Induced Acceleration and Power Analyses of Human Motion

  • Anne K. Silverman
Reference work entry


Induced acceleration and power analyses are tools that are used to determine principles of muscle coordination and the functional roles of muscles during movement. This chapter describes how these analyses are performed using an underlying musculoskeletal model and movement simulation. Induced acceleration analyses use the dynamic equations of motion of the musculoskeletal system to determine the effects of individual muscles, and other modeled actuators, on the body’s movement, such as the acceleration of specific joints and/or the body’s mass center. Induced power analyses build upon induced acceleration analyses to evaluate mechanical power that is generated to, absorbed from, and/or transferred between body segments and can reveal how muscles work together to achieve a dynamic task. Examples of application of induced acceleration and power analyses to human performance and clinical questions are provided. In addition, limitations of these analyses and potential impacts on the interpretation of the results are discussed. Future directions include the use of induced acceleration and power analyses with improved accuracy of musculoskeletal models and computational approaches to distill large quantities of information into clinical decision-making.


Muscle function Musculoskeletal model Movement simulation Muscle coordination Induced acceleration Segment power 


  1. Ackermann M, van den Bogert AJ (2010) Optimality principles for model-based prediction of human gait. J Biomech 43(6):1055–1060CrossRefGoogle Scholar
  2. Ackland DC, Lin Y-C, Pandy MG (2012) Sensitivity of model predictions of muscle function to changes in moment arms and muscle–tendon properties: a Monte-Carlo analysis. J Biomech 45(8):1–9CrossRefGoogle Scholar
  3. Ackland DC et al (2015) Prosthesis loading after temporomandibular joint replacement surgery: a musculoskeletal modeling study. J Biomech Eng 137(4):41001CrossRefGoogle Scholar
  4. Anderson FC, Pandy MG (2003) Individual muscle contributions to support in normal walking. Gait Posture 17(2):159–169CrossRefGoogle Scholar
  5. Arnold EM et al (2010) A model of the lower limb for analysis of human movement. Ann Biomed Eng 38(2):269–279CrossRefGoogle Scholar
  6. Bosmans L et al (2015) Sensitivity of predicted muscle forces during gait to anatomical variability in musculotendon geometry. J Biomech 48(10):2116–2123CrossRefGoogle Scholar
  7. Bosmans L et al (2016) The role of altered proximal femoral geometry in impaired pelvis stability and hip control during CP gait: a simulation study. Gait Posture 44:61–67CrossRefGoogle Scholar
  8. Bruno AG, Bouxsein ML, Anderson DE (2015) Development and validation of a musculoskeletal model of the fully articulated thoracolumbar spine and rib cage. J Biomech Eng 137(8):81003CrossRefGoogle Scholar
  9. Caruthers EJ et al (2016) Muscle forces and their contributions to vertical and horizontal acceleration of the center of mass during sit-to-stand transfer in young, healthy adults. J Appl Biomech 32(5):487–503CrossRefGoogle Scholar
  10. Cazzola D et al (2017) Cervical spine injuries: a whole-body musculoskeletal model for the analysis of spinal loading. PLoS One 12:1–24CrossRefGoogle Scholar
  11. Christophy M et al (2012) A musculoskeletal model for the lumbar spine. Biomech Model Mechanobiol 11(1–2):19–34CrossRefGoogle Scholar
  12. Debaere S et al (2015) Control of propulsion and body lift during the first two stances of spring running: a simulation study. J Sports Sci 33(19):2016–2024CrossRefGoogle Scholar
