543551 research-article2014
POI0010.1177/0309364614543551Prosthetics and Orthotics InternationalFatone et al.
INTERNATIONAL SOCIETY FOR PROSTHETICS AND ORTHOTICS
Original Research Report
A three-dimensional model to assess the effect of ankle joint axis misalignments in ankle–foot orthoses
Prosthetics and Orthotics International 1–7 © The International Society for Prosthetics and Orthotics 2014 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav DOI: 10.1177/0309364614543551 poi.sagepub.com
Stefania Fatone, William Brett Johnson and Kerice Tucker
Abstract Background: Misalignment of an articulated ankle–foot orthosis joint axis with the anatomic joint axis may lead to discomfort, alterations in gait, and tissue damage. Theoretical, two-dimensional models describe the consequences of misalignments, but cannot capture the three-dimensional behavior of ankle–foot orthosis use. Objectives: The purpose of this project was to develop a model to describe the effects of ankle–foot orthosis ankle joint misalignment in three dimensions. Study design: Computational simulation. Methods: Three-dimensional scans of a leg and ankle–foot orthosis were incorporated into a link segment model where the ankle–foot orthosis joint axis could be misaligned with the anatomic ankle joint axis. The leg/ankle–foot orthosis interface was modeled as a network of nodes connected by springs to estimate interface pressure. Motion between the leg and ankle–foot orthosis was calculated as the ankle joint moved through a gait cycle. Results: While the three-dimensional model corroborated predictions of the previously published two-dimensional model that misalignments in the anterior -posterior direction would result in greater relative motion compared to misalignments in the proximal -distal direction, it provided greater insight showing that misalignments have asymmetrical effects. Conclusions: The three-dimensional model has been incorporated into a freely available computer program to assist others in understanding the consequences of joint misalignments. Clinical relevance Models and simulations can be used to gain insight into functioning of systems of interest. We have developed a threedimensional model to assess the effect of ankle joint axis misalignments in ankle–foot orthoses. The model has been incorporated into a freely available computer program to assist understanding of trainees and others interested in orthotics. Keywords Ankle foot orthosis, model Date received: 24 March 2014; accepted: 18 June 2014
Background Accurate alignment of the mechanical joint axis with respect to the anatomic joint axis is an important principle in the fabrication of articulated ankle–foot orthoses (AFOs).1–4 Bottlang et al.5 showed that misaligning an external mechanical joint axis about a cadaver ankle increased the mechanical energy needed to move the ankle. They reported that translating the external mechanical axis 5 mm from the anatomic axis could double the amount of work needed to move the ankle over a range from 15° dorsiflexion to 25° plantar flexion. Similar increases in energy
may result from relative motion between an AFO and leg. When orthotic and anatomic ankle joints are misaligned, additional work is required in the deformation of the AFO Department of Physical Medicine and Rehabilitation, Feinberg School of Medicine, Prosthetics-Orthotics Center, Northwestern University, Chicago, IL, USA Corresponding author: Stefania Fatone, Northwestern University, Chicago, IL 60611, USA. Email: [email protected]
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or soft tissues as they move with respect to each other. Deformation of the AFO increases friction in the mechanical joints, which requires even more energy, and deforming forces applied to the soft tissues of the leg may stretch tendons and ligaments around the ankle and increase resistance to motion.5 Increased work in moving the ankle and pressures applied to soft tissues through deforming forces may cause discomfort, gait deviations, and/or tissue damage.5,6 An understanding of the effects of joint misalignments would guide orthotists in minimizing their potentially deleterious effects. Orthotic joint axis misalignment consists of two components: linear (anterior–posterior and proximal–distal) and angular (transverse and coronal plane) misalignments.1 Previous theoretical work described the hypothetical relative motion created by linear joint misalignments.7 Fatone and Hansen8 further explored these ideas using a two-dimensional (2D) model based on a sliding linkage, showing that anterior–posterior misalignments resulted in greater relative motion between the AFO and limb than proximal–distal misalignments. While this information is useful, it is limited to the sagittal plane, but ankle motion and AFO joint misalignments also occur outside the sagittal plane. Modeling axis misalignments in three dimensions would yield greater insights about how misalignments affect motion of the AFO with respect to the leg. Hence, the aim of this project was to develop a computer-based three-dimensional (3D) model that would simulate the effects of orthotic ankle axis misalignments. The predictions of the 3D model were compared to the previously published 2D model6 to demonstrate how adding the third dimension affects the predicted outcomes of linear misalignments and to determine to what extent the two models corroborate one another. The proposed 3D model has been incorporated into a freely available computer program for trainees and others interested in orthotics.9
Methods Description of the model A computer simulation was developed using custom MATLAB software (The MathWorks, Nattick, MA) that, over the course of a gait cycle, tracks relative motion between an idealized representation of the lower leg and an AFO caused by 3D misalignments of the mechanical and anatomic joint axes. A link segment model was used to characterize the relative motions of the thigh, lower leg, foot, and AFO. Each leg segment had a reference frame and set of coordinates adapted from Zygote Media Group’s (American Fork, UT) leg model that defined the segment’s surface. The motion of the lower leg and foot were derived by rotating the leg segments relative to one another using published joint
