{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,3]],"date-time":"2026-10-03T00:17:46Z","timestamp":1790986666135,"version":"4.1.0"},"reference-count":45,"publisher":"ASME International","issue":"11","content-domain":{"domain":["asmedigitalcollection.asme.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2012,11,1]]},"abstract":"<jats:p>Unilateral below-knee amputees develop abnormal gait characteristics that include bilateral asymmetries and an elevated metabolic cost relative to non-amputees. In addition, long-term prosthesis use has been linked to an increased prevalence of joint pain and osteoarthritis in the intact leg knee. To improve amputee mobility, prosthetic feet that utilize elastic energy storage and return (ESAR) have been designed, which perform important biomechanical functions such as providing body support and forward propulsion. However, the prescription of appropriate design characteristics (e.g., stiffness) is not well-defined since its influence on foot function and important in vivo biomechanical quantities such as metabolic cost and joint loading remain unclear. The design of feet that improve these quantities could provide considerable advancements in amputee care. Therefore, the purpose of this study was to couple design optimization with dynamic simulations of amputee walking to identify the optimal foot stiffness that minimizes metabolic cost and intact knee joint loading. A musculoskeletal model and distributed stiffness ESAR prosthetic foot model were developed to generate muscle-actuated forward dynamics simulations of amputee walking. Dynamic optimization was used to solve for the optimal muscle excitation patterns and foot stiffness profile that produced simulations that tracked experimental amputee walking data while minimizing metabolic cost and intact leg internal knee contact forces. Muscle and foot function were evaluated by calculating their contributions to the important walking subtasks of body support, forward propulsion and leg swing. The analyses showed that altering a nominal prosthetic foot stiffness distribution by stiffening the toe and mid-foot while making the ankle and heel less stiff improved ESAR foot performance by offloading the intact knee during early to mid-stance of the intact leg and reducing metabolic cost. The optimal design also provided moderate braking and body support during the first half of residual leg stance, while increasing the prosthesis contributions to forward propulsion and body support during the second half of residual leg stance. Future work will be directed at experimentally validating these results, which have important implications for future designs of prosthetic feet that could significantly improve amputee care.<\/jats:p>","DOI":"10.1115\/1.4007824","type":"journal-article","created":{"date-parts":[[2012,10,11]],"date-time":"2012-10-11T11:20:50Z","timestamp":1349954450000},"update-policy":"https:\/\/doi.org\/10.1115\/crossmarkpolicy-asme","source":"Crossref","is-referenced-by-count":109,"title":["Optimization of Prosthetic Foot Stiffness to Reduce Metabolic Cost and Intact Knee Loading During Below-Knee Amputee Walking: A Theoretical Study"],"prefix":"10.1115","volume":"134","author":[{"given":"Nicholas P.","family":"Fey","sequence":"first","affiliation":[{"name":"Department of Mechanical Engineering, The University of Texas at Austin, Austin, TX 78712"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Glenn K.","family":"Klute","sequence":"additional","affiliation":[{"name":"Department of Veterans Affairs, Puget Sound Health Care System, Seattle, WA 98108"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Richard R.","family":"Neptune","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, The University of Texas at Austin, Austin, TX 