Development and validation of the finite element model for the human lower limb of pedestrians

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Takahashi, Yukou¹; Kikuchi, Yuji¹; Konosu, Atsuhiro²; Ishikawa, Hirotoshi²

Development and validation of the finite element model for the human lower limb of pedestrians

Stapp Car Crash J. 2000;44:335-355

Affiliations

¹Honda R&D Co., Ltd. Tochigi R&D Center

²Japan Automobile Research Institute
Abstract

An impact test procedure with a legform addressing lower limb injuries in car-pedestrian accidents has been proposed by EEVC/WG17. Although a high frequency of lower limb fractures is observed in recent accident data, this test procedure assesses knee injuries with a focus on trauma to the ligamentous structures.

The goal of this study is to establish a methodology to understand injury mechanisms of both ligamentous damages and bone fractures in car-pedestrian accidents. A finite element (FE) model of the human lower limb was developed using PAM-CRASH™. The commercially available H-Dummy™ lower limb model developed by Nihon ESI for a seated position was modified to represent the standing posture of pedestrians. Mechanical properties for both bony structures and knee ligaments were determined from our extensive literature survey, and were carefully implemented in the model considering their strain rate dependency in order to simulate the dynamic response of the lower limb accurately. The element elimination option in PAMCRASHTM was used to simulate both bone fractures and ligamentous ruptures. Bone models were validated against test results obtained from literature in both static and dynamic conditions. The dynamic response of the knee joint was validated against the response corridors from a series of experiments with Post-Mortem Human Subject (PMHS) presented in the literature. In addition, the lower limb model was validated against published experiments with isolated lower limbs subjected to lateral impact simulating car-pedestrian accidents.

The validated FE lower limb model was integrated with an upper body model with rigid segments to obtain a fullbody pedestrian model. Computer simulations using both the pedestrian model and a FE model for the car front were conducted to reconstruct a published carpedestrian impact test with PMHS. Leg fracture observed in the experiment was reproduced from the FE carpedestrian model. The developed FE model can be used as an effective tool to investigate injury mechanisms of the lower limb in car-pedestrian accidents.
Links

PubMed: 17458735

SAE: 2000-01-SC22

Cited Works (67)

