Interpreting Ground Reaction Forces in Gait
This chapter provides a description of ground reaction forces (GRFs) in gait, detailing the technology used to measure them and their use in gait analysis. Representative ground reaction force data is provided, and information on how data is analyzed and interpreted is discussed. In addition, examples of how GRF data has been used to gain an understanding of healthy and pathological gait (scoliosis, cerebral palsy, stroke, multiple sclerosis) are provided and discussed. This chapter highlights that the GRF is an essential part of any clinical gait analysis and contributes to both surgical and conservative clinical management involving gait.
KeywordsGround reaction force Center of pressure Shear force Gait analysis Human kinetics Walking
The examination of forces as the cause of movement is termed kinetics. Force describes the interaction of an object and its surroundings. Major forces involved in human locomotion are the ground reaction force (GRF), joint reaction force (JRF), and muscle force (MF). Force provided by a supporting horizontal surface is known as the ground reaction force (GRF). This in turn can be resolved into three components, namely, vertical, mediolateral, and anterior-posterior. The center of pressure (COP) represents the point of application of the resultant GRF. It is simply the central point of pressure exerted on the foot.
Mechanical interactions between a muscle and its surroundings result in human movement. A force exerted by a muscle is transmitted through its tendon to bone and leads to a movement of the body segments. Muscle can only generate a tensile force and not a compressive force; simply put – muscles cannot push but can only pull. Ligament and bony contact forces exerted across a joint are transmitted from one body segment to another. These forces are essential in some aspects of musculoskeletal biomechanics and are normally called a joint reaction force (JRF). JRF, for example, is essential in the design of prosthesis and prosthetic joints. Detailed explanation of JRF is provided elsewhere (Winter 1990), and it is beyond the scope of this chapter. Since the JRF does not represent the absolute bone-to-bone force, it may have significant magnitude (Whiting and Zernicke 1998). Another important parameter within human kinetics which involves both force and displacement is the moment. This can be defined as the product of the magnitude of the force and the perpendicular distance to its line of action.
Recording and understanding of kinematic and kinetic parameters is required in order to analyze the function of the musculoskeletal system operating to generate and transmit forces and counteract external forces to perform smooth movement. Gait analysis plays an important role in orthopedics, physical medicine, and rehabilitation and has been applied to the assessment of clinical conditions such as cerebral palsy (Gage and Koop 1995), Parkinson’s disease (Koozekanani et al. 1987; Defebvre et al. 1996), scoliosis (Giakas et al. 1996; Schizas et al. 1998), amputation (Hill et al. 1997), Paget’s disease (Gainey et al. 1989), Alzheimer’s disease (Alexander et al. 1995), and multiple sclerosis (Gehlsen et al. 1986) and in the development of orthoses and prostheses (Andriacchi and Hurwitz 1997; Sanderson and Martin 1996). While a description of gait, its phases, and its detailed analysis can be found elsewhere, this chapter focuses on GRF.
State of the Art
Technology for Ground Reaction Force Measurement
There are a number of types of force platforms which are used to record ground reaction forces. The majority either consist of strain gauge transducers or piezoelectric crystal transducers. The application of stress (force) to a structure changes its geometry, in turn changing its resistance. This change of resistance is calibrated to indicate the applied force in strain gauge devices. On the other hand, a nonconducting crystal which generates an electrical charge when subjected to mechanical strain is used in piezoelectric devices. Both these types of platform measure forces indirectly, based on a calibration matrix. Technical characteristics and advantages are described elsewhere (Vaughan et al. 1992), and these are beyond the scope of this chapter. In addition to force platforms, there are several pressure measurement systems. These have been descried in detail elsewhere (Razak et al. 2012) and are available both as in-shoe systems and platforms. These can give an indication of the vertical component of the GRF. Given the technical nature and the setup of the pressure measurement systems, current commercially available systems cannot measure shear (or horizontal) components (for further information see “Assessing Pediatric Foot Deformities by Pedobarography,” “Assessing Clubfoot and Cerebral Palsy by Pedobarography,” “Low Density Pedoboragraphy as a Gait Analysis Tool,” “Integration of Foot Pressure and Foot Kinematics Measurements for Medical Applications”).