kinematics of able-bodied walking.10 Interactions between the lower leg and AFO were constrained by seven assumptions: 1. anatomic ankle rotations occur about a single axis fixed between the lateral and medial malleoli; 2. the AFO ankle joint is a single axis that rotates freely; 3. the AFO is rigid; 4. the AFO foot shell does not move relative to the anatomic foot; 5. there is no slippage between the AFO and the surface of the leg; 6. the AFO does not alter leg kinematics during gait; 7. the AFO will adopt an ideal joint angle that minimizes the energy of the leg–AFO interface. For implementation of this final assumption, the leg– AFO interface was modeled as a network of corresponding nodes connected by springs between the outer surface of the leg and the inner surface of the AFO. The displacement of the springs was set to zero when the ankle was in the neutral position. The stiffness of these springs varied with their location on the leg to emulate the effect of varying stiffnesses of the different tissues surrounding the leg. For example, anterior points along the tibial crest were assigned an arbitrary high level of stiffness to represent the hard bone close to the surface of the skin, while posterior points overlying the calf muscle belly were assigned an arbitrary lower level of stiffness to represent the more compliant soft tissue. (See online supplemental material for additional information on assignment of stiffness levels.) As the AFO moves relative to the lower leg, the resulting displacement between corresponding nodes stores potential energy within the springs. Energy stored from motion where the AFO moved away from the leg was ignored since the surface of an AFO cannot actually pull on the leg. However, energy stored from motion where the AFO pressed into the leg was used to calculate the total energy of the leg–AFO interface at specific ankle and AFO joint angles. In order to find the ideal AFO angle for a given ankle angle, the total energy of the interface was calculated for a range of AFO joint angles about the anatomic ankle angle, and the AFO angle associated with the lowest energy was identified as the ideal angle.
Description of the program The computer program based on this model operates within two graphical user interface (GUI) windows—one which serves as a control panel (Figure 1(a)) allowing the user to select simulation parameters while the other window displays the output of the simulation using an animation of the lower leg and AFO moving through a gait cycle (Figure 1(b)).
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Figure 1. Screen shots of the downloadable computer program incorporating the proposed three-dimensional model. The program runs in two windows: (a) a control window where the user defines the parameters of the simulation and (b) a display window that shows the results of the simulation. Note that the display window appears in color in the program and color mapping is used to indicate levels of compression of the leg by the AFO. AFO: ankle–foot orthosis.
Using the control panel, the user may vary the position and orientation of the AFO joint axis with respect to the anatomic ankle axis. The program allows the user to input any combination of misalignments by applying a series of rotations and/or translations to the mechanical joint axis of the AFO about the anatomic ankle axis. Misalignments ranging from −20 to +20 mm in the anterior–posterior and proximal–distal directions can be applied to the mechanical axis and the resulting relative motion of the AFO with respect to the lower leg calculated for the ankle angles experienced during normal gait. Relative motion is calculated as the distance between a single tracking point on the AFO and a corresponding tracking point on the lower leg. At a neutral ankle angle (i.e. 90° between lower leg and foot), both points are coincident and located on the long axis of the lower leg at 75% of its length, which is the approximate height of a typical AFO. The difference between the positions of these two points is plotted in the lower portion of the output display (Figure 1(b)). By selecting a check box in the control panel, the AFO can be made invisible during the animation to reveal a color-coded map projected over the lower leg, representing how the surface of the AFO moves with respect to the surface of the leg. Red shades indicate that the AFO moves
into the leg, while blue shades show where the AFO moves away from the leg. This color map can be used to assess where the AFO is likely to compress the leg, providing insights as to the axis configurations that may cause discomfort. (See online supplemental material for an example of the color maps.) Users are also able to vary the speed of the animation, zoom in to show detail, choose different viewing angles, and pick what portion of the gait cycle to animate. Additionally, users may choose from five different AFO designs for simulation (see online supplemental material for images of the AFO designs currently included in the simulation). The computer program can be downloaded for free from the Northwestern University ProstheticsOrthotics Center web site.9
Comparison with 2D model The predictions of the proposed 3D model were compared to those of a previously published 2D model.7 Both models calculated relative displacement between the AFO and lower leg using tracking points located in the same location on the AFO and leg. The absolute magnitudes of these displacements were calculated for each model over the same range of misalignments: ±20 mm in both the
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anterior–posterior and proximal–distal directions. These calculations were repeated over five different ankle angles: 20° and 10° plantar flexion, neutral (0°), and 10° and 20° dorsiflexion. The results of both models were compared for each misalignment and each ankle angle.
