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Estimating subsurface shear stress in the neuropathic foot from plantar pressure distribution
696
Abstracts / Clinical Biomechanics 23 (2008) 662–720
tions of the sole were subject to the most load, and the front part when walking down the plane. Higher maximum local pressures were recorded during the movement of a subject in a downward direction along the plane. Contact of the foot surface increased with the increased inclination of the plane, during both ascent and descent by the subjects. Maximum force was inconspicuously lower during the ascent of the subject on an inclined plane. An nearly imperceptible increase was recorded with the increased inclination of this plane. doi:10.1016/j.clinbiomech.2008.03.039 Fig. 1. Impact of the inclination angle on the contact area between foot and surface.
from the base 12 cm), 2–10°500 (distance from the base 24 cm), 3–7°300 (distance from the base 32 cm), 4–14°200 (distance from the base 48 cm), 5–17°500 (distance from the base 60 cm). The markings of individual levels correspond to the levels noted in Fig. 1. With the help of software, values were determined for maximum pressure and its occurrence on the sole of the foot, maximum force and contact with the surface. These values were acquired throughout the entire course of walking, separately for the right foot and the left foot, and also in individual parts of the sole of the foot, which were divided into masks. Results and discussion By monitoring the load at individual levels of an inclined plane during movement of a subject, the following observations were recorded: the contact of the affected surface of the foot with the base increases with the declining angle of the inclined plane (Fig. 1), displayed graphically as a summary of the contact surfaces for the right and left feet. When ascending the plane, the average values for maximum force on the right and left feet (633 ± 138) N and when descending the plane (636 ± 147) N. The highest pressures were recorded during movement down the plane and achieved values of (537 ± 180) kPa. The lowest pressures on the surface occurred during movement on the platform in the nil position (442 ± 139) kPa. Conclusion The occurrence of maximum pressure on the sole of the foot was observed not only with the health status of the foot of individual subjects, but was also affected by the direction of movement along the inclined plane and its angle. During the movement of a subject down the plane, according to the graphic 3D or 2D display system of Emed, it is possible to say that the front and rear sec-
Estimating subsurface shear stress in the neuropathic foot from plantar pressure distribution Dequan Zou, David R. Sinacore, Kathryn L. Bohnert, Michael J. Mueller Program in Physical Therapy, Washington University School of Medicine, St. Louis, MO, USA
Introduction The pressure distribution on the plantar surface of the foot may provide insights into the stresses within the subsurface tissues of patients with diabetes mellitus and peripheral neuropathy who are at risk for skin breakdown. The purposes of this study were to (1) incorporate the theory of potentials with numerical schemes to estimate the stress distribution in the subsurface soft tissue from a measured surface pressure distribution and (2) determine the relationships between peak maximum shear stress (PMSS), depth of PMSS (D_PMSS) and characteristics of the surface pressure distribution. Methods A pressure load on the plantar surface may be characterized by the peak plantar pressure (PPP) and the peak pressure gradient (PPG) which is the spatial change in plantar pressure (Mueller et al., 2005). We assumed that the subsurface tissues of the foot were bounded by an infinite plane (plantar surface) under a pressure distribution p(x, y). The potential functions H(x, y, z) and H1(x, y, z) (harmonic functions satisfying Laplace’s equation) were used to calculate the stress components by Hook’s law assuming small-strain, small-deformation theory of elasticity at any point within the body: 1 oH 1 o2 H 1 o2 H rx ¼ 2v z 2 ð1 2vÞ 2 2p ox oz ox 1 oH 1 o2 H 1 o2 H 2v ry ¼ z 2 ð1 2vÞ 2 2p oy oz oy
Abstracts / Clinical Biomechanics 23 (2008) 662–720
1 oH 1 o2 H 1 z 2 rz ¼ 2p oz oz 2 1 o H1 o2 H z þ ð1 2vÞ sxy ¼ 2p oxoy oxoy
697
may help investigators predict skin injury more than using PPP alone. Additional research is required to determine the validity of using surface pressure distribution to estimate subsurface stress.