  13. Dorn TW, Schache AG, Pandy MG (2012a) Muscular strategy shift in human running: dependence of running speed on hip and ankle muscle performance. J Exp Biol 215:1944–1956CrossRefGoogle Scholar
  14. Dorn TW, Lin Y-C, Pandy MG (2012b) Estimates of muscle function in human gait depend on how foot-ground contact is modelled. Comput Methods Biomech Biomed Engin 15(6):657–668CrossRefGoogle Scholar
  15. Fox MD et al (2009) Mechanisms of improved knee flexion after rectus femoris transfer surgery. J Biomech 42(5):614–619CrossRefGoogle Scholar
  16. Fregly BJ, Zajac FE (1996) A state-space analysis of mechanical energy generation, absorption, and transfer during pedaling. J Biomech 29(1):81–90CrossRefGoogle Scholar
  17. Hall AL et al (2011) Relationships between muscle contributions to walking subtasks and functional walking status in persons with post-stroke hemiparesis. Clin Biomech 26(5):509–515CrossRefGoogle Scholar
  18. Hamner SR, Delp SL (2013) Muscle contributions to fore-aft and vertical body mass center accelerations over a range of running speeds. J Biomech 46(4):780–787CrossRefGoogle Scholar
  19. Hamner SR et al (2013) A rolling constraint reproduces ground reaction forces and moments in dynamic simulations of walking, running, and crouch gait. J Biomech 46(10):1772–1776CrossRefGoogle Scholar
  20. Hegarty AK et al (2017) Evaluating the effects of Ankle Foot Orthosis mechanical property assumptions on gait simulation muscle force results. J Biomech Eng 139(3):1–8CrossRefGoogle Scholar
  21. Hunter BV, Thelen DG, Dhaher YY (2009) A three-dimensional biomechanical evaluation of quadriceps and hamstrings function using electrical stimulation. IEEE Trans Neural Syst Rehabil Eng 17(2):167–175CrossRefGoogle Scholar
  22. Li K et al (2013) Trunk muscle action compensates for reduced quadriceps force during walking after total knee arthroplasty. Gait Posture 38(1):79–85CrossRefGoogle Scholar
  23. Lin Y et al (2015) Muscle coordination of support, progression and balance during stair ambulation. J Biomech 48(2):340–347CrossRefGoogle Scholar
  24. McGowan CP, Neptune RR, Kram R (2008) Independent effects of weight and mass on plantar flexor activity during walking: implications for their contributions to body support and forward propulsion. J Appl Physiol 105:486–494CrossRefGoogle Scholar
  25. McGowan CP, Neptune RR, Herzog W (2013) A phenomenological muscle model to assess history dependent effects in human movement. J Biomech 46(1):151–157CrossRefGoogle Scholar
  26. Myers CA et al (2015) A probabilistic approach to quantify the impact of uncertainty propagation in musculoskeletal simulations. Ann Biomed Eng 43(5):1098–1111CrossRefGoogle Scholar
  27. Neptune RR, Kautz SA, Zajac FE (2000) Muscle contributions to specific biomechanical functions do not change in forward versus backward pedaling. J Biomech 33:155–164CrossRefGoogle Scholar
  28. Neptune RR, Kautz SA, Zajac FE (2001) Contributions of the individual ankle plantar flexors to support, forward progression and swing initiation during walking. J Biomech 34(11):1387–1398CrossRefGoogle Scholar
  29. Neptune RR, Zajac FE, Kautz SA (2004) Muscle force redistributes segmental power for body progression during walking. Gait Posture 19(2):194–205CrossRefGoogle Scholar
  30. Neptune RR, Sasaki K, Kautz SA (2008) The effect of walking speed on muscle function and mechanical energetics. Gait Posture 28(1):135–143CrossRefGoogle Scholar
  31. Pandy MG, Lin Y-C, Kim HJ (2010) Muscle coordination of mediolateral balance in normal walking. J Biomech 43(11):2055–2064CrossRefGoogle Scholar
  32. Peterson CL et al (2010) Pre-swing deficits in forward propulsion, swing initiation and power generation by individual muscles during hemiparetic walking. J Biomech 43(12):2348–2355CrossRefGoogle Scholar