Year	Entry
1970	Yamada H. Strength of Biological Materials. Evans FG, ed. Baltimore, MD: Williams & Wilkins Company; 1970.
1983	Parfitt AM, Mathews CH, Villanueva AR, Kleerekoper M, Frame B, Rao DS. Relationships between surface, volume, and thickness of iliac trabecular bone in aging and in osteoporosis: implications for the microanatomic and cellular mechanisms of bone loss. J Clin Invest. October 1983;72(4):1396-1409.
1985	Gibson LJ. The mechanical behaviour of cancellous bone. J Biomech. 1985;18(5):317-328.
1983	Goldstein SA, Wilson DL, Sonstegard DA, Matthews LS. The mechanical properties of human tibial trabecular bone as a function of metaphyseal location. J Biomech. 1983;16(12):965-969.
1986	Butler DL, Kay MD, Stouffer DC. Comparison of material properties in fascicle-bone units from human patellar tendon and knee ligaments. J Biomech. 1986;19(6):425-432.
1974	Behrens JC, Walker PS, Shoji H. Variations in strength and structure of cancellous bone at the knee. J Biomech. 1974;7(3):201-207.
1996	Crandall JR, Portier L, Petit P, Hall GW, Bass CR, Klopp GS, Hurwitz S, Pilkey WD, Trosseille X, Tarrière C, Lassau J-P. Biomechanical response and physical properties of the leg, foot, and ankle. In: Proceedings of the 40th Stapp Car Crash Conference. November 4-6, 1996; Albuquerque, NM. Warrendale, PA: Society of Automotive Engineers:173-192. SAE 962424.
1979	Aldman B, Lundell B, Thorngren L, Bunketorp O, Romanus B. Physical simulation of human leg-bumper impacts. In: Proceedings of the 1979 International IRCOBI Conference on the Biomechanics of Impact. September 5-7, 1979; Goeteborg, Sweden.232-242.
1983	Stone JL, Beaupre GS, Hayes WC. Multiaxial strength characteristics of trabecular bone. J Biomech. 1983;16(9):743-752.
1985	Cezayirlioglu H, Bahniuk E, Davy DT, Heiple KG. Anisotropic yield behavior of bone under combined axial force and torque. J Biomech. 1985;18(1):61-69.
1999	Kajzer J, Matsui Y, Ishikawa H, Schroeder G, Bosch U. Shearing and bending effects at the knee joint at low speed lateral loading. In: Proceedings of the SAE International Congress & Exposition. March 1-4, 1999; Detroit, MI. Warrendale, PA: Society of Automotive Engineers. SAE 1999-01-0712.
1988	Ruff CB, Hayes WC. Sex differences in age‐related remodeling of the femur and tibia. J Orthop Res. November 1988;6(6):886-896.
1997	Kajzer J, Schroeder G, Ishikawa H, Matsui Y, Bosch U. Shearing and bending effects at the knee joint at high speed lateral loading. In: Proceedings of the 41st Stapp Car Crash Conference. November 13-14, 1997; Lake Buena Vista, FL. Warrendale, PA: Society of Automotive Engineers:151-165. SAE 973326.
1975	Girgis FG, Marshall JL, Al Monajem ARS. The cruciate ligaments of the knee joint: anatomical, functional and experimental analysis. Clin Orthop Relat Res. January–February 1975;106:216-231.
1966	McElhaney JH. Dynamic response of bone and muscle tissue. J Appl Physiol. 1966;21(4):1231-1236.
1975	Currey JD, Butler G. The mechanical properties of bone tissue in children. J Bone Joint Surg. September 1975;57A(6):810-814.
1966	Sedlin‌ ED, Hirsch C. Factors affecting the determination of the physical properties of femoral cortical bone. Acta Orthop Scand. 1966;37(1):29-48.
1976	Lindahl O. Mechanical properties of dried defatted spongy bone. Acta Orthop Scand. 1976;47(1):11-19.
1994	Bermond F, Ramet M, Bouquet R, Cesari D. A finite element model of the pedestrian leg in lateral impact. In: Proceedings of the 14th International Technical Conference on the Enhanced Safety of Vehicles (ESV). May 23-26, 1994; Munich, Germany.199-209.
1993	Bermond F, Ramet M, Bouquet R, Cesari D. A finite element model of the pedestrian knee-joint in lateral impact. In: Proceedings of the 1993 International IRCOBI Conference on the Biomechanics of Impact. September 8-10, 1993; Eindhoven, The Netherlands.117-129.
1976	Carter DR, Hayes WC. Bone compressive strength: the influence of density and strain rate. Science. September 10, 1976;194(4270):1174-1176.
1977	Carter DR, Hayes WC. The compressive behavior of bone as a two-phase porous structure. J Bone Joint Surg. 1977;59A(7):954-962.
1995	Courtney AC, Wachtel EF, Myers ER, Hayes WC. Age-related reductions in the strength of the femur tested in a fall-loading configuration. J Bone Joint Surg. March 1995;77A(3):387-395.