syz ¼
1 o2 H 1 z 2p oyoz
Acknowledgements
szx ¼
1 o2 H 1 z 2p oxoz
Funded by NCMRR, NIH (RO1 HD36895) and NIDDK (RO1 DK59224).
where m is the Poisson’s ratio. For the case of an array of uniform pressures on rectangular areas (measured by the insole or platform sensors), the complete solution is obtainable in closed form and by the method of superposition. A computer program has been developed by means of the potential theory to estimate the stress components (PMSS and D_PMSS) in the subsurface soft tissues. Plantar pressure data during self-selected walking were collected using an EMED-ST P-2 platform sampled at 70 HZ on 12 subjects (6 males/6 females, mean age 54 ± 8 years, mean BMI 34.1 ± 4.7 kg/m2) with Type 2 DM mean duration 12 ± 9 years, PN, and a history of a plantar ulcer.
References Mueller et al., 2005. Diabetes Care 28, 2908–2912. doi:10.1016/j.clinbiomech.2008.03.040
Short-term and long-term follow-up of patients with diabetes mellitus with minor amputations Vadim B. Bregovsky a, Tatiana L. Tsvetkova b a b
City Diabetological Centre, St.-Petersburg, Russia Novel SPb, St.-Petersburg, Russia
Results and discussion The calculated PMSS vs. D_PMSS in the subsurface tissue at the forefoot and the rearfoot for a typical subject is shown in Fig. 1. PPP and PPG affect the stresses in the subsurface tissues. PMSS was highly correlated with PPP (r = 0.98) and with PPG (r = 0.95). Depth of the maximum PMSS was negatively correlated with the PPP (r = 0.82) and with the PPG (r = 0.87). According to these estimates, a surface pressure distribution that contains high PPP and high PPG will lead to relatively high maximal PMSS that are located near the skin surface and can contribute to skin breakdown. The influence of the pressure distribution characteristics (PPP and PPG) on the subsurface stress distribution at the different foot regions appear to be substantial. We speculate that PPG, the predicted maximal PMSS and its location to the plantar surface,
Peak maximum shear stress (PMSS) Forefoot: PPP = 845 kPa, PPG = 95 kPa/mm Rearfoot: PPP = 410 kPa, PPG = 15kPa/mm
PMSS @ forefoot
PMSS @ rearfoot
PMSS (kPa)
200 150 100 50 0 0
5
10 15 Depth of PMSS (mm)
20
25
Fig. 1. PMSS and depth of PMSS in subsurface tissue estimated from surface pressure distribution.
Introduction Patients with amputations mostly continue to develop plantar ulcers with subsequent new amputations. The aim of this study is to determine the correlation between pressure distribution parameters measured in different time periods in patients with toes amputations.
Methods Thirty patients, 10 men and 20 women (age 58 ± 11 years, BMI 27 ± 6 kg/m2), diagnosed with diabetes mellitus with toes amputations were examined several times. All patients were divided into three groups in dependence on definite toe amputation: big toe (gr. 1–10 patients), second toe (gr. 2–8 patients), any or combination of lateral toes (gr. 3–12 patients). Short-term (ST) and long-term (LT) periods between the measurements were equal to 26 ± 7 and 56 ± 10 months correspondingly. Plantar pressure distributions were performed with emed-AT 25 system (Novel, Munich, Germany). Five dynamic records of each foot were made with first step protocol. Novel database diabetes was used to collect clinical and pressure measurement data. Peak pressure (PP), mean pressure (MP), maximum force (MF), force–time integral (FTI), and contact time (CT) were calculated in novel-projects with novel automask for hindfoot (HF), midfoot (MF), five metatarsal heads (MH1–MH5), big toe (T1), second toe (T2), and lateral toes (T345). Parameters were calculated for each subject. The relationship between the pressure distribution parameters under the foot areas in different
Abstracts / Clinical Biomechanics 23 (2008) 662–720
tions of the sole were subject to the most load, and the front part when walking down the plane. Higher maximum local pressures were recorded during the movement of a subject in a downward direction along the plane. Contact of the foot surface increased with the increased inclination of the plane, during both ascent and descent by the subjects. Maximum force was inconspicuously lower during the ascent of the subject on an inclined plane. An nearly imperceptible increase was recorded with the increased inclination of this plane. doi:10.1016/j.clinbiomech.2008.03.039 Fig. 1. Impact of the inclination angle on the contact area between foot and surface.