Ground Reaction Force and Its Measurements During Gait
The GRF acting on the foot during upright movements is a major external force, normally recorded and measured in three dimensions using a force platform. It comprises of a single vertical and a pair of horizontal shear force components acting in the anterior-posterior and mediolateral directions. Force platform data also provide coordinates of the point of application of the resultant vector relative to the platform origin.
Force platforms are widely used in the biomechanical assessment of human movement, especially in gait analysis. There is a plethora of studies that used GRFs and the COP to reflect the acceleration of the center of mass (COM) (MacKinnon and Winter 1993), to assess balance (Winter et al. 1990), or combined with anthropometric and kinematic data to determine the joint dynamics (Koopman et al. 1995). Accurate estimation of these parameters is affected by the calibration. COP is an important derivative of the GRF. Its misposition by 1 cm would result in approximately 7% and 14% errors in the calculation of peak and average joint moments of the lower segments during running (McCaw and Devita 1995). In gait analysis, it was shown that high errors in the net joint dynamics could result mainly from uncertainties due to marker position, anthropometric data, and COP (Davis et al. 1997). These errors are amplified when joint dynamics of proximal segments are calculated due to the cumulative input of errors from distal segments. While there are studies which consider various options for calibration (Chockalingam et al. 2002), current commercially available systems have improved options for calibration.
Vertical Component of the Ground Reaction Force
Anterior-Posterior Component of the Ground Reaction Force
At IC the foot applies a force in an anterior direction causing the body to decelerate. This results in a posterior shear force that peaks during early stance (Fig. 1b – F4). As the body moves over the stance limb, the posterior shear force reduces until the end of MS (F5). From this crossover point, the COM moves ahead of the foot, and the foot applies a force in a posterior direction causing an anterior shear force that propels an individual forward. Peak anterior GRF occurs during late stance (F6). The reduction that follows relates to the transference of force to the front foot.
Mediolateral Component of the Ground Reaction Force
At IC a shear force is applied by the foot to the ground that is directed medially. This creates a lateral shear force that peaks during LR (Fig. 1c – F7). A lateral directed force applied by the foot to the ground from mid LR onward is applied that results in a medial shear force that is characterized by two peaks approximately at the beginning of MS (F8) and toward the end of TS (F9).
Walking speed can influence the three GRF profiles over time. Regarding the vertical GRF, for example, a reduced acceleration of the body’s COM while walking at a slower speed results in a decrease in the height of the peaks and depth of the MS trough. A reduced first peak could also be attributed to the presence of pain. For a comparison on the effects of walking speed on the components of the GRF, readers are directed elsewhere (Schwartz et al. 2008; Nilsson and Thorstensson 1989).
Center of Pressure (COP)
COP is the location of the GRF, and during normal gait, the COP progresses from the heel to toe during the stance phase. Initially the COP is in a medial position at the heel and rapidly moves to the lateral side of the mid-foot. It remains there during the mid-support period and then rapidly transfers to the medial side of the fore foot. To maintain balance while walking, the support force has to be on the same line from the point of ground support (COP) to the COM.
Analysis of Ground Reaction Forces
Recorded GRFs can be analyzed in two ways. Conventional time domain analysis examines specific force and time values, such as the magnitude of local peaks (highest point in a known gait phase) as well as their time of occurrence (Fig. 1a – F1 and F3). Examples of normal (Cavanagh and Lafortune 1980; Williams et al. 1987; Buczek and Cavanagh 1990) and pathological (Koozekanani et al. 1987; Giakas et al. 1996; Sanderson and Martin 1996; Schizas et al. 1998) GRF data can be found in the literature. In contrast, frequency domain analysis allows the study of harmonic coefficients.
In other instances, individuals may have instability problems, as in Parkinson’s disease or other neurological disorders. Here the first priority is to reduce the tremor, so the most appropriate approach is the examination of the entire force-time pattern and not just isolated time domain parameters. This measurement is achieved by frequency domain analysis. Using this technique, higher frequencies in the total signal can be evaluated, leading to the quantification of signal oscillations.