Results In comparing the outputs of the 2D and 3D models, Figure 2 clearly shows that the magnitude of the relative displacement between the tracking points on the AFO and leg increased as the magnitude of the misalignment increased. The magnitude of the displacement for any given misalignment also increased as the ankle angle moved away from neutral. Displacements varied more with respect to misalignments in the anterior–posterior direction than those in the proximal–distal direction for both models. While relative displacements caused by proximal–distal misalignments appear fairly symmetrical about the zero line for the 2D model (as shown in both Figures 2 and 3), the 3D model demonstrated asymmetrical behavior: misalignments in the proximal direction yielded different displacements than corresponding misalignments in the opposing, distal direction, dependent on ankle angle. Asymmetries became more pronounced as the ankle angle increased. Figure 3 shows relative motion between the tracking points for both models for proximal–distal misalignments from 20° dorsiflexion to 20° plantar flexion.
Discussion Comparison of the 2D and 3D models suggests that they respond similarly to linear misalignments of the ankle joint axis. Both models predict that the magnitude of tracking point displacement increases as the magnitude of linear misalignments increases and as the ankle angle increases. Additionally, both models show that misalignments in the anterior–posterior direction have a greater effect on tracking point displacement than those in the proximal–distal direction. Since these models are based on different approaches and assumptions, this corroboration provides some confidence in the models’ abilities to predict the behavior of the actual AFO–leg system. Although the models describe similar relationships for linear misalignments and the magnitudes of the predicted tracking point displacements are comparable, the predictions are not exactly the same. This discrepancy is not surprising given that the 3D model includes medial–lateral elements of the displacement, while the 2D model does not. Also, the 2D model simplifies the leg and AFO to two dimensionless points that do not affect one another, while the 3D model represents them as rigid bodies that interact with one another. Interaction between the leg and AFO provides insights as to the effects of joint misalignments that the 2D model cannot describe, such as the asymmetric
response of the relative displacement between the tracking points to misalignments in the proximal–distal direction shown in Figures 2 and 3. Both AFO design and the distribution of different spring stiffnesses in the model affect how the AFO and leg interact and can lead to asymmetric responses to misalignments. The design of the AFO determines the size and shape of the leg–AFO interface, and thus the number of springs used in the model. Asymmetric interface shapes, such as a typical AFO with an open anterior and closed posterior shell, can cause opposing misalignments to engage different numbers of springs. Increasing the number of engaged springs increases the total energy of the leg–AFO interface, and the 3D model changes the AFO joint angle to minimize this energy. These changes affect the displacement between the two tracking points; therefore, misalignments in opposing directions can have asymmetric effects on displacement when the design of the AFO is asymmetric. Asymmetries within the distribution of spring stiffnesses in the model cause similar asymmetric responses. When different regions of the leg have different stiffnesses assigned, opposing misalignments engage springs of differing stiffnesses. The stiffness of a spring is directly proportional to the energy it can store. Therefore, opposing misalignments cause different amounts of energy to be stored within the leg–AFO interface, and different tracking point displacements would result from minimizing these energies. Both the design of the AFO and the distribution of different stiffnesses across the leg contributed to the asymmetric behavior seen in Figure 3. The AFO design featured a proximal anterior band, and the 3D model deviated most from the 2D model when the combination of misalignments and ankle angle caused the AFO to press into the anterior surface of the leg. Since the springs on the anterior surface of the leg have the highest stiffnesses in the model, it is likely that deviations from the 2D model occurred as the 3D model acted to minimize the energy stored within the stiffer springs. Not only do the springs within the 3D model help account for the effects of AFO design and varying tissue stiffness, they can also show the patterns of pressure exerted on the leg for a given misalignment of the AFO axis. The stiffnesses defined in the 3D model can be used to convert these relative displacements into forces, and, assuming the surface area of the leg is constant, these forces indicate relative pressures experienced by different regions on the lower leg. Since pressures on the lower leg may lead to discomfort and tissue injury, the model may provide insights into the clinical consequences of AFO ankle joint misalignment. Currently, the 3D model predicts relative differences in pressure between stiff and compliant regions of the leg. Exact predictions of pressure cannot be made as the
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Figure 2. Three-dimensional surface plots of the absolute value of displacement (Z axis) as it varies with the magnitude of AFO axis misalignments in both the anterior–posterior (Y axis) and proximal–distal directions (X axis). Plots in the 2D column show displacements calculated using the 2D model, and similarly for the 3D column. Plots are shown for −20°, −10°, 0°, 10°, and 20° of ankle angle (negative values indicate plantar flexion angles). Online supplemental material shows a color version of this figure. 2D: two-dimensional; 3D: three-dimensional; AFO: ankle–foot orthosis.