from the base 12 cm), 2–10°500 (distance from the base 24 cm), 3–7°300 (distance from the base 32 cm), 4–14°200 (distance from the base 48 cm), 5–17°500 (distance from the base 60 cm). The markings of individual levels correspond to the levels noted in Fig. 1. With the help of software, values were determined for maximum pressure and its occurrence on the sole of the foot, maximum force and contact with the surface. These values were acquired throughout the entire course of walking, separately for the right foot and the left foot, and also in individual parts of the sole of the foot, which were divided into masks. Results and discussion By monitoring the load at individual levels of an inclined plane during movement of a subject, the following observations were recorded: the contact of the affected surface of the foot with the base increases with the declining angle of the inclined plane (Fig. 1), displayed graphically as a summary of the contact surfaces for the right and left feet. When ascending the plane, the average values for maximum force on the right and left feet (633 ± 138) N and when descending the plane (636 ± 147) N. The highest pressures were recorded during movement down the plane and achieved values of (537 ± 180) kPa. The lowest pressures on the surface occurred during movement on the platform in the nil position (442 ± 139) kPa. Conclusion The occurrence of maximum pressure on the sole of the foot was observed not only with the health status of the foot of individual subjects, but was also affected by the direction of movement along the inclined plane and its angle. During the movement of a subject down the plane, according to the graphic 3D or 2D display system of Emed, it is possible to say that the front and rear sec-
Estimating subsurface shear stress in the neuropathic foot from plantar pressure distribution Dequan Zou, David R. Sinacore, Kathryn L. Bohnert, Michael J. Mueller Program in Physical Therapy, Washington University School of Medicine, St. Louis, MO, USA
Introduction The pressure distribution on the plantar surface of the foot may provide insights into the stresses within the subsurface tissues of patients with diabetes mellitus and peripheral neuropathy who are at risk for skin breakdown. The purposes of this study were to (1) incorporate the theory of potentials with numerical schemes to estimate the stress distribution in the subsurface soft tissue from a measured surface pressure distribution and (2) determine the relationships between peak maximum shear stress (PMSS), depth of PMSS (D_PMSS) and characteristics of the surface pressure distribution. Methods A pressure load on the plantar surface may be characterized by the peak plantar pressure (PPP) and the peak pressure gradient (PPG) which is the spatial change in plantar pressure (Mueller et al., 2005). We assumed that the subsurface tissues of the foot were bounded by an infinite plane (plantar surface) under a pressure distribution p(x, y). The potential functions H(x, y, z) and H1(x, y, z) (harmonic functions satisfying Laplace’s equation) were used to calculate the stress components by Hook’s law assuming small-strain, small-deformation theory of elasticity at any point within the body: 1 oH 1 o2 H 1 o2 H rx ¼ 2v z 2 ð1 2vÞ 2 2p ox oz ox 1 oH 1 o2 H 1 o2 H 2v ry ¼ z 2 ð1 2vÞ 2 2p oy oz oy
Abstracts / Clinical Biomechanics 23 (2008) 662–720
1 oH 1 o2 H 1 z 2 rz ¼ 2p oz oz 2 1 o H1 o2 H z þ ð1 2vÞ sxy ¼ 2p oxoy oxoy
697
may help investigators predict skin injury more than using PPP alone. Additional research is required to determine the validity of using surface pressure distribution to estimate subsurface stress.