78712"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"33","published-online":{"date-parts":[[2012,10,26]]},"reference":[{"key":"2019100411304677700_c1","doi-asserted-by":"publisher","first-page":"126","DOI":"10.1016\/S0966-6362(97)01112-0","article-title":"Lower Extremity Kinematic and Kinetic Adaptations in Unilateral Below-Knee Amputees During Walking","volume":"6","author":"Sanderson","journal-title":"Gait and Posture"},{"issue":"5","key":"2019100411304677700_c2","doi-asserted-by":"publisher","first-page":"361","DOI":"10.1016\/0021-9290(88)90142-X","article-title":"Biomechanics of Below-Knee Amputee Gait","volume":"21","author":"Winter","journal-title":"J. Biomech."},{"issue":"1","key":"2019100411304677700_c3","doi-asserted-by":"crossref","first-page":"42","DOI":"10.2106\/00004623-197658010-00007","article-title":"Energy Cost of Walking of Amputees: The Influence of Level of Amputation","volume":"58","author":"Waters","journal-title":"J. Bone Jt. Surg. Am."},{"issue":"8","key":"2019100411304677700_c4","doi-asserted-by":"crossref","first-page":"898","DOI":"10.1093\/ptj\/57.8.898","article-title":"Accelerographic, Temporal, and Distance Gait Factors in Below-Knee Amputees","volume":"57","author":"Robinson","journal-title":"Phys. Ther."},{"issue":"1","key":"2019100411304677700_c5","doi-asserted-by":"publisher","first-page":"81","DOI":"10.1191\/0269215505cr819oa","article-title":"Chronic Low Back Pain in Traumatic Lower Limb Amputees","volume":"19","author":"Kulkarni","journal-title":"Clin. Rehabil."},{"issue":"10","key":"2019100411304677700_c6","doi-asserted-by":"publisher","first-page":"1910","DOI":"10.1016\/j.apmr.2005.03.031","article-title":"Phantom Pain, Residual Limb Pain, and Back Pain in Amputees: Results of a National Survey","volume":"86","author":"Ephraim","journal-title":"Arch. Phys. Med. Rehabil."},{"key":"2019100411304677700_c7","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1097\/00003086-199904000-00005","article-title":"Phantom Limb, Residual Limb, and Back Pain After Lower Extremity Amputations","volume":"361","author":"Smith","journal-title":"Clin. Orthop. Relat. Res."},{"issue":"3","key":"2019100411304677700_c8","doi-asserted-by":"publisher","first-page":"252","DOI":"10.1136\/ard.37.3.252","article-title":"Bone and Joint Changes in Lower Limb Amputees","volume":"37","author":"Burke","journal-title":"Ann. Rheum. Dis."},{"issue":"1","key":"2019100411304677700_c9","doi-asserted-by":"publisher","first-page":"15","DOI":"10.1682\/JRRD.2006.11.0147","article-title":"Review of Secondary Physical Conditions Associated With Lower-Limb Amputation and Long-Term Prosthesis Use","volume":"45","author":"Gailey","journal-title":"J. Rehabil. Res. Dev."},{"issue":"11","key":"2019100411304677700_c10","doi-asserted-by":"publisher","first-page":"1387","DOI":"10.1016\/S0021-9290(01)00105-1","article-title":"Contributions of the Individual Ankle Plantar Flexors to Support, Forward Progression and Swing Initiation During Walking","volume":"34","author":"Neptune","journal-title":"J. Biomech."},{"issue":"1","key":"2019100411304677700_c11","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1682\/JRRD.2013.01.0024","article-title":"Transtibial Energy-Storage-and-Return Prosthetic Devices: A Review of Energy Concepts and a Proposed Nomenclature","volume":"39","author":"Hafner","journal-title":"J. Rehabil. Res. Dev."},{"issue":"14","key":"2019100411304677700_c12","doi-asserted-by":"publisher","first-page":"2623","DOI":"10.1016\/j.jbiomech.2005.08.017","article-title":"Muscles That Support the Body Also Modulate Forward Progression During Walking","volume":"39","author":"Liu","journal-title":"J. Biomech."