1987	Linde F, Hvid I. Stiffness behaviour of trabecular bone specimens. J Biomech. 1987;20(1):83-89.
1999	Matsui Y, Ishikawa H, Sasaki A, Kajzer J, Schroeder G. Impact response and biofidelity of pedestrian legform impactors. In: Proceedings of the 1999 International IRCOBI Conference on the Biomechanics of Impact. September 23-24, 1999; Sitges, Spain.343-354.
1993	Ishikawa H, Kajzer J, Schroeder G. Computer simulation of impact response of the human body in car-pedestrian accidents. In: Proceedings of the 37th Stapp Car Crash Conference. November 7-8, 1993; San Antonio, TX. Warrendale, PA: Society of Automotive Engineers:235-248. SAE 933129.
1998	Takeuchi K, Bunketorp O, Ishikawa H, Kajzer J. Car-pedestrian accidents in gothenburg during ten years. In: Proceedings of the 1998 International IRCOBI Conference on the Biomechanics of Impact. September 16-18, 1998; Göteberg, Sweden.87-98.
1989	Linde F, Hvid I. The effect of constraint on the mechanical behaviour of trabecular bone specimens. J Biomech. 1989;22(5):485-490.
1981	Bunketorp O, Aldman B, Jonson R, Romanus B, Roos B, Thorngren L. Experimental studies on leg injuries in car-pedestrian accidents. In: Proceedings of the 1981 International IRCOBI Conference on the Biomechanics of Impact. September 8-10, 1981; Salon de Provence, France.243-255.
1973	Pugh JW, Rose RM, Radin EL. Elastic and viscoelastic properties of trabecular bone: dependence on structure. J Biomech. 1973;6(5):475-485.
1988	Rice JC, Cowin SC, Bowman JA. On the dependence of the elasticity and strength of cancellous bone on apparent density. J Biomech. 1988;21(2):155-168.
1974	Reilly DT, Burstein AH, Frankel VH. The elastic modulus for bone. J Biomech. May 1974;7(3):271-275.
1975	Reilly DT, Burstein AH. The elastic and ultimate properties of compact bone tissue. J Biomech. 1975;8(6):393-405.
1990	Katsamanis F, Raftopoulos DD. Determination of mechanical properties of human femoral cortical bone by the Hopkinson bar stress technique. J Biomech. 1990;23(11):1173-1184.
1974	Reilly DT, Burstein AH. The mechanical properties of cortical bone. J Bone Joint Surg. 1974;56A(5):1001-1022.
1976	Kennedy JC, Hawkins RJ, Willis RB, Danylchuck KD. Tension studies of human knee ligaments: yield point, ultimate failure, and disruption of the cruciate and tibial collateral ligaments. J Bone Joint Surg. April 1976;58A(3):350-355.
1994	Race A, Amis AA. The mechanical properties of the two bundles of the human posterior cruciate ligament. J Biomech. January 1994;27(1):13-24.
2000	Wittek A, Ishikawa H, Matsui Y, Konosu A. Validation and parameter study of a multi-body model for simulation of knee joint responses in lateral impacts representing car-pedestrian accidents: influences of ligament properties and boundary conditions on model responses. In: Proceedings of the 2000 International IRCOBI Conference on the Biomechanics of Impact. September 20-22, 2000; Montpellier, France.85-99.
1983	Bunketorp O, Romanus B, Hansson T, Aldman B, Thorngren L, Eppinger RH. Experimental study of a compliant bumper system. In: Proceedings of the 27th Stapp Car Crash Conference. October 17-19, 1983; San Diego, CA. Warrendale, PA: Society of Automotive Engineers:287-297. SAE 831623.
1967	Evans FG, Bang S. Differences and relationships between the physical properties and the microscopic structure of human femoral, tibial and fibular cortical bone. Am J Anat. January 1967;120(1):79-88.
1982	Williams JL, Lewis JL. Properties and an anisotropic model of cancellous bone from the proximal tibial epiphysis. J Biomech Eng. February 1982;104(1):50-56.
1992	Yang J, Kajzer J. Computer simulation of impact response of the human knee joint in car-pedestrian accidents. In: Proceedings of the 36th Stapp Car Crash Conference. November 2-4, 1992; Seattle, WA. Warrendale, PA: Society of Automotive Engineers:203-217. SAE 922525.
1993	Yang JK, Rzymkowski C, Kajzer J. Development and validation of a mathematical breakable leg model. In: Proceedings of the 1993 International IRCOBI Conference on the Biomechanics of Impact. September 8-10, 1993; Eindhoven, The Netherlands.175-186.
