Introduction of PCA and Introduction of PCA and energy flow pattern in energy flow pattern in lower limblower limb

Reporter: Yu-shin ChangDate: 99/02/05

Questions ?Questions ?

Would healthy elders with decreased ankle joint power tend to adopt hip strategies when walking faster?

Weaker plantar flexor muscle induced lesser ankle joint power generation in elders would cause energy flow disruption and redistribution thus disturb propulsion

Would healthy elders reveal distinct power coordination from healthy young adults?

ObjectiveTo investigate lower limb energy

transfer, changes in joint coordination and compensation that elders adopt due to aging.

DesignPrincipal component analysis(PCA)Mechanical energy model

Participants11 healthy elder(mean=68 yrs)

11 healthy young adults(mean=25yrs)

All subjects walked along a 10m walkway in self-selected speed & faster speed

Choose 3 successful trials to analysis

Main outcome measurements:Temporal-spatial parameters and

kinematic and kinetic parameters◦Joint angles◦Joint moment ◦Joint power◦Segmental power

Results:Elders:

◦reduced peak ankle power generation

◦More knee power absorption◦More hip flexor powerweak plantar-flexors in elders for

locomotion.◦At fast speed generate more hip

concentric power than self-selected speed

hip strategy

Conclusion:Decreased ankle power in elders induce

compensation of other muscular. energy distributing abnormally thus evoke

hip flexor and knee extensor simultaneously act to balance.

Lower thigh segment energy due to insufficient ankle power and need mor hip flexor power for larger stride length.

Produced lesser power from transverse and frontal plane

more instable in gait.

Kinematic data analysisHip, knee, ankle joint anglesLinear / angular velocity

Kinetic data analysisCOP: calculated from GRF and moment

measured on force plate.Joint reaction force and moment: use

inverse dynamicsJoint power: product of joint moment and

angular velocity

Data analysis

Segment mechanical energy

◦Kinetic energy(Ek): the energy possessed by a body in motion Ek= 1/2mv2 + 1/2 Iω2

(linear) + (rotation)

◦Potential energy(Ep): the energy is acquired through a change in

configuration of body Ep=mgh

total mechanical energy E = Ek + Ep

Segmental power terms◦ Segmental joint force power(translation) Pft = F ● V

+: energy flow “into ”segment

- : energy fow “out ” segment

◦ Segmental joint force power(rotation) Pfr = ωs

● (r x F)

◦ Segment joint moment power(Pm)

Pm = M

● ωs

+: flow of energy from muscle into segment

- : flow of energy into muscle

Segmental total power(Ps)

Ps = (Pftp+ Pftd)+(Pfrp + Pfrd ) +(Pmp + Pmd )

Segmental power termsSegmental power termsPower flow pattern model

the lower extremity was treated as 4 segment linked system.

◦ Pelvis◦ Thigh◦ Shank◦ Foot

Principal component Principal component analysis (PCA)analysis (PCA)

PCA modelPCA model

PCA model(Principal Components Analysis):◦ reduce data dimensionality by

performing a covariance analysis between variables and expressiong the data in such a way to highlight their similarities and differences.

◦Find the direction in the data with the most variation

Use 2 PCA models to identify ◦joint coordination by using power flow

terms that across joints and segments

◦The most important factors that could discriminate gait pattern of healthy elders from healthy young

PCA model 1◦Step1: calculate the covariance matirx of

data parameters

◦Step2: determine eigenvalue and eigenvector of C

E ： principle component base λ ： degree of variance in data

• Step 3: principle component

-determine 1st q component to analysis depends on how much ability of these components can express variance.

-the higher eigenvalue the more variance it was explained.

• Step4: name and explain each component

PCA model 