stiffness levels utilized by the model provided approximations of the relative magnitudes but were arbitrary in their absolute values. Given the effects that distribution of stiffnesses within the model can have on calculating the AFO joint angle and predicting the pressures exerted on the leg, incorporating actual leg tissue stiffness is important to
improve model accuracy. Although the stiffnesses of tissues on the anterior surface of the leg have been measured11 and may be incorporated into the model, stiffnesses for other regions are required to meaningfully improve the model’s predictions. Incorporating the viscoelastic properties of tissue would also improve the accuracy of the model
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Figure 3. Plots of displacement over misalignment in the proximal–distal direction for both the 2D (dashed line) and 3D models (solid line). Displacements calculated at (a) 20° of ankle plantar flexion and (b) 20° of ankle dorsiflexion. 2D: two-dimensional; 3D: three-dimensional.
and allow investigation of the effects of walking speed. Additionally, including the mechanical properties of the AFO in the model would eliminate overestimation errors caused by assuming that the AFO is rigid. Future work should focus on including these elements within the model as the measurements become available. Other assumptions within the model can lead to error or limit its applicability. The ankle joint is not a fixed hinge joint as assumed in the model, which may lead to errors in the calculated displacements. Assuming that the AFO joint rotates freely about a fixed axis limits the applicability of this model to AFOs with fixed joints and no mechanical stops. Assuming the AFO does not move with respect to the foot was necessary to make the model tractable; however, it limits model predictions to the maximum possible
values of displacement for the shank and the minimum possible values for the foot. Despite these limitations, the model is able to illustrate general concepts that help understanding of the relationships between relative motion and ankle joint misalignment.
Conclusion The 3D model of the AFO and leg predicted similar behavior in the sagittal plane as the previously proposed 2D model. However, unlike the 2D model, the 3D model has the ability to explore effects of misalignments beyond the sagittal plane constraints of the 2D model and to show how misalignments contribute to pressures exerted on the lower leg. The 3D model can be used in future work to investigate
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Fatone et al. the effect of combinations of these misalignments in more detail. Additionally, by making this model freely available as a downloadable computer program, it may serve as an educational tool for exploring the effects of orthotic ankle joint misalignment on the leg. Acknowledgements The authors wish to acknowledge Andrew Hansen, PhD, for help with initial planning of this project and both Andrew Hansen, PhD, and Steven Gard, PhD, for critical review of the article.
Author contribution All authors contributed equally in the preparation of this article.
Declaration of conflicting interests None declared.
Funding This research was funded by the National Institute on Disability and Rehabilitation Research (NIDRR) of the US Department of Education under Grant No. H133E080009 (principal investigators: Steven Gard and Stefania Fatone). The opinions contained in this publication are those of the grantee and do not necessarily reflect those of the Department of Education.
References 1. Lamoreux LW. UC-BL dual-axis ankle-control system: engineering design. Bull Prosthet Res 1969; 10(11): 146–183.
