kinetics during treadmill running.

Level of Evidence

4, Controlled laboratory study

INTRODUCTION

While previous research suggests that the development of running-related overuse injuries is multifactorial with a wide range of suspected risk factors, it is important to note that many of these investigations have been conducted retrospectively.¹ Davis et al² conducted a prospective investigation to assess vertical impact loading in female runners with medically diagnosed injuries. They found that impact loading was greatest in the injured runners and lowest in the never-injured group and higher impact loading was associated with bony and soft-tissue injuries. These authors concluded that reducing vertical loading rates associated with impacts could be an effective means to reduce injury risk in female runners.²

High school cross country runners have been shown to have increased injury rates in comparison to other sports with the knee and leg being the most frequently reported injury locations.^3,4 Running-related lower extremity overuse injuries include anterior knee pain, medial tibial stress syndrome, stress fractures, and compartment syndromes. Other research findings have supported that higher average vertical loading rates are associated with anterior knee pain and leg pain in female runners.^5,6

Based on current research, it would appear to be important for clinicians to be cognizant of and if possible, assess ground reaction forces and loading rates in high school cross-country runners either as part of a management program or during pre-season screening. Unfortunately, ground reaction forces are seldom evaluated in the typical clinical setting because of the cost of required equipment (3-dimensional multiple camera system with in ground force plates), space limitations, and time constraints as well as the complexity of the data analysis. As a result, clinical running analyses are usually limited to a qualitative 2-dimensional kinematic analysis using a single video camera.

In an attempt to address a practitioner's ability to obtain kinetic measurements for runners in the clinical setting, Wille and colleagues⁷ assessed if lower extremity kinetic measures typically used to describe lower extremity loading during running could be estimated from sagittal plane kinematic variables. Using a linear mixed effects model, they found that selected kinetic variables could be obtained from step rate and a subset of sagittal plane kinematic variables common to a clinical running analysis. These authors reported an adjusted R² value of 0.48 for estimated peak vertical ground reaction force and an adjusted R² of 0.04 for estimated average loading rate.⁷ In their conclusion, the authors suggested that although they had used kinematic variables captured using 3-dimensional motion analysis to predict running kinetic variables, 2-dimensional motion analysis would likely be sufficient to capture step rate and the sagittal plane kinematic variables required for predicting running kinetics.⁷ Wille et al⁷ also noted that the relationships they identified in their study could be generalized to a simplified 2-dimensional approach if a single video camera with an adequate frame rate (greater than 100 frames per sec) was used for motion capture. These conclusions are supported from prior research that has demonstrated a strong correlation between 2-dimensional and 3-dimensional sagittal plane motions during running.^8,9

Accurate prediction of kinetic measurements using 2-dimensional motion analysis would be highly beneficial in the management of running-related injuries and would be especially advantageous for those clinicians working with high school cross-country runners in light of the higher rates of lower extremity overuse injuries identified with this population. Thus, the purpose of this study was to determine if kinetic measures commonly used to describe lower extremity loading characteristics could be estimated from step rate and specific sagittal plane kinematic variables captured using 2-dimensional motion analysis during treadmill running. It was hypothesized that 2-dimensional sagittal plane kinematic variables would more accurately predict peak vertical ground reaction force as compared to predicting average loading rate.

METHODS

This cross-sectional study was conducted at the Regis University biomechanics research lab in August and September 2017. A sample of convenience was used based on a three-month period of subject recruitment and excluding those high school athletes who did not meet inclusion criteria. Participants were recruited from local area high schools through community advertisements and public information sessions. The Regis University Institutional Review Board approved the study protocol and all participants provided written informed assent in addition to parental consent prior to participating in the study.

Participant Characteristics

Ten high school cross-country runners (4 men and 6 women) voluntarily consented to participate in this study. The mean age of the 10 participants was 15 years, with a range of 14 to 17 years. All participants selected for this study met the following inclusion criteria: (1) between the ages of 14 to 18 years; (2) ran on average at least 18 miles per week for one-year prior to participation in the study; (3) had experience running on a treadmill; (4) no previous history of lower extremity congenital or traumatic deformity or previous surgery that resulted in altered bony alignment; and (5) no acute injury three months prior to the start of the study that led to inability to run at least three consecutive days during that time.