While it is relatively simple to measure external forces, the measurement of internal forces acting on body segments remains difficult. Direct measurement of forces acting on a joint or within a body segment would require instrumentation attached to each tendon. Hence, direct measurement is not always possible. However, with the help of known anthropometric and kinematic data, it is possible to calculate and predict these forces using inverse dynamics. The dynamics within a joint indicate the mechanical cause of movement and contribute to the understanding of compensatory mechanisms adopted by the body to any disturbances within the central nervous system (Winter 1990). Inverse dynamics calculation requires the measurement of mass, location of COM and moment of inertia of the segments examined, and location of joint centers. This investigation also requires kinetic information such as the gravitational force and the GRF. Several studies have been conducted to demonstrate the usefulness of inverse dynamics (Koopman et al. 1995; Mommersteeg et al. 1997; Risher et al. 1997). Most commercial gait analysis software available today uses inverse dynamics, requiring minimum input from the operator. However, an understanding of convention reference frames on which moments are calculated requires careful consideration (Manal et al. 2002; Schache and Baker 2007). There has been much work on the standardization of data collection and management in clinical gait analysis which has led to the reliability and repeatability (Wu and Cavanagh 1995; Benedetti et al. 1998).
Time Domain Analysis
The features of the GRF which are typically analyzed include the peak forces, initial slopes, and symmetry between limbs. For example, for the vertical GRF, commonly assessed variables include the maximum vertical forces (first peak usually termed F1, second peak termed F3), the minimal vertical force (the valley termed F2), and loading/unloading rates (Hesse et al. 1994).
Kesar et al. (2011a) reported the minimal detectable change for gait variables, including peak anterior GRF and mean vertical GRF, providing references to help interpret the magnitudes of changes in poststroke gait variables. Also statistical methods such as signal correlation coefficient matrix can be applied to time domain GRF data, to assess poststroke gait during gait retraining (Szczerbik et al. 2014) (see also “Time Series Analysis in Biomechanics”).
Frequency Domain Analysis
As opposed to time domain analysis which is limited to selected points on force-time graphs, frequency domain analysis allows examination of the entire waveform. This type of analysis has been shown useful in the identification of gait abnormalities in clinical condition such as cerebral palsy using harmonic analysis (White et al. 2005) and multiple sclerosis using fast Fourier transformation (Wundeman et al. 2011). In a study comparing the GRF between patients with scoliosis and healthy participants, Giakas et al. (1996) demonstrated the usefulness of frequency domain analysis as opposed to simple time domain analysis. The time domain data of various components did not show any changes, but the frequency content in the mediolateral component of patients was higher than the healthy participants indicating that there is a change balance parameter.
Traditionally kinetic and kinematic gait data is normalized to percentage of the gait cycle. In addition, normalization techniques are used to compare gait data between individuals of significantly different heights and/or bodyweights; GRF data is often normalized to body weight.
There are numerous methods available to normalize gait data (Lulić et al. 2008; Chockalingam et al. 2008, Dixon et al. 2014a). Moisio et al. (2003) demonstrated that the application of two normalization techniques (body mass and bodyweight times height) was highly effective in reducing height and weight differences when examining joint moments. Research by Stansfield et al. (2003) examined normalization of gait data in children and recommended the use of nondimensional normalization as opposed to semi-dimensional normalization (see also “Time Series Analysis in Biomechanics”).
Ground Reaction Force in the Understanding of Walking
Researchers have utilized measurement of the GRF during walking gait to understand the normal functioning of the lower limbs. Hunt et al. (2001) used motion capture and force plates to examine walking gait in participants. This study showed that most of the intersegmental range of motion (rear-foot segment relative to the leg and forefoot segment relative to the rear-foot) occurred at the beginning and end of the stance phase when support was only on the rear-foot or forefoot and the GRF was maximal. These findings confirm the significance of midfoot joints in foot function. Using GRF data from the second force peak (Fig. 1) of the stance phase, Jacob (2001) estimated forces acting across the joints of the first and second rays of the forefoot in order to understand the physiological function of the foot. Results showed that the resultant force on the first metatarsal head amounts to about 119% body weight and the second metatarsal bone is also significantly loaded, however more in bending.