2. Lehneis HR. Principles of orthotic fit and alignment. In: New York University (ed.) Lower-limb orthotics: including orthotists’ supplement. New York: Prosthetics and Orthotics, New York University Post-Graduate Medical School, 1974, pp. 181–189. 3. Mann RA. Chapter 5: Biomechanics of the foot. In: Bunch WH, Keagy R, Kritter AE, et al. (eds) Atlas of orthotics: biomechanical principles and application. 2nd ed. St. Louis, MO: C.V. Mosby Co., 1985 pp. 112–125. 4. Bowker P, Condie DN, Bader DL, et al. Biomechanical basis of orthotic management. Oxford: ButterworthHeinemann, 1993. 5. Bottlang M, Marsh JL and Brown TD. Articulated external fixation of the ankle: minimizing motion resistance by accurate axis alignment. J Biomech 1999; 32: 63–70. 6. Lehneis HR. Brace alignment considerations. Orthot Prosthet Appl J 1964; 18: 110–114. 7. New York University. Lower-limb orthotics: including orthotists’ supplement. New York: Prosthetics and Orthotics, New York University Post-Graduate Medical School, 1974. 8. Fatone S and Hansen AH. A model to predict the effect of ankle joint misalignment on calf band movement in anklefoot orthoses. Prosthet Orthot Int 2007; 31: 76–87. 9. http://nupoc.northwestern.edu/research/projects/orthotics/ afo3d.html 10. Whittle M. Gait analysis: an introduction. 4th ed. Edinburgh; New York: Butterworth-Heinemann, 2007. 11. Sangeorzan B, Harrington R, Wyss C, et al. Circulatory and mechanical response of skin to loading. J Orthop Res 1989; 7: 425–431.
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POI0010.1177/0309364614543551Prosthetics and Orthotics InternationalFatone et al.
INTERNATIONAL SOCIETY FOR PROSTHETICS AND ORTHOTICS
Original Research Report
A three-dimensional model to assess the effect of ankle joint axis misalignments in ankle–foot orthoses
Prosthetics and Orthotics International 1–7 © The International Society for Prosthetics and Orthotics 2014 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav DOI: 10.1177/0309364614543551 poi.sagepub.com
Stefania Fatone, William Brett Johnson and Kerice Tucker
Abstract Background: Misalignment of an articulated ankle–foot orthosis joint axis with the anatomic joint axis may lead to discomfort, alterations in gait, and tissue damage. Theoretical, two-dimensional models describe the consequences of misalignments, but cannot capture the three-dimensional behavior of ankle–foot orthosis use. Objectives: The purpose of this project was to develop a model to describe the effects of ankle–foot orthosis ankle joint misalignment in three dimensions. Study design: Computational simulation. Methods: Three-dimensional scans of a leg and ankle–foot orthosis were incorporated into a link segment model where the ankle–foot orthosis joint axis could be misaligned with the anatomic ankle joint axis. The leg/ankle–foot orthosis interface was modeled as a network of nodes connected by springs to estimate interface pressure. Motion between the leg and ankle–foot orthosis was calculated as the ankle joint moved through a gait cycle. Results: While the three-dimensional model corroborated predictions of the previously published two-dimensional model that misalignments in the anterior -posterior direction would result in greater relative motion compared to misalignments in the proximal -distal direction, it provided greater insight showing that misalignments have asymmetrical effects. Conclusions: The three-dimensional model has been incorporated into a freely available computer program to assist others in understanding the consequences of joint misalignments. Clinical relevance Models and simulations can be used to gain insight into functioning of systems of interest. We have developed a threedimensional model to assess the effect of ankle joint axis misalignments in ankle–foot orthoses. The model has been incorporated into a freely available computer program to assist understanding of trainees and others interested in orthotics. Keywords Ankle foot orthosis, model Date received: 24 March 2014; accepted: 18 June 2014
Background Accurate alignment of the mechanical joint axis with respect to the anatomic joint axis is an important principle in the fabrication of articulated ankle–foot orthoses (AFOs).1–4 Bottlang et al.5 showed that misaligning an external mechanical joint axis about a cadaver ankle increased the mechanical energy needed to move the ankle. They reported that translating the external mechanical axis 5 mm from the anatomic axis could double the amount of work needed to move the ankle over a range from 15° dorsiflexion to 25° plantar flexion. Similar increases in energy
may result from relative motion between an AFO and leg. When orthotic and anatomic ankle joints are misaligned, additional work is required in the deformation of the AFO Department of Physical Medicine and Rehabilitation, Feinberg School of Medicine, Prosthetics-Orthotics Center, Northwestern University, Chicago, IL, USA Corresponding author: Stefania Fatone, Northwestern University, Chicago, IL 60611, USA. Email: [email protected]