Data Acquisition

Upon arrival to the testing center, each participant's height, weight, and blood pressure were recorded. Next, each participant was asked to begin running with their self-selected shoes on a fully instrumented treadmill (Bertec Corporation, Columbus, OH) for at least five minutes so that they could acclimate to the treadmill as well as determine their preferred running speed for testing. Participants were asked to run at a speed comparable to a typical distance training run. Once the preferred running speed was self-selected and the participant indicated that they were acclimated to the treadmill, the runner stopped running and 9 mm spherical reflective markers were placed on each lower extremity over the following locations: anterior superior iliac spine (ASIS), posterior superior iliac spine (PSIS), lateral epicondyle of the femur, lateral malleolus, lower posterior calf above the Achilles tendon (two markers), and over the midline of the heel (two markers). These locations are consistent with the marker set used in a previous study examining the reliability of 2-dimensional kinematic analysis.¹⁰ To minimize ASIS and PSIS marker movement, elastic self-adhesive wrapping was applied around the participant's waist prior to marker placement.

Once all markers were attached, the participant was then asked to resume running on the treadmill at his or her pre-selected running speed. When the subject indicated they were in their typical running pattern, they continued to run at their preferred speed for a minimum of five minutes. After three minutes of running at their preferred running speed, the participant's step rate (STEP_RATE) was counted by one of the investigators (MFR). After running for four minutes at their preferred running speed, video data were recorded for the left and then right sagittal plane (side view) for 60 sec using a single high-speed camera (Model# EX FH25, Casio America Inc., Dover, NJ 07801) at 240 frames per second. Three dimensional ground reaction forces were recorded (1000 Hz) through the instrumented treadmill deck for 10 sec.

Variables and Data Analysis

The left and right sagittal video clip for each runner was assessed by a single rater (TGM) with over 12 years of experience performing 2-dimensional video-based running analyses on collegiate and recreational runners. The rater selected a stride for analysis after the third foot strike on the video clip to allow an opportunity to observe the runner's gait pattern and enhance the rater's ability to identify initial foot contact. The following six sagittal plane kinematic variables were assessed on the left and right lower extremities for all 10 runners: 1) angle of the shoe to treadmill at initial contact (SHOE_ANG), 2) angle of the lower leg at initial contact (LEG_ANG), 3) knee flexion at initial contact (KN_FL_IC), 4) knee flexion at midstance (KN_FL_MS), 5) vertical position of the estimated center of mass (center of line connecting ASIS and PSIS) at midstance, and 6) vertical position of the estimated center of mass at double float. KN_FL_IC was subtracted from KN_FL_MS to calculate total knee flexion (KN_FL_Tot). The vertical position of the estimated center of mass at double float was subtracted from the vertical position of the estimated center of mass at midstance to calculate total vertical excursion of the center of mass (COM_VtEx). All angles were measured in degrees and all distance measurements were recorded in centimeters using a free-access video analysis software program (Kinovea, version 0.8.15, http://www.kinovea.org). In a previously published study, in comparison to another rater with a similar level of experience, the rater in this study (TGM) demonstrated intra-rater levels of reliability between 0.75 to 0.98 (ICC) and inter-rater reliability values between 0.76 to 0.97 (ICC) for all kinematic variables assessed in the current study.¹⁰

Ground reaction force data were filtered using a fourth-order, zero-lag low-pass Butterworth filter at a 30 Hz cutoff. The peak vertical force component of the ground reaction force (Vert_GRF) and the average loading rate (AVG_Load_Rate) were measured for five consecutive running cycles for the left and right lower extremities with the average of the five cycles used for further analysis. The Vert_GRF was reported in N x body weight in kg (BW) and AVG_Load_Rate was reported in N/kg/sec. As in the Wille et al study,⁷ the AVG_Load_Rate was defined as the rate of change in the vertical GRF from 20% to 80% of the period beginning with initial contact to the vertical force impact peak.

Statistical Analysis

In addition to descriptive statistics, a series of t-tests were performed to determine if there were differences between left and right extremities for all six kinematic variables assessed in this study. Seven variables (SHOE_Ang, LEG_Ang, KN_FL_IC, KN_FL_MS, KN_FL_Tot, COM_VtEx, and STEP_RATE) were entered into a stepwise forward linear regression to determine the most parsimonious set of variables associated with Vert_GRF and AVG_Load_Rate. To permit comparison to published studies,⁷ the amount of variance in the kinetic parameters explained by the kinematic measures and step rate for each particular model was reported as the R² value as well as the adjusted R² value. All statistical analyses were performed using SPSS software, Version 23 (IBM, Armonk, NY, 10504). An alpha level of .05 was established for all tests of significance.