1981	Carter DR, Caler WE, Spengler DM, Frankel VH. Fatigue behavior of adult cortical bone: the influence of mean strain and strain range. Acta Orthop Scand. 1981;52(5):481-490.
1980	Carter DR, Schwab GH, Spengler DM. Tensile fracture of cancellous bone. Acta Orthop Scand. 1980;51(5):733-741.
1996	Yang JK, Wittek A, Kajzer J. Finite element model of the human lower extremity skeleton system in a lateral impact. In: Proceedings of the 1996 International IRCOBI Conference on the Biomechanics of Impact. September 11-13, 1996; Dublin, Ireland.377-388.
1994	Yang J-K, Kajzer J. Mathematical model of pedestrian lower extremity. In: Proceedings of the 14th International Technical Conference on the Enhanced Safety of Vehicles (ESV). May 23-26, 1994; Munich, Germany.220-232.
1993	McCalden RW, McGeough JA, Barker MB, Court-Brown CM. Age-related changes in the tensile properties of cortical bone: the relative importance of changes in porosity, mineralization, and microstructure. J Bone Joint Surg. 1993;75A(8):1193-1205.
1976	Yoon HS, Katz JL. Ultrasonic wave propagation in human cortical bone, II: measurements of elastic properties and microhardness. J Biomech. 1976;9(7):459-464.
1979	Wall JC, Chatterji SK, Jeffery JW. Age-related changes in the density and tensile strength of human femoral cortical bone. Calcif Tiss Int. December 1979;27(1):105-108.
1977	Ducheyne P, Heymans L, Martens M, Aernoudt E, Meester Pd, Mulier JC. The mechanical behaviour of intracondylar cancellous bone of the femur at different loading rates. J Biomech. 1977;10(11-12):747-762.
1985	Aldman B, Kajzer J, Bunketorp O, Eppinger R. An experimental study of a modified compliant bumper. In: Proceedings of the 10th International Technical Conference on Experimental Safety Vehicles (ESV). July 1-4, 1985; Oxford, England.1035-1040. SAE 856118.
1991	Lotz JC, Gerhart TN, Hayes WC. Mechanical properties of metaphyseal bone in the proximal femur. J Biomech. 1991;24(5):317-329.
1976	Noyes FR, Grood ES. The strength of the anterior cruciate ligament in humans and Rhesus monkeys. J Bone Joint Surg. 1976;58A(8):1074-1082.
1967	Lindahl O, Lindgren ÅGH. Cortical bone in man, II: variation in tensile strength with age and sex. Acta Orthop Scand. 1967;38(2):141-147.
1976	Saha S, Hayes WC. Tensile impact properties of human compact bone. J Biomech. 1976;9(4):243-251.
1989	Cesari D, Cavallero C, Roche H. Mechanisms producing lower extremity injuries in pedestrian accident situations. In: 33rd Annual Proceedings, Association for the Advancement of Automotive Medicine (AAAM). October 2-4, 1989; Baltimore, MD.415-422.
1987	Bonfield W. Advances in the fracture mechanics of cortical bone. J Biomech. 1987;20(11-12):1071-1081.
1982	Leichter I, Margulies JY, Weinreb A, Mizrahi J, Robin GC, Conforty B, Makin M, Bloch B. The relationship between bone density, mineral content, and mechanical strength in the femoral neck. Clin Orthop Relat Res. March 1982;163:272-281.
1980	Wismans JSHM. A Three-Dimensional Mathematical Model of the Human Knee Joint [PhD thesis]. Eindhoven University of Technology; 1980.
1978	Carter DR, Spengler DM. Mechanical properties and composition of cortical bone. Clin Orthop Relat Res. September 1978;135:192-217.
1983	Martens M, Van Audekercke R, Delport P, De Meester P, Mulier JC. The mechanical characteristics of cancellous bone at the upper femoral region. J Biomech. 1983;16(12):971-983.
1976	Burstein AH, Reilly DT, Martens M. Aging of bone tissue: mechanical properties. J Bone Joint Surg. 1976;58A(1):82-86.
1995	Kress TA, Porta DJ, Snider JN, Fuller PM, Psihogios JP, Heck WL, Frick SJ, Wasserman JF. Fracture patterns of human cadaver long bones. In: Proceedings of the 1995 International IRCOBI Conference on the Biomechanics of Impact. September 13-15, 1995; Brunnen, Switzerland.155-169.
1980	Brown TD, Ferguson AB Jr. Mechanical property distributions in the cancellous bone of the human proximal femur. Acta Orthop Scand. 1980;51(1):429-437.
1976	Trent PS, Walker PS, Wolf B. Ligament length patterns, strength, and rotational axes of the knee joint. Clin Orthop Relat Res. June 1976;117:263-270.
1970	Currey JD. The mechanical properties of bone. Clin Orthop Relat Res. November–December 1970;73:210-231.