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or soft tissues as they move with respect to each other. Deformation of the AFO increases friction in the mechanical joints, which requires even more energy, and deforming forces applied to the soft tissues of the leg may stretch tendons and ligaments around the ankle and increase resistance to motion.5 Increased work in moving the ankle and pressures applied to soft tissues through deforming forces may cause discomfort, gait deviations, and/or tissue damage.5,6 An understanding of the effects of joint misalignments would guide orthotists in minimizing their potentially deleterious effects. Orthotic joint axis misalignment consists of two components: linear (anterior–posterior and proximal–distal) and angular (transverse and coronal plane) misalignments.1 Previous theoretical work described the hypothetical relative motion created by linear joint misalignments.7 Fatone and Hansen8 further explored these ideas using a two-dimensional (2D) model based on a sliding linkage, showing that anterior–posterior misalignments resulted in greater relative motion between the AFO and limb than proximal–distal misalignments. While this information is useful, it is limited to the sagittal plane, but ankle motion and AFO joint misalignments also occur outside the sagittal plane. Modeling axis misalignments in three dimensions would yield greater insights about how misalignments affect motion of the AFO with respect to the leg. Hence, the aim of this project was to develop a computer-based three-dimensional (3D) model that would simulate the effects of orthotic ankle axis misalignments. The predictions of the 3D model were compared to the previously published 2D model6 to demonstrate how adding the third dimension affects the predicted outcomes of linear misalignments and to determine to what extent the two models corroborate one another. The proposed 3D model has been incorporated into a freely available computer program for trainees and others interested in orthotics.9
Methods Description of the model A computer simulation was developed using custom MATLAB software (The MathWorks, Nattick, MA) that, over the course of a gait cycle, tracks relative motion between an idealized representation of the lower leg and an AFO caused by 3D misalignments of the mechanical and anatomic joint axes. A link segment model was used to characterize the relative motions of the thigh, lower leg, foot, and AFO. Each leg segment had a reference frame and set of coordinates adapted from Zygote Media Group’s (American Fork, UT) leg model that defined the segment’s surface. The motion of the lower leg and foot were derived by rotating the leg segments relative to one another using published joint
kinematics of able-bodied walking.10 Interactions between the lower leg and AFO were constrained by seven assumptions: 1. anatomic ankle rotations occur about a single axis fixed between the lateral and medial malleoli; 2. the AFO ankle joint is a single axis that rotates freely; 3. the AFO is rigid; 4. the AFO foot shell does not move relative to the anatomic foot; 5. there is no slippage between the AFO and the surface of the leg; 6. the AFO does not alter leg kinematics during gait; 7. the AFO will adopt an ideal joint angle that minimizes the energy of the leg–AFO interface. For implementation of this final assumption, the leg– AFO interface was modeled as a network of corresponding nodes connected by springs between the outer surface of the leg and the inner surface of the AFO. The displacement of the springs was set to zero when the ankle was in the neutral position. The stiffness of these springs varied with their location on the leg to emulate the effect of varying stiffnesses of the different tissues surrounding the leg. For example, anterior points along the tibial crest were assigned an arbitrary high level of stiffness to represent the hard bone close to the surface of the skin, while posterior points overlying the calf muscle belly were assigned an arbitrary lower level of stiffness to represent the more compliant soft tissue. (See online supplemental material for additional information on assignment of stiffness levels.) As the AFO moves relative to the lower leg, the resulting displacement between corresponding nodes stores potential energy within the springs. Energy stored from motion where the AFO moved away from the leg was ignored since the surface of an AFO cannot actually pull on the leg. However, energy stored from motion where the AFO pressed into the leg was used to calculate the total energy of the leg–AFO interface at specific ankle and AFO joint angles. In order to find the ideal AFO angle for a given ankle angle, the total energy of the interface was calculated for a range of AFO joint angles about the anatomic ankle angle, and the AFO angle associated with the lowest energy was identified as the ideal angle.
Description of the program The computer program based on this model operates within two graphical user interface (GUI) windows—one which serves as a control panel (Figure 1(a)) allowing the user to select simulation parameters while the other window displays the output of the simulation using an animation of the lower leg and AFO moving through a gait cycle (Figure 1(b)).
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Figure 1. Screen shots of the downloadable computer program incorporating the proposed three-dimensional model. The program runs in two windows: (a) a control window where the user defines the parameters of the simulation and (b) a display window that shows the results of the simulation. Note that the display window appears in color in the program and color mapping is used to indicate levels of compression of the leg by the AFO. AFO: ankle–foot orthosis.