},{"issue":"2","key":"2019100411304677700_c13","doi-asserted-by":"publisher","first-page":"194","DOI":"10.1016\/S0966-6362(03)00062-6","article-title":"Muscle Force Redistributes Segmental Power for Body Progression During Walking","volume":"19","author":"Neptune","journal-title":"Gait and Posture"},{"issue":"7","key":"2019100411304677700_c14","doi-asserted-by":"publisher","first-page":"528","DOI":"10.1016\/S0268-0033(00)00005-X","article-title":"Knee Joint Loading in Forward versus Backward Pedaling: Implications for Rehabilitation Strategies","volume":"15","author":"Neptune","journal-title":"Clin. Biomech. (Bristol, Avon)"},{"issue":"Pt 5","key":"2019100411304677700_c15","doi-asserted-by":"publisher","first-page":"738","DOI":"10.1242\/jeb.023267","article-title":"The Relationships Between Muscle, External, Internal and Joint Mechanical Work During Normal Walking","volume":"212","author":"Sasaki","journal-title":"J. Exp. Biol."},{"issue":"14","key":"2019100411304677700_c16","doi-asserted-by":"publisher","first-page":"2780","DOI":"10.1016\/j.jbiomech.2010.06.011","article-title":"Individual Muscle Contributions to the Axial Knee Joint Contact Force During Normal Walking","volume":"43","author":"Sasaki","journal-title":"J. Biomech."},{"issue":"11","key":"2019100411304677700_c17","doi-asserted-by":"publisher","first-page":"1948","DOI":"10.1249\/01.mss.0000180404.86078.ff","article-title":"Muscle, Ligament, and Joint-Contact Forces at the Knee During Walking","volume":"37","author":"Shelburne","journal-title":"Med. Sci. Sports Exercise"},{"issue":"50","key":"2019100411304677700_c18","doi-asserted-by":"publisher","first-page":"1329","DOI":"10.1098\/rsif.2010.0084","article-title":"Stance and Swing Phase Costs in Human Walking","volume":"7","author":"Umberger","journal-title":"J. R. Soc., Interface"},{"issue":"10","key":"2019100411304677700_c19","doi-asserted-by":"publisher","first-page":"1025","DOI":"10.1016\/j.clinbiomech.2011.06.007","article-title":"The Influence of Energy Storage and Return Foot Stiffness on Walking Mechanics and Muscle Activity in Below-Knee Amputees","volume":"26","author":"Fey","journal-title":"Clin. Biomech. (Bristol, Avon)"},{"issue":"3","key":"2019100411304677700_c20","doi-asserted-by":"publisher","first-page":"298","DOI":"10.1016\/j.clinbiomech.2010.10.003","article-title":"The Effects of Prosthetic Ankle Dorsiflexion and Energy Return on Below-Knee Amputee Leg Loading","volume":"26","author":"Ventura","journal-title":"Clin. Biomech. (Bristol, Avon)"},{"issue":"2","key":"2019100411304677700_c21","doi-asserted-by":"publisher","first-page":"220","DOI":"10.1016\/j.gaitpost.2010.11.009","article-title":"The Effect of Prosthetic Ankle Energy Storage and Return Properties on Muscle Activity in Below-Knee Amputee Walking","volume":"33","author":"Ventura","journal-title":"Gait and Posture"},{"issue":"8","key":"2019100411304677700_c22","doi-asserted-by":"publisher","first-page":"1824","DOI":"10.1016\/j.jbiomech.2006.07.009","article-title":"Mechanical Energetic Contributions From Individual Muscles and Elastic Prosthetic Feet During Symmetric Unilateral Transtibial Amputee Walking: A Theoretical Study","volume":"40","author":"Zmitrewicz","journal-title":"J. Biomech."},{"issue":"8","key":"2019100411304677700_c23","doi-asserted-by":"publisher","first-page":"757","DOI":"10.1109\/10.102791","article-title":"An Interactive Graphics-Based Model of the Lower Extremity to Study Orthopaedic Surgical Procedures","volume":"37","author":"Delp","journal-title":"IEEE Trans. Biomed. Eng."},{"issue":"5","key":"2019100411304677700_c24","doi-asserted-by":"publisher","first-page":"561","DOI":"10.1016\/S0003-9993(00)90035-2","article-title":"Walking Symmetry and Energy Cost in Persons With Unilateral Transtibial Amputations: Matching Prosthetic and Intact Limb Inertial Properties","volume":"81","author":"Mattes","journal-title":"Arch. Phys. Med. Rehabil."