The analysis of GRF has also been used to examine the effect of footwear and orthoses. Nester et al. (2003) examined the effect of foot orthoses (medially and laterally wedged) on the kinematics and kinetics of walking gait (for further information please refer to the chapter titled: “Functional Effects of Foot Orthoses”). Examination of the GRFs found that medially wedged orthoses increased the laterally directed GRF during the stance phase, suggesting reduced shock attenuation, while laterally wedged orthoses were found to decrease the laterally directed GRF, suggesting increased shock attenuation. A comparison of the kinetics of high-heeled walking gait (Esenyel et al. 2003) compared walking in low-heeled sports shoes to high-heeled dress shoes, showing that when walking in high heels muscle moments and work are reduced at the ankle which resulted in compensatory increases in these variables at the hip and knee.
Ground Reaction Force in the Assessment of Clinical Conditions
Adolescent idiopathic scoliosis (AIS) is a spinal deformity that regularly develops during the period of rapid growth. While the causes and progression of AIS are still not understood, biomechanical factors require careful consideration (Burwell et al. 2000; Stokes 1997). In gait analysis the majority of investigations have focused on kinematic measurements. Therefore, establishing a relationship between kinematic and kinetic data could lead to a better understanding of the etiology of scoliosis.
Both angular and translational asymmetry of the vertebrae of the rib cage and back surface are associated with AIS (Stokes and Gardner-Morse, Stokes and Gardner-Morse 1991). As a result of this structural deformity, the position of the COM and the weight distribution about the lower limb are altered. This would have implications on the three components of the GRF. An analysis of GRF measurements have indicated significant differences between scoliotic and healthy children that was mostly in the mediolateral direction (Giakas et al. 1996). In contrast, an examination of the GRFs revealed no relationship between a gait asymmetry and a scoliotic curve (Schizas et al. 1998).
Another study considered the vertical component of the ground reaction force to report differences in the symmetry indices (SIs) within various reported parameters (Chockalingam et al. 2004). Although the SIs did not exceed the range reported in previous studies, there was a marked difference between the left and right side impulse.
The reported results indicated that the patients with a left compensation curve had a greater SI for a left side impulse and subjects with very little or no compensation had a greater right side impulse. This was considered to be due to the compensation in gait where the subjects compensate on the opposite pelvis/lower limb. Although a previous investigation (Giakas et al. 1996) had indicated that there were no differences in the peak force values in the time domain, the results showed differences in the frequency domain. Chockalingam et al. 2004 were the first group to consider impulse. Since impulse is the rate of change of momentum and represented by product of force and time, if either of the values is higher, the estimated impulse will be higher. While results indicated that the average peak force values are not that different between left and right sides, the interpretation was that the subjects had a higher stance time on the side of major curve in the lumbar or lower thoracic region.
One of the previous investigations (Kim and Eng 2003) looking into the temporal parameters of gait in stroke patients showed asymmetries with swing phase time. However, this investigation did not consider gait speed or the timing of various phases. From the descriptive statistics, it appears that the standard deviations for the vertical force peaks and the peaks of shear forces sum were small, indicating the variability of the gait parameters was relatively low. Parameters showing highest deviation were the loading and unloading rates. Previous studies indicate higher symmetry for vertical forces and lower symmetry for mediolateral forces (Herzog et al. 1989; Kim and Eng 2003). Taking this factor of higher asymmetry for vertical forces into consideration and since the results indicate differences between left and right side impulse, this method could be extended to detect the severity of the curve and gait compensation in scoliotic subjects.
Chockalingam et al. (2004) while highlighting the relationship between the side of the scoliotic curve and impulse showcased the value of using kinetic parameters in developing further understanding of the pathogenesis and etiology of scoliosis and similar conditions.