Using the control panel, the user may vary the position and orientation of the AFO joint axis with respect to the anatomic ankle axis. The program allows the user to input any combination of misalignments by applying a series of rotations and/or translations to the mechanical joint axis of the AFO about the anatomic ankle axis. Misalignments ranging from −20 to +20 mm in the anterior–posterior and proximal–distal directions can be applied to the mechanical axis and the resulting relative motion of the AFO with respect to the lower leg calculated for the ankle angles experienced during normal gait. Relative motion is calculated as the distance between a single tracking point on the AFO and a corresponding tracking point on the lower leg. At a neutral ankle angle (i.e. 90° between lower leg and foot), both points are coincident and located on the long axis of the lower leg at 75% of its length, which is the approximate height of a typical AFO. The difference between the positions of these two points is plotted in the lower portion of the output display (Figure 1(b)). By selecting a check box in the control panel, the AFO can be made invisible during the animation to reveal a color-coded map projected over the lower leg, representing how the surface of the AFO moves with respect to the surface of the leg. Red shades indicate that the AFO moves
into the leg, while blue shades show where the AFO moves away from the leg. This color map can be used to assess where the AFO is likely to compress the leg, providing insights as to the axis configurations that may cause discomfort. (See online supplemental material for an example of the color maps.) Users are also able to vary the speed of the animation, zoom in to show detail, choose different viewing angles, and pick what portion of the gait cycle to animate. Additionally, users may choose from five different AFO designs for simulation (see online supplemental material for images of the AFO designs currently included in the simulation). The computer program can be downloaded for free from the Northwestern University ProstheticsOrthotics Center web site.9
Comparison with 2D model The predictions of the proposed 3D model were compared to those of a previously published 2D model.7 Both models calculated relative displacement between the AFO and lower leg using tracking points located in the same location on the AFO and leg. The absolute magnitudes of these displacements were calculated for each model over the same range of misalignments: ±20 mm in both the
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anterior–posterior and proximal–distal directions. These calculations were repeated over five different ankle angles: 20° and 10° plantar flexion, neutral (0°), and 10° and 20° dorsiflexion. The results of both models were compared for each misalignment and each ankle angle.
Results In comparing the outputs of the 2D and 3D models, Figure 2 clearly shows that the magnitude of the relative displacement between the tracking points on the AFO and leg increased as the magnitude of the misalignment increased. The magnitude of the displacement for any given misalignment also increased as the ankle angle moved away from neutral. Displacements varied more with respect to misalignments in the anterior–posterior direction than those in the proximal–distal direction for both models. While relative displacements caused by proximal–distal misalignments appear fairly symmetrical about the zero line for the 2D model (as shown in both Figures 2 and 3), the 3D model demonstrated asymmetrical behavior: misalignments in the proximal direction yielded different displacements than corresponding misalignments in the opposing, distal direction, dependent on ankle angle. Asymmetries became more pronounced as the ankle angle increased. Figure 3 shows relative motion between the tracking points for both models for proximal–distal misalignments from 20° dorsiflexion to 20° plantar flexion.
Discussion Comparison of the 2D and 3D models suggests that they respond similarly to linear misalignments of the ankle joint axis. Both models predict that the magnitude of tracking point displacement increases as the magnitude of linear misalignments increases and as the ankle angle increases. Additionally, both models show that misalignments in the anterior–posterior direction have a greater effect on tracking point displacement than those in the proximal–distal direction. Since these models are based on different approaches and assumptions, this corroboration provides some confidence in the models’ abilities to predict the behavior of the actual AFO–leg system. Although the models describe similar relationships for linear misalignments and the magnitudes of the predicted tracking point displacements are comparable, the predictions are not exactly the same. This discrepancy is not surprising given that the 3D model includes medial–lateral elements of the displacement, while the 2D model does not. Also, the 2D model simplifies the leg and AFO to two dimensionless points that do not affect one another, while the 3D model represents them as rigid bodies that interact with one another. Interaction between the leg and AFO provides insights as to the effects of joint misalignments that the 2D model cannot describe, such as the asymmetric