syz ¼
1 o2 H 1 z 2p oyoz
Acknowledgements
szx ¼
1 o2 H 1 z 2p oxoz
Funded by NCMRR, NIH (RO1 HD36895) and NIDDK (RO1 DK59224).
where m is the Poisson’s ratio. For the case of an array of uniform pressures on rectangular areas (measured by the insole or platform sensors), the complete solution is obtainable in closed form and by the method of superposition. A computer program has been developed by means of the potential theory to estimate the stress components (PMSS and D_PMSS) in the subsurface soft tissues. Plantar pressure data during self-selected walking were collected using an EMED-ST P-2 platform sampled at 70 HZ on 12 subjects (6 males/6 females, mean age 54 ± 8 years, mean BMI 34.1 ± 4.7 kg/m2) with Type 2 DM mean duration 12 ± 9 years, PN, and a history of a plantar ulcer.
References Mueller et al., 2005. Diabetes Care 28, 2908–2912. doi:10.1016/j.clinbiomech.2008.03.040
Short-term and long-term follow-up of patients with diabetes mellitus with minor amputations Vadim B. Bregovsky a, Tatiana L. Tsvetkova b a b
City Diabetological Centre, St.-Petersburg, Russia Novel SPb, St.-Petersburg, Russia
Results and discussion The calculated PMSS vs. D_PMSS in the subsurface tissue at the forefoot and the rearfoot for a typical subject is shown in Fig. 1. PPP and PPG affect the stresses in the subsurface tissues. PMSS was highly correlated with PPP (r = 0.98) and with PPG (r = 0.95). Depth of the maximum PMSS was negatively correlated with the PPP (r = 0.82) and with the PPG (r = 0.87). According to these estimates, a surface pressure distribution that contains high PPP and high PPG will lead to relatively high maximal PMSS that are located near the skin surface and can contribute to skin breakdown. The influence of the pressure distribution characteristics (PPP and PPG) on the subsurface stress distribution at the different foot regions appear to be substantial. We speculate that PPG, the predicted maximal PMSS and its location to the plantar surface,
Peak maximum shear stress (PMSS) Forefoot: PPP = 845 kPa, PPG = 95 kPa/mm Rearfoot: PPP = 410 kPa, PPG = 15kPa/mm
PMSS @ forefoot
PMSS @ rearfoot
PMSS (kPa)
200 150 100 50 0 0
5
10 15 Depth of PMSS (mm)
20
25
Fig. 1. PMSS and depth of PMSS in subsurface tissue estimated from surface pressure distribution.
Introduction Patients with amputations mostly continue to develop plantar ulcers with subsequent new amputations. The aim of this study is to determine the correlation between pressure distribution parameters measured in different time periods in patients with toes amputations.
Methods Thirty patients, 10 men and 20 women (age 58 ± 11 years, BMI 27 ± 6 kg/m2), diagnosed with diabetes mellitus with toes amputations were examined several times. All patients were divided into three groups in dependence on definite toe amputation: big toe (gr. 1–10 patients), second toe (gr. 2–8 patients), any or combination of lateral toes (gr. 3–12 patients). Short-term (ST) and long-term (LT) periods between the measurements were equal to 26 ± 7 and 56 ± 10 months correspondingly. Plantar pressure distributions were performed with emed-AT 25 system (Novel, Munich, Germany). Five dynamic records of each foot were made with first step protocol. Novel database diabetes was used to collect clinical and pressure measurement data. Peak pressure (PP), mean pressure (MP), maximum force (MF), force–time integral (FTI), and contact time (CT) were calculated in novel-projects with novel automask for hindfoot (HF), midfoot (MF), five metatarsal heads (MH1–MH5), big toe (T1), second toe (T2), and lateral toes (T345). Parameters were calculated for each subject. The relationship between the pressure distribution parameters under the foot areas in different