Modelbildung des Bewegungsapparates

design guide to determine mass geometry for human space flight

Assumptions:

• rigid body: 15 segments - simple geometry

• anthropometric variables: 25

• homogenous density in each segment

• regression equation

• joints as balls & socket joints

Position of CoM:

• rel. position along segment length

• experimental data fram PMHS

• suffictly accurate representation of segment by simple geometric shape

• deviation in head & torso: due to difficulties in determining CoM experimentally

Density of Segemtns:

• large deviations: hand & foot segments

• approximation as: frustrum of a cone & sphere = crude (no big influence on body mass)

• all other segments: within range of 10%

Conclusion:

• good prediction of CoM position & density values

• largest error: hand & feet

• positional error: total body CoM: +- 1,8cm

• rel error: Mass moment of inertia: +-10%

• ICoM around z-axis: more sensitive to uncertanities in posture

• rigid bodies: 17 segments

• anthropometric variables: 242

• shoulder = seperate

• Male - Female

• change in crosssectional profiles along segmt. axis

• inhomogenous density values within cs & along segmt. axis

• subcutaneous fat

• asymmetric segments

• morphological differences - pregnancy

• also valid for children

• 11 movable segments

• 40 geometric bodies

• anthropometric variables: 95

• Neck, wrist & ankle = fixed

• homogenous density values for each geometric body

• Mass moment of inertia of body in question M

  • IM = I0 - ml^2

  • I0 = FG * ltao^2 / 4pi^2

• Dampster 1955:

  • fresh and frozen segment

  • joint center = supporting points

• Chandler 1975:

  • accuracy > 5% by eliminating systematic errors

  • full inertia torso using 6 different supplying points

• uses: Torsional Table

  • I0 = k(tao^2 - tao0^2)

• accuracy > 0.8%

• k determined using test bodies

• 66 people measured in different postures

• with accuracy of 2-8%

• some numbers for selected postures

• mapping houndsfields units to density values:

  • roh = A*n + B

• accuracy > 2%

• muscles prestretched to withstand external forces

• instantaneous drop of external forces = acceleration of body segments

I0 = F*l / phi

• reproducibility: 3%

• Rigid body assumption:

  • femur & pelvis: rigid bodies to simplify calculations - ignoring flexibility & defo under load

• Simplified Joint mechanics:

  • model hip joimnts as ball & sockets

  • Joint = no friction and perfect congruance

• Uniform material properties

• use simplified geometrical shapes = cylinder & cone

• neglect small forces

• assume steady state loading conditions & basic scenarios (standing)

Anatomical:

• femoral geometry

• bone density

• weight of body

• material properties

• muscle & hip joint forces

• gait cycle data

Methods to determine input data:

• MRI, CT, EMG

• force plates

• direct movement

• cadaver studies or in vivo measurement

• biomechanical testing to simulate loading conditions on physical femoral modulus

• statistical - or cross validation: compare models prediction with those from other established models

• indirect validation

• Tendon = Hill type model

• Rigid body assumption: bones of foot & lower leg

• simplified ankle joint: modelled as hinge joint with single degree of freedom

• uniform material properties for achilles tendon

• ignoring dynamic effects like acceleration

• assume isotropic properties

• length, width & orientation of foot & lower leg bones

• length, CSA & attachement point of tendon

• elastic modulus of tendon & surrounding tissue

• ankle & foot angles

• GRF

• direction & magnitude of forces

! Forces cant be measured directly: indirect validation

• Force plate

• Cameras

• EMG

• max. number of bridges that can attach and pull actin

• when there are no cross bridges = active force drops to zero with distance of 1.6micrometer between actin molecules (length of myosin)

• If myosin is already at stage of actin = crossbridges drag actin & compress myosin

• Force on actin = force on myosin whcih cancels out the reaction foreces -> no active force in muscle

• both curves: belly shaped = reflecting typical length = force relationship of muscle = showing max. peak

• Muscle with larger PCSA: will have higher peak force

• PCSA: measure of the total area of muscle fibers in CS, perpendicular to fibers

• more muscle fiber = more actin/myosin filaments that can interact more force can be produced

• Force that muscle can exert: relativ to number of cross bridges & to PCSA

  
  

• Muscle power: P = F*V

  -> consider force producing capacity & contraction velocity (dependent of muscle fiber)

• Contraction velocity inversly related to force it produces

• If velocity is same for both muscles: muscle producing more force will have more power (same with higher volume)

• max. power generated at: 1/3 of max. contraction velocity

• even though muscle B have lower max. velocity = its significalty higher force often means that its power output is still greater at these optimal velocities

  • P0 = Pmax = 0.095*FoVo

    Muscle	PCSA	length	contraction velocity	force	power output
    A	large	short	low	high	moderate
    B	short	long	high	low	moderate

• point of toe off in a GRF diagram corresponds to zero

• moment when foot leaves the ground during gait, typically at end of stance phase

• Point characterised by rapid decrease in vertical GRF to zero (occuring at around 80% of gait cycle)

• Midstance: Force peakes as body weight is fully supported by foot

• Heel strike: force rises as the foot makes contact with ground

• from Anterior / Posteria Graph

• it displays forward / backwards forces & therfore all acceleration / deceleration is non

  -> deceleration is exactly offset by acceleration

• Integral: F dt = 0 from ant / post forces = 0, cancel each other out (Fant = Fpost)

  -> when integrated over a complete gait cycle = net force is the condition to get max. power output:

  • optimal shortening velocity

  • larger muscle volume = more power

  • fiber type (fast twitching = higher power)

• from Vertical graph

• Path of CoM:

  • shows trajectory of CoM over time as person walks - indicating both movements in vertical & horizontal directions

• Path of CoM combines two vertical & horizontal movements:

  • CoM follows smooth, wave-like trajectory, oscilliating up & down & shifting side to side

-> Path resembles sinusoidal wave when looked from the side