RESULTS

Participant characteristics (mean ± SD) for the 10 runners included age (15 ± 1.2 years), height (163.8 ± 10.2 cm), mass (49.4 ± 7.6 kg), preferred step rate (176 ± 5.3 steps per minute), and running speed (3.01 ± 0.4 m/s). Descriptive statistics for all kinetic and kinematic measurements are listed in Table 1. The data for each of the seven variables were normally distributed and t-tests used to determine the mean values between the left and right extremities for all 10 participants were not significantly different. Based on these results, data for the left and right extremities were grouped (n = 20) for all further analyses. The stepwise forward regression to predict Vert_GRF resulted in a five-variable model (F = 3.62; p < 0.02) with R² = 0.56 and the adjusted R² = 0.41. The five measures that were included in the model were SHOE_Ang, LEG_Ang, KN_FL_Tot, COM_VtEx, and STEP_RATE. The stepwise forward regression to predict AVG_Load_Rate also resulted in a five-variable model (F = 2.89; p < 0.054) with R² = 0.51 and the adjusted R² = 0.33. The five measures that were included in the model were SHOE_Ang, LEG_Ang, KN_FL_IC, COM_VtEx, and STEP_RATE.

Table 1.

Means and Standard Deviations for Kinematic and Kinetic Variables (units).

VARIABLE	LEFT (n = 10)	RIGHT (n = 10)	COMBINED (n = 20)
Peak Vertical Component of the Ground Reaction Force (VERT_GRF) (N x body mass in kg)	2.38 ± 0.23	2.40 ± 0.28	2.39 ± 0.25
Average Loading Rate (AVG_Load_Rate) (N/kg/sec)	47.79 ± 16.00	51.90 ± 19.42	49.85 ± 17.44
Angle of the Shoe to Treadmill at Initial Contact (SHOE_ANG) (degs)	9.4 ± 10.96	8.30 ± 10.85	8.85 ± 10.63
Angle of the lower leg at Initial Contact (LEG_ANG) (degs)	9.30 ± 2.1	7.70 ± 2.83	8.50 ± 2.59
Knee Flexion Angle at Initial Contact (KN_FL_IC) (degs)	10.30 ± 4.11	8.60 ± 4.93	9.45 ± 4.50
Knee Flexion at Midstance (KN_FL_MS) (degs)	38.50 ± 4.48	38.60 ± 4.55	38.55 ± 4.39
Total Knee Flexion (KN_FL_Tot) (degs)	28.20 ± 3.36	30.00 ± 4.11	29.10 ± 3.77
Total Vertical Excursion of the Center of Mass (COM_VtEx) (cm)	7.31 ± 2.08	7.30 ± 1.80	7.30 ± 1.89

DISCUSSION

Previous researchers using kinematic measures obtained from 3-dimensional motion analysis were able to explain approximately 50% of the variance associated with VERT_GRF during treadmill running and suggested that 2-dimensional motion analysis would likely be sufficient to capture the sagittal plane kinematic variables required for predicting running kinetics.⁷ The ability to predict running kinetics would be especially advantageous for those clinicians working with high school cross-country runners since previous research has identified higher rates of lower extremity overuse injuries with this population. Thus, the intent of this study was to determine if kinetic measures commonly used to describe lower extremity loading characteristics could be estimated from step-rate and six sagittal plane kinematic variables captured using 2-dimensional motion analysis during treadmill running.