  33. Pickle NT et al (2016) The functional roles of muscles during sloped walking. J Biomech 49(14):3244–3251CrossRefGoogle Scholar
  34. Rankin JW, Richter WM, Neptune RR (2011) Individual muscle contributions to push and recovery subtasks during wheelchair propulsion. J Biomech 44(7):1246–1252CrossRefGoogle Scholar
  35. Sasaki K, Neptune RR (2006) Differences in muscle function during walking and running at the same speed. J Biomech 39(11):2005–2013CrossRefGoogle Scholar
  36. Sasaki K, Neptune RR (2010) Individual muscle contributions to the axial knee joint contact force during normal walking. J Biomech 43(14):2780–2784CrossRefGoogle Scholar
  37. Saul KR et al (2015) Benchmarking of dynamic simulation predictions in two software platforms using an upper limb musculoskeletal model. Comput Methods Biomech Biomed Engin 18(13):1445–1458CrossRefGoogle Scholar
  38. Schappacher-Tilp G et al (2015) A novel three-filament model of force generation in eccentric contraction of skeletal muscles. PLoS One 10(3):1–16CrossRefGoogle Scholar
  39. Silverman AK, Neptune RR (2012) Muscle and prosthesis contributions to amputee walking mechanics: a modeling study. J Biomech 45(13):2271–2278CrossRefGoogle Scholar
  40. Silverman AK, Neptune RR (2014) Three-dimensional knee joint contact forces during walking in unilateral transtibial amputees. J Biomech 47(11):2556–2562CrossRefGoogle Scholar
  41. Steele KM et al (2010) Muscle contributions to support and progression during single-limb stance in crouch gait. J Biomech 43(11):2099–2105CrossRefGoogle Scholar
  42. Suderman BL, Vasavada AN (2012) Moving muscle points provide accurate curved muscle paths in a model of the cervical spine. J Biomech 45(2):400–404CrossRefGoogle Scholar
  43. Thelen DG, Lenz A, Hernandez A (2011) Measurement and simulation of joint motion induced via biarticular muscles during human walking. Procedia IUTAM 2:290–296CrossRefGoogle Scholar
  44. Ventura JD, Klute GK, Neptune RR (2015) Individual muscle contributions to circular turning mechanics. J Biomech 48(6):1067–1074CrossRefGoogle Scholar
  45. Wesseling M et al (2015) Muscle optimization techniques impact the magnitude of calculated hip joint contact forces. J Orthop Res 33(3):430–438CrossRefGoogle Scholar
  46. Wesseling M et al (2016) Subject-specific geometrical detail rather than cost function formulation affects hip loading calculation. Comput Methods Biomech Biomed Engin 19(14):1475–1488CrossRefGoogle Scholar
  47. Yamaguchi GT (2006) Dynamic modeling of musculoskeletal motion softcover. Springer, New YorkGoogle Scholar
  48. Zajac FE (1989) Muscle and tendon: properties, models, scaling, and application to biomechanics and motor control. Crit Rev Biomed Eng 17(4):359–411Google Scholar
  49. Zajac FE, Gordon ME (1989) Determining muscle’s force and action in multi-articular movement. Exerc Sport Sci Rev 17(1):187–230Google Scholar
  50. Zajac FE, Neptune RR, Kautz SA (2002) Biomechanics and muscle coordination of human walking. Part I: introduction to concepts, power transfer, dynamics and simulations. Gait Posture 16(3):215–232CrossRefGoogle Scholar
  51. Zajac FE, Neptune RR, Kautz SA (2003) Biomechanics and muscle coordination of human walking: part II: lessons from dynamical simulations and clinical implications. Gait Posture 17(1):1–17CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Functional Biomechanics Laboratory, Department of Mechanical EngineeringColorado School of MinesGoldenUSA

Section editors and affiliations

  • William Scott Selbie
    • 1
  1. 1.Has-Motion Inc.KingstonCanada

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