Recent research (Park et al. 2016) identified that asymmetry indices of GRF magnitudes in walking positively correlated with adjusted Cobb’s angle and maximum Cobb’s angle, while asymmetry indices of GRF time variables positively correlated with pelvic tilt. (For further information please refer to the chapter titled: “Impact of Scoliosis on Gait”).
People with cerebral palsy (CP) often experience difficulty in walking. These individuals can display difficulty in supporting their bodyweight during the late stance phase of gait and utilize compensatory mechanisms to prevent collapse of the affected limb (Williams et al. 2011). While it has been shown that spatiotemporal parameters in this population are reproducible measures, only selected GRF parameters (vertical peak force in terminal stance and terminal stance time) have shown acceptable stability and reproducibility (White et al. 1999).
Traditionally clinical gait analysis solely consists of the assessment of straight-line walking; however recent research has examined the differences in kinematic and kinetics between typically developing children and children with CP during turning tasks (Dixon et al. 2014b, 2016). Significant differences were evident between the typically developing children and those with CP for a number of spatiotemporal parameters, and in many individuals, the intra-subject differences between straight-line walking and turning gait were larger in the children with CP than the typically developing children. The authors propose that turning gait may be a better discriminant of pathology than straight-line walking and could be used to improve the management of gait abnormalities (see also “Swing Phase Problems in Cerebral Palsy,” “Strength Related Stance Phase Problems in Cerebral Palsy,” “Foot and Ankle Motion in Cerebral Palsy”).
Multiple lower extremity joints can be affected by stroke resulting in individuals experiencing gait abnormalities poststroke. Anterior GRFs in the nonparetic and paretic limbs of individuals’ poststroke are lower than those of healthy individuals, while medial GRFs remain unaffected by stroke and lateral GRF shows some differences which are dependent on the side of lesion (Sharma et al. 2015). Examination of muscle activity during gait suggests the reduction in anterior GRF is related to exaggerated flexor muscle activity which may counteract the effects of the plantar flexors by offloading the leg (Turns et al. 2007). Gait retraining in this population has been shown to increase the GRFs, but asymmetry between the limbs may remain (Hesse et al. 1994). In this population more symmetrical weight bearing is related to more symmetrical temporal but not distance measures during gait (Kim and Eng 2003).
Poststroke individuals are found to increase nonparetic propulsive forces when changing walking speed; however, with gait retraining increases in paretic propulsive forces can be observed which contribute to increased self-selected walking speeds (Hsiao et al. (2016). Recent research has shown that fast treadmill walking in combination with function electrical stimulation (FES) showed improvement in peak anterior ground reaction force when compared to self-selected walking speed with FES (Kesar et al. 2011b), suggesting its potential in gait retraining. (For further information please refer to the chapter titled: “Gait Disorders in Persons After Stroke”.)
The combined effects of skeletal muscle weakness, sensory disturbances, spasticity, gait ataxia, and reduction in aerobic capacity lead to gait abnormalities in this population (Rodgers et al. 1999). Research into gait classifications in this population is limited; recent research found a number of variables (taken from 2D gait analysis, EMG, and GRFs) that suggest insufficient ankle push-off in this population (Kempen et al. 2016). Frequency content analysis has identified a lower frequency content in this population when compared to healthy controls, suggesting lesser vertical oscillation of the center of gravity (Wundeman et al. 2011).
Various treatment interventions are used which aim to improve gait in these individuals. A 6-month aerobic training program was found to have minimal effect on gait abnormalities (Rodgers et al. 1999). While the use of textured insoles has been shown to alter gait patterns, their contribution to improving the gait pattern with sufficient propulsion from the ankle plantarflexors is uncertain (Kelleher et al. 2010). (For further information please refer to the chapter titled: “Gait and Multiple Sclerosis”.)
The majority of scientific and clinical studies using force plates and GRF are of gait analysis. Force plates are an integral part of any gait analysis protocol, and the data is used for analyzing the gait pattern and the development of effective clinical management.