Based on the findings of the regression analysis, the use of the following five variables, SHOE_Ang, LEG_Ang, KN_FL_Tot, COM_VtEx, and STEP_RATE, assessed using 2-dimensional kinematic analysis can explain 56% of the variance of Vert_GRF. Using these results, the clinician can predict the Vert_GRF using the following formula:

$$\begin{array}{l}-1.094 + (0.070 \times \text{SHOE}\_\text{Ang}) + (-0.001 \times \text{LEG}\_\text{Ang}) +\\ (-0.021 \times \text{KN}\_\text{FL}\_\text{Tot}) + (0.108 \times \text{COM}\_\text{VtEx}) +\\ (0.018 \times \text{STEP}\_\text{RATE})\end{array}$$

Using this prediction formula, the mean value was calculated for the predicted Vert_GRF (2.31 N x BW) and compared using a t-test to the actual measured mean obtained for Vert_GRF (2.40 N x BW) for 14 randomly selected extremities. The results of the t-test were not significant (p = 0.15) and the error of the mean (0.04) was small which further validates the prediction formula for Vert_GRF.

Based on the findings of the regression analysis, the use of SHOE_Ang, LEG_Ang, KN_FL_IC, COM_VtEx, and STEP_RATE assessed using 2-dimensional kinematic analysis can explain 51% of the variance of AVG_Load_Rate. Using these results, the clinician can predict the AVG_Load_Rate using the following formula:

$$\begin{array}{l}-200.80 + (1.070 \times \text{SHOE}\_\text{Ang}) + (-3.316 \times \text{LEG}\_\text{Ang}) +\\ (-1.349 \times \text{KN}\_\text{FL}\_\text{IC}) + (2.620 \times \text{COM}\_\text{VtEx}) +\\ (1.487 \times \text{STEP}\_\text{RATE})\end{array}$$

Using this prediction formula, the mean value was calculated for the predicted AVG_Load_Rate (47.50 N/kg/sec) and compared using a t-test to the actual measured mean obtained for AVG_Load_Rate (46.38 N/kg/sec) for 14 randomly selected extremities. The results of the t-test were not significant (p = 0.43) and the error of the mean (2.98) was small which further validates the prediction formula for AVG_Load_Rate.

The outcomes of the current study are similar to the findings reported by Wille et al.⁷ In their study using 3-dimensional motion analysis, they reported that 48% of the variance for peak vertical ground reaction force could be explained using the kinematic variables shoe inclination angle at initial contact and the center of mass vertical excursion.⁷ They also reported that none of the kinematic variables assessed could be used to predict loading rate between 20% to 80% from initial contact to the vertical impact peak.⁷ In the current study, at least 50% of the variance associated with VERT_GRF and AVG_Load_Rate could be explained using a five-variable model. Based on these findings, the authors rejected the study hypothesis that 2-dimensional sagittal plane kinematic variables would be more predictive of peak vertical ground reaction force in comparison to average loading rate.

The results of this investigation would support the suggestion by Wille et al⁷ that 2-dimensional motion analysis would likely be sufficient to capture the sagittal plane kinematic variables required for predicting running kinetics. Using the prediction models provided, a clinician can reasonably predict the Vert_GRF and AVG_Load_Rate in high school cross-country runners using 2-dimensional kinematic variables readily collected in a clinical setting without the need for an expensive force platform or 3-dimensional motion analysis system. Although a small sample of high school runners was used in the current investigation, the results of this study may also be applicable to collegiate and adult recreational runners, but further research is required with these specific populations.

A limitation in the current study was the use of treadmill to assess both kinetic and kinematic variables during running. Several studies have reported on the validity of using a treadmill for running analysis with the major concern being the alteration of the runner's pattern of lower extremity movement as well as ground reaction forces. In one of the only studies to compare overground versus treadmill running kinematics and kinetics using a force-transducer instrumented treadmill, Riley et al.¹¹ reported that a treadmill-based analysis of running mechanics can be generalized to overground running mechanics, provided the running speed on the treadmill is similar to individuals overground running speed. Another limitation was the use of a single high-speed camera to capture sagittal plane (2-dimensional) kinematics of the lower extremities during running. As previously noted, McClay and Manal⁹ as well as Areblad et al⁸ have reported that the use of 2-dimensional techniques to assess angular values in the sagittal plane during running are similar to values obtained using 3-dimensional motion analysis techniques.

CONCLUSIONS

The results of this study indicate that step rate and sagittal plane kinematic variables measured using a simplified 2-dimensional motion analysis approach with a single high-speed camera can provide the clinician with a reasonable estimate of ground reaction force kinetics during treadmill running. The clinician can use the predictive models provided in this paper to estimate running kinetics when treating high school runners with lower extremity injuries or as part of a pre-season screening assessment.