},{"issue":"1","key":"2019100411304677700_c25","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/0021-9290(89)90179-6","article-title":"A Planar Model of the Knee Joint to Characterize the Knee Extensor Mechanism","volume":"22","author":"Yamaguchi","journal-title":"J. Biomech."},{"issue":"4","key":"2019100411304677700_c26","doi-asserted-by":"publisher","first-page":"321","DOI":"10.1080\/10255840008915275","article-title":"A Method for Numerical Simulation of Single Limb Ground Contact Events: Application to Heel-Toe Running","volume":"3","author":"Neptune","journal-title":"Comput. Methods Biomech. Biomed. Eng."},{"issue":"3","key":"2019100411304677700_c27","doi-asserted-by":"publisher","first-page":"201","DOI":"10.1080\/10255849908907988","article-title":"A Dynamic Optimization Solution for Vertical Jumping in Three Dimensions","volume":"2","author":"Anderson","journal-title":"Comput. Methods Biomech. Biomed. Eng."},{"issue":"2","key":"2019100411304677700_c28","doi-asserted-by":"publisher","first-page":"187","DOI":"10.1016\/0021-9290(87)90310-1","article-title":"A Dynamic Optimization Technique for Predicting Muscle Forces in the Swing Phase of Gait","volume":"20","author":"Davy","journal-title":"J. Biomech."},{"issue":"5","key":"2019100411304677700_c29","doi-asserted-by":"publisher","first-page":"509","DOI":"10.1016\/j.clinbiomech.2010.12.010","article-title":"Relationships Between Muscle Contributions to Walking Subtasks and Functional Walking Status in Persons With Post-Stroke Hemiparesis","volume":"26","author":"Hall","journal-title":"Clin. Biomech. (Bristol, Avon)"},{"issue":"4","key":"2019100411304677700_c30","first-page":"359","article-title":"Muscle and Tendon: Properties, Models, Scaling, and Application to Biomechanics and Motor Control","volume":"17","author":"Zajac","journal-title":"Crit. Rev. Biomed. Eng."},{"issue":"6","key":"2019100411304677700_c31","doi-asserted-by":"publisher","first-page":"595","DOI":"10.1016\/S0021-9290(96)00188-1","article-title":"Muscle Coordination of Maximum-Speed Pedaling","volume":"30","author":"Raasch","journal-title":"J. Biomech."},{"issue":"12","key":"2019100411304677700_c32","doi-asserted-by":"publisher","first-page":"1027","DOI":"10.1016\/0021-9290(88)90249-7","article-title":"Estimated Mechanical Properties of Synergistic Muscles Involved in Movements of a Variety of Human Joints","volume":"21","author":"Winters","journal-title":"J. Biomech."},{"issue":"2","key":"2019100411304677700_c33","doi-asserted-by":"publisher","first-page":"99","DOI":"10.1080\/1025584031000091678","article-title":"A Model of Human Muscle Energy Expenditure","volume":"6","author":"Umberger","journal-title":"Comput. Methods Biomech. Biomed. Eng."},{"issue":"1","key":"2019100411304677700_c34","doi-asserted-by":"publisher","first-page":"015001","DOI":"10.1115\/1.4000166","article-title":"Manufacture of Energy Storage and Return Prosthetic Feet Using Selective Laser Sintering","volume":"132","author":"South","journal-title":"J. Biomech. Eng."},{"issue":"1\u20132","key":"2019100411304677700_c35","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1016\/0304-4076(94)90038-8","article-title":"Global Optimization of Statistical Functions With Simulated Annealing","volume":"60","author":"Goffe","journal-title":"J. Econometr."},{"issue":"4","key":"2019100411304677700_c36","doi-asserted-by":"publisher","first-page":"602","DOI":"10.1016\/j.gaitpost.2008.04.005","article-title":"Compensatory Mechanisms in Below-Knee Amputee Gait in Response to Increasing Steady-State Walking Speeds","volume":"28","author":"Silverman","journal-title":"Gait and Posture"},{"issue":"1","key":"2019100411304677700_c37","doi-asserted-by":"publisher","first-page":"135","DOI":"10.1016\/j.gaitpost.2007.11.004","article-title":"The Effect of Walking Speed on Muscle Function and Mechanical Energetics","volume":"28","author":"Neptune","journal-title":"Gait and Posture"},{"issue":"1","key":"2019100411304677700_c38","doi-asserted-by":"publisher","first-page":"81","DOI":"10.1016\/0021-9290(95)00011-9","article-title":"A State-Space Analysis of Mechanical Energy Generation, Absorption, and Transfer During Pedaling","volume":"29","author":"Fregly","journal-title":"J. Biomech."