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2001	Konosu A, Ishikawa H, Tanahashi M. Reconsideration of injury criteria for pedestrian subsystem legform test: problems of rigid legform impactor. In: Proceedings of the 17th International Technical Conference on the Enhanced Safety of Vehicles (ESV). June 4-7, 2001; Amsterdam, The Netherlands.
2003	Yamamoto S, Saito A, Nagasaka K, Sugimoto S, Mizuno K, Tanaka E, Kabayama M. The strain-rate dependence of mechanical properties of rabbit knee ligaments. In: Proceedings of the 18th International Technical Conference on the Enhanced Safety of Vehicles (ESV). May 19-22, 2003; Nagoya, Japan.
2003	Takahashi Y, Kikuchi Y, Mori F, Konosu A. Advanced FE lower limb model for pedestrians. In: Proceedings of the 18th International Technical Conference on the Enhanced Safety of Vehicles (ESV). May 19-22, 2003; Nagoya, Japan.
2003	Dokko Y, Anderson R, Manavis J, Blumburgs P, McLean J, Zhang L, Yang KH, King AI. Validation of the human head FE model against pedestrian accident and its tentative application to the examination of the existing tolerance curve. In: Proceedings of the 18th International Technical Conference on the Enhanced Safety of Vehicles (ESV). May 19-22, 2003; Nagoya, Japan.
2003	Bhalla K, Bose D, Madeley NJ, Kerrigan J, Crandall J, Longhitano D, Takahashi Y. Evaluation of the response of mechanical pedestrian knee joint impactors in bending and shear loading. In: Proceedings of the 18th International Technical Conference on the Enhanced Safety of Vehicles (ESV). May 19-22, 2003; Nagoya, Japan.
2003	van Rooij L, Bhalla K, Meissner M, Ivarsson J, Crandall J, Longhitano D, Takahashi Y, Dokko Y, Kikuchi Y. Pedestrian crash reconstruction using multi-body modeling with geometrically detailed, validated vehicle models and advanced pedestrian injury criteria. In: Proceedings of the 18th International Technical Conference on the Enhanced Safety of Vehicles (ESV). May 19-22, 2003; Nagoya, Japan.
2007	Neale M, Thomas R, Bateman H, Hynd D. A finite element modelling investigation of lower leg injuries. In: Proceedings of the 20th International Technical Conference on the Enhanced Safety of Vehicles (ESV). June 18-21, 2007; Lyon, France.
2007	Soni A, Chawla A, Mukherjee S. Effect of muscle contraction on knee loading for a standing pedestrian in lateral impacts. In: Proceedings of the 20th International Technical Conference on the Enhanced Safety of Vehicles (ESV). June 18-21, 2007; Lyon, France.
2011	Takayama S, Yamamoto Y, Ejima S, Ono K, Kamiji K, Yasuki T. The clarification of individual injury mechanism difference in pedestrian FE model utilizing cadaver scaling and posturing techniques. In: Proceedings of the 22nd International Technical Conference on the Enhanced Safety of Vehicles (ESV). June 13-16, 2011; Washington, DC.
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2011	Yue N, Shin J, Untaroiu CD. Blunt injury response of occupant lower extremity during automotive crashes: a finite element study. In: Proceedings of the 39th International Workshop on Human Subjects for Biomechanical Research. 2011.
2003	Kerrigan JR, Ivarsson BJ, Bose D, Madeley NJ, Millington SA, Bhalla KS, Crandall JR. Rate-sensitive constitutive and failure properties of human collateral knee ligaments. In: Proceedings of the 2003 International IRCOBI Conference on the Biomechanics of Impact. September 25, 2003; Lisbon, Portugal.177-190.
2003	Teresiński G, Mądro R. A comparison of mechanisms of ankle, knee, pelvis and neck injuries in pedestrians and in cyclists according to the direction of impact and type of vehicle. In: Proceedings of the 2003 International IRCOBI Conference on the Biomechanics of Impact. September 25, 2003; Lisbon, Portugal.121-132.
2005	Dunmore M, Brooks R, McNally DS, Madeley NJ. Development of an alternative frangible knee element for a pedestrian safety legform. In: Proceedings of the 2005 International IRCOBI Conference on the Biomechanics of Impact. September 21-23, 2005; Prague, Czech Republic.455-458.