One also needs to appreciate that the force plates and GRF have also been used in a wide range of medical and clinical applications, other than gait analysis. These include the examination of postural sway during quiet standing, for example, in elderly patients (Patla et al. 1992), the initiation of stepping (Patla et al. 1993), the study of standing up in the elderly (Ikeda et al. 1991), and the analysis of stair climbing (Andriacchi et al. 1980). Force plates as a technology have also been found to be useful for nonmedical applications. For example, they are used in ergonomics, in car impact tests, and in studies of the biomechanics of equine gait. While GRFs are commonly used in sports to help optimize performance, force plates and reaction forces have even been used on the space shuttle to measure astronauts’ ability to apply forces and moments in a weightless environment.
As such, as indicated within this chapter, GRF is an essential part of any clinical gait analysis and contributes not only to the description of gait in the time domain but also to the assessment of joint moments. Overall, GRF is a crucial part of both surgical and conservative clinical management involving gait.
- Burwell RG, Dangerfield PH, Lowe TG, Margulies JY (2000) Etiology of adolescent idiopathic scoliosis, State of the art reviews. Hanley & Belfus Inc., PhiladelphiaGoogle Scholar
- Davis BL, de Vasconcellos AS, Lundin TM (1997) Uncertainty in 3-D joint moments associated with human gait. In: Proceedings of the XVI congress of the international society of biomechanics. University of Tokyo, Tokyo, p 136Google Scholar
- Gage JR, Koop SE (1995) Clinical gait analysis: application to management of cerebral palsy. In: Allard P, Stokes IAF, Blanchi JP (eds) Three dimensional analysis of human movement. Human Kinetics. Champaign, IL, pp 349–362Google Scholar
- Gehlsen G, Beekman K, Assmann N, Winant D, Seidle M, Carter A (1986) Gait characteristics in multiple sclerosis: progressive changes and effects on parameters. Arch Phys Med Rehabil 67(8):536–539Google Scholar
- Herzog W, Nigg BM, Read LJ, Olsson E (1989) Asymmetries in ground reaction force patterns in normal human gait. Med Sci Sports Exerc 21:10–114Google Scholar
- Hsiao H, Awad LN, Palmer JA, Higginson JS, Binder-Macleod SA (2016) Contribution of paretic and nonparetic limb peak propulsive forces to changes in walking speed in individuals poststroke. Neurorehabil Neural Repair 30(8):743–52Google Scholar
- Koozekanani SH, Balmaseda MT Jr, Fatehi MT, Lowney ED (1987) Ground reaction forces during ambulation in parkinsonism: pilot study. Arch Phys Med Rehabil 68(1):28–30Google Scholar
- Lulić TJ, Susić A, Kodvanj J (2008) Effects of arm swing on mechanical parameters of human gait. Coll Antropol 32(3):869–873Google Scholar
- Patla AE, Frank JS, Winter DA (1992) Balance control in the elderly: Implications for clinical assessment and rehabilitation. Can J Public Health 83(Suppl 2):S29–S33Google Scholar
- Perry J, Burnfield J (2010) Gait analysis: normal and pathological function, 2nd edn. SLACK Inc., ThorofareGoogle Scholar
- Rodgers MM, Mulcare JA, King DL, Mathews T, Gupta SC, Glaser RM (1999) Gait characteristics of individuals with multiple sclerosis before and after a 6-month aerobic training program. J Rehabil Res Dev 36(2):183–188Google Scholar
- Szczerbik E, Krawczyk M, Syczewska M (2014) Ground reaction force analysed with correlation coefficient matrix in group of stroke patients. Acta Bioeng Biomech 16(2):3–9Google Scholar
- Vaughan CL, Davis BL, O’Connor J (1992) Gait analysis laboratory. Human Kinetics, ChampaignGoogle Scholar
- Whiting WC, Zernicke RF (1998) Biomechanics of musculoskeletal injury. Human Kinet:41–85Google Scholar
- Winter DA (1990) Biomechanics and motor control of human movement. Wiley, New YorkGoogle Scholar