},{"issue":"10","key":"2019100411304677700_c39","doi-asserted-by":"publisher","first-page":"1326","DOI":"10.1002\/jor.20876","article-title":"Evaluation of Predicted Knee-Joint Muscle Forces During Gait Using an Instrumented Knee Implant","volume":"27","author":"Kim","journal-title":"J. Orthop. Res."},{"issue":"5","key":"2019100411304677700_c40","doi-asserted-by":"publisher","first-page":"945","DOI":"10.1016\/j.jbiomech.2009.10.048","article-title":"Simultaneous Prediction of Muscle and Contact Forces in the Knee During Gait","volume":"43","author":"Lin","journal-title":"J. Biomech."},{"issue":"4","key":"2019100411304677700_c41","doi-asserted-by":"publisher","first-page":"868","DOI":"10.1016\/j.jbiomech.2007.10.016","article-title":"Gait and Neuromuscular Pattern Changes are Associated With Differences in Knee Osteoarthritis Severity Levels","volume":"41","author":"Astephen","journal-title":"J. Biomech."},{"issue":"1","key":"2019100411304677700_c42","doi-asserted-by":"publisher","first-page":"44","DOI":"10.1016\/j.clinbiomech.2003.08.007","article-title":"Alterations in Lower Extremity Movement and Muscle Activation Patterns in Individuals With Knee Osteoarthritis","volume":"19","author":"Childs","journal-title":"Clin. Biomech. (Bristol, Avon)"},{"issue":"1","key":"2019100411304677700_c43","doi-asserted-by":"publisher","first-page":"86","DOI":"10.1016\/j.gaitpost.2006.01.007","article-title":"Biomechanical Features of Gait Waveform Data Associated With Knee Osteoarthritis: An Application of Principal Component Analysis","volume":"25","author":"Deluzio","journal-title":"Gait and Posture"},{"issue":"4","key":"2019100411304677700_c44","doi-asserted-by":"publisher","first-page":"372","DOI":"10.1016\/j.clinbiomech.2009.02.001","article-title":"Differences in Gait Parameters Between Healthy Subjects and Persons With Moderate and Severe Knee Osteoarthritis: A Result of Altered Walking Speed?","volume":"24","author":"Zeni","journal-title":"Clin. Biomech. (Bristol, Avon)"},{"issue":"2","key":"2019100411304677700_c45","doi-asserted-by":"publisher","first-page":"159","DOI":"10.1016\/S0966-6362(02)00073-5","article-title":"Individual Muscle Contributions to Support in Normal Walking","volume":"17","author":"Anderson","journal-title":"Gait and Posture"}],"container-title":["Journal of Biomechanical Engineering"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/asmedigitalcollection.asme.org\/biomechanical\/article-pdf\/doi\/10.1115\/1.4007824\/5774369\/111005_1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"http:\/\/asmedigitalcollection.asme.org\/biomechanical\/article-pdf\/doi\/10.1115\/1.4007824\/5774369\/111005_1.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,10,4]],"date-time":"2019-10-04T15:32:38Z","timestamp":1570203158000},"score":1,"resource":{"primary":{"URL":"https:\/\/asmedigitalcollection.asme.org\/biomechanical\/article\/doi\/10.1115\/1.4007824\/426477\/Optimization-of-Prosthetic-Foot-Stiffness-to"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,10,26]]},"references-count":45,"journal-issue":{"issue":"11","published-print":{"date-parts":[[2012,11,1]]}},"URL":"https:\/\/doi.org\/10.1115\/1.4007824","relation":{},"ISSN":["0148-0731","1528-8951"],"issn-type":[{"value":"0148-0731","type":"print"},{"value":"1528-8951","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,10,26]]},"article-number":"111005"}}