2005	Teresiński G. Assessment of the mechanism of limb amputation in car-to-pedestrian accident victims. In: Proceedings of the 2005 International IRCOBI Conference on the Biomechanics of Impact. September 21-23, 2005; Prague, Czech Republic.463-466.
2006	Lanz C, Walz FH, Muser MH, Schmitt K-U, Otte D. Incidence and injury mechanisms of tibia head fractures among. In: Proceedings of the 2006 International IRCOBI Conference on the Biomechanics of Impact. September 20-22, 2006; Madrid, Spain.289-302.
2007	Ito O, Okamoto M, Takahashi Y, Mori F, Meissner MU, Untaroiu CD, Crandall JR. Validation of a human FE lower limb model for a child pedestrian against accident data. In: Proceedings of the 2007 International IRCOBI Conference on the Biomechanics of Impact. September 19-21, 2007; Maastricht, The Netherlands.367-370.
2009	Crandall J. Simulating the road forward: the role of computational modeling in realizing future opportunities in traffic safety. In: Proceedings of the 2009 International IRCOBI Conference on the Biomechanics of Impact. September 9-11, 2009; York, UK.3-27.
2015	Klug C, Weinberger M, Tomasch E, Feist F, Sinz W, Steffan H, Kinsky T, Roth F, Praxl N, Buenger B. Pelvic and femoral injuries in car-to-pedestrian accidents. In: Proceedings of the 2015 International IRCOBI Conference on the Biomechanics of Injury. September 9-11, 2015; Lyon, France.49-63.
2015	Shen M, Zhu F, Jiang B, Sanghavi V, Fan H, Cai Y, Wang Z, Kalra A, Jin X, Chou CC, Yang KH. Development and a limited validation of a whole‐body finite element pedestrian and occupant models of a 10‐year‐old child. In: Proceedings of the 2015 International IRCOBI Conference on the Biomechanics of Injury. September 9-11, 2015; Lyon, France.672-688.
2004	Bose D, Bhalla K, Rooij L, Millington S, Studley A, Crandall J. Response of the knee joint to the pedestrian impact loading environment. In: Proceedings of the SAE World Congress & Exhibition. March 8-11, 2004; Detroit, MI. Warrendale, PA: Society of Automotive Engineers. SAE 2004-01-1608.
2005	van Dommelen JAW, Ivarsson BJ, Jolandan MM, Millington SA, Raut M, Kerrigan JR, Crandall JR, Diduch DR. Characterization of the rate-dependent mechanical properties and failure of human knee ligaments. In: Proceedings of the SAE World Congress & Exhibition. April 11-14, 2005; Detroit, MI. Warrendale, PA: Society of Automotive Engineers. SAE 2005-01-0293.
2006	Kikuchi Y, Takahashi Y, Mori F. Development of a finite element model for a pedestrian pelvis and lower limb. In: Proceedings of the SAE World Congress & Exhibition. April 3-6, 2006; Detroit, MI. Warrendale, PA: Society of Automotive Engineers. SAE 2006-01-0683.
2006	Untaroiu C, Kerrigan J, Crandall J. Material identification using successive response surface methodology, with application to a human femur subjected to three-point bending loading. In: Proceedings of the SAE World Congress & Exhibition. April 3-6, 2006; Detroit, MI. Warrendale, PA: Society of Automotive Engineers. SAE 2006-01-0063.
2001	Beillas P, Begeman PC, Yang KH, King AI, Arnoux P-J, Kang H-S, Kayvantash K, Brunet C, Cavallero C, Prasad P. Lower limb: advanced FE model and new experimental data. Stapp Car Crash J. 2001;45:469-494. SAE 2001-22-0022.
2002	Dhaliwal TS, Beillas P, Chou CC, Prasad P, Yang KH, King AI. Structural response of lower leg muscles in compression: a low impact energy study employing volunteers, cadavers and the Hybrid III. Stapp Car Crash J. 2002;46:229-243. SAE 2002-22-0012.
2003	Van Hoof J, De Lange R, Wismans JSHM. Improving pedestrian safety using numerical human models. Stapp Car Crash J. 2003;47:401-436. SAE 2003-22-0018.
2005	Kim YS, Choi HH, Cho YN, Park YJ, Lee JB, Yang KH, King AI. Numerical investigations of interactions between the knee-thigh-hip complex with vehicle interior structures. Stapp Car Crash J. 2005;49:85-115. SAE 2005-22-0005.
2005	Untaroiu C, Darvish K, Crandall J, Deng B, Wang J-T. A finite element model of the lower limb for simulating pedestrian impacts. Stapp Car Crash J. 2005;49:157-181. SAE 2005-22-0008.
2007	Untaroiu C, Kerrigan J, Kam C, Crandall J, Yamazaki K, Fukuyama K, Kamiji K, Yasuki T, Funk J. Correlation of strain and loads measured in the long bones with observed kinematics of the lower limb during vehicle-pedestrian impacts. Stapp Car Crash J. 2007;51:433-466. SAE 2007-22-0018.