response of the relative displacement between the tracking points to misalignments in the proximal–distal direction shown in Figures 2 and 3. Both AFO design and the distribution of different spring stiffnesses in the model affect how the AFO and leg interact and can lead to asymmetric responses to misalignments. The design of the AFO determines the size and shape of the leg–AFO interface, and thus the number of springs used in the model. Asymmetric interface shapes, such as a typical AFO with an open anterior and closed posterior shell, can cause opposing misalignments to engage different numbers of springs. Increasing the number of engaged springs increases the total energy of the leg–AFO interface, and the 3D model changes the AFO joint angle to minimize this energy. These changes affect the displacement between the two tracking points; therefore, misalignments in opposing directions can have asymmetric effects on displacement when the design of the AFO is asymmetric. Asymmetries within the distribution of spring stiffnesses in the model cause similar asymmetric responses. When different regions of the leg have different stiffnesses assigned, opposing misalignments engage springs of differing stiffnesses. The stiffness of a spring is directly proportional to the energy it can store. Therefore, opposing misalignments cause different amounts of energy to be stored within the leg–AFO interface, and different tracking point displacements would result from minimizing these energies. Both the design of the AFO and the distribution of different stiffnesses across the leg contributed to the asymmetric behavior seen in Figure 3. The AFO design featured a proximal anterior band, and the 3D model deviated most from the 2D model when the combination of misalignments and ankle angle caused the AFO to press into the anterior surface of the leg. Since the springs on the anterior surface of the leg have the highest stiffnesses in the model, it is likely that deviations from the 2D model occurred as the 3D model acted to minimize the energy stored within the stiffer springs. Not only do the springs within the 3D model help account for the effects of AFO design and varying tissue stiffness, they can also show the patterns of pressure exerted on the leg for a given misalignment of the AFO axis. The stiffnesses defined in the 3D model can be used to convert these relative displacements into forces, and, assuming the surface area of the leg is constant, these forces indicate relative pressures experienced by different regions on the lower leg. Since pressures on the lower leg may lead to discomfort and tissue injury, the model may provide insights into the clinical consequences of AFO ankle joint misalignment. Currently, the 3D model predicts relative differences in pressure between stiff and compliant regions of the leg. Exact predictions of pressure cannot be made as the
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Figure 2. Three-dimensional surface plots of the absolute value of displacement (Z axis) as it varies with the magnitude of AFO axis misalignments in both the anterior–posterior (Y axis) and proximal–distal directions (X axis). Plots in the 2D column show displacements calculated using the 2D model, and similarly for the 3D column. Plots are shown for −20°, −10°, 0°, 10°, and 20° of ankle angle (negative values indicate plantar flexion angles). Online supplemental material shows a color version of this figure. 2D: two-dimensional; 3D: three-dimensional; AFO: ankle–foot orthosis.
stiffness levels utilized by the model provided approximations of the relative magnitudes but were arbitrary in their absolute values. Given the effects that distribution of stiffnesses within the model can have on calculating the AFO joint angle and predicting the pressures exerted on the leg, incorporating actual leg tissue stiffness is important to
improve model accuracy. Although the stiffnesses of tissues on the anterior surface of the leg have been measured11 and may be incorporated into the model, stiffnesses for other regions are required to meaningfully improve the model’s predictions. Incorporating the viscoelastic properties of tissue would also improve the accuracy of the model
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Figure 3. Plots of displacement over misalignment in the proximal–distal direction for both the 2D (dashed line) and 3D models (solid line). Displacements calculated at (a) 20° of ankle plantar flexion and (b) 20° of ankle dorsiflexion. 2D: two-dimensional; 3D: three-dimensional.
and allow investigation of the effects of walking speed. Additionally, including the mechanical properties of the AFO in the model would eliminate overestimation errors caused by assuming that the AFO is rigid. Future work should focus on including these elements within the model as the measurements become available. Other assumptions within the model can lead to error or limit its applicability. The ankle joint is not a fixed hinge joint as assumed in the model, which may lead to errors in the calculated displacements. Assuming that the AFO joint rotates freely about a fixed axis limits the applicability of this model to AFOs with fixed joints and no mechanical stops. Assuming the AFO does not move with respect to the foot was necessary to make the model tractable; however, it limits model predictions to the maximum possible
values of displacement for the shank and the minimum possible values for the foot. Despite these limitations, the model is able to illustrate general concepts that help understanding of the relationships between relative motion and ankle joint misalignment.
Conclusion The 3D model of the AFO and leg predicted similar behavior in the sagittal plane as the previously proposed 2D model. However, unlike the 2D model, the 3D model has the ability to explore effects of misalignments beyond the sagittal plane constraints of the 2D model and to show how misalignments contribute to pressures exerted on the lower leg. The 3D model can be used in future work to investigate
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Fatone et al. the effect of combinations of these misalignments in more detail. Additionally, by making this model freely available as a downloadable computer program, it may serve as an educational tool for exploring the effects of orthotic ankle joint misalignment on the leg. Acknowledgements The authors wish to acknowledge Andrew Hansen, PhD, for help with initial planning of this project and both Andrew Hansen, PhD, and Steven Gard, PhD, for critical review of the article.
Author contribution All authors contributed equally in the preparation of this article.
Declaration of conflicting interests None declared.
Funding This research was funded by the National Institute on Disability and Rehabilitation Research (NIDRR) of the US Department of Education under Grant No. H133E080009 (principal investigators: Steven Gard and Stefania Fatone). The opinions contained in this publication are those of the grantee and do not necessarily reflect those of the Department of Education.
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