2008	Chang C-Y, Rupp JD, Kikuchi N, Schneider LW. Development of a finite element model to study the effects of muscle forces on knee-thigh-hip injuries in frontal crashes. Stapp Car Crash J. 2008;52:475-504. SAE 2008-22-0018.
2010	El-Jawahri RE, Laituri TR, Ruan JS, Rouhana SW, Barbat SD. Development and validation of age-dependent FE human models of a mid-sized male thorax. Stapp Car Crash J. 2010;54:407-430. SAE 2010-22-0017.
2015	Schoell SL, Weaver AA, Urban JE, Jones DA, Stitzel JD, Hwang E, Reed MP, Rupp JD. Development and validation of an older occupant finite element model of a mid-sized male for investigation of age-related injury risk. Stapp Car Crash J. November 2015;59:359-383.
2010	Untaroiu CD. A numerical investigation of mid-femoral injury tolerance in axial compression and bending loading. Int J Crashworthiness. 2010;15(1):83-92.
2010	Untaroiu CD, Crandall JR, Takahashi Y, Okamoto M, Ito O, Fredriksson R. Analysis of running child pedestrians impacted by a vehicle using rigid-body models and optimization techniques. Safety Sci. February 2010;48(2):259-267.
2002	Liu XJ, Yang JK, Lövsund P. A study of influences of vehicle speed and front structure on pedestrian impact responses using mathematical models. Traffic Inj Prev. 2002;3(1):31-42.
2022	Mühlbauer JA. Entwicklung regionaler Validierungsexperimente mit Freiwilligen für aktive Finite-Elemente Menschmodelle [PhD thesis]. Ludwig Maximilian University of Munich; 2022.
2016	Martinez AA. The Effect of Load Rate on the Axial Fracture Tolerance of the Isolated Tibia During Automotive and Military Impacts [Master's thesis]. Hamilton, ON: McMaster University; 2016.
2009	Chang C-Y. Prediction of the Effects of Lower-Extremity Muscle Forces on Knee, Thigh, and Hip Injuries in Frontal Motor Vehicle Crashes [PhD thesis]. University of Michigan; 2009.
2014	Tan K. Characterising the Viscoelasticity of Soft Biological Tissues Under Large Deformation [PhD thesis]. University of New South Wales; March 2014.
2004	Bose D. Experimental Evaluation of the Human Knee Joint in Pedestrian-Car Impact Loading Environment [Master's thesis]. Charlottesville, VA: University of Virginia; August 2004.
2005	Untaroiu CD. Development and Validation of a Finite Element Model of Human Lower Limb: Including Detailed Geometry, Physical Material Properties, and Component Validations for Pedestrian Injuries [PhD thesis]. Charlottesville, VA: University of Virginia; May 2005.
2007	Meissner MU. Crash Reconstruction of Vehicle-to-Pedestrian Crash Events Using Optimization Software [Master's thesis]. Charlottesville, VA: University of Virginia; August 2007.
2019	Yue N. A Numerical Investigation of Biomechanical Response and Injury of Occupant Lower Extremities in Automotive Frontal Impact Scenario [Master's thesis]. Charlottesville, VA: University of Virginia; December 2019.
2011	Burkhart TA. Biomechanics of the Upper Extremity in Response to Dynamic Impact Loading Indicative of a Forward Fall: An Experimental and Numerical Investigation [PhD thesis]. University of Windsor; 2011.
2019	Pak W. Development and Validation of Human Body Finite Element Models for Pedestrian Protection [PhD thesis]. Virginia Polytechnic Institute and State University; September 17, 2019.
2023	Grindle DM. Protection of Standing and Seated Pedestrians Using Finite Element Analysis [PhD thesis]. Virginia Polytechnic Institute and State University; April 27, 2023.
2005	Shah S. Skull Fracture Prediction Using Finite Element Model With Skull Thickness Variation [Master's thesis]. Detroit, MI: Wayne State University; 2005.
2017	Shen M. Development of a Finite Element Pelvis and Lower Extremity Model With Growth Plates for Pediatric Pedestrian Protection [PhD thesis]. Detroit, MI: Wayne State University; August 2017.
2009	Quenneville CE. Experimental and Numerical Assessments of Injury Criteria for Short-Duration, High-Force Impact Loading of the Tibia [PhD thesis]. University of Western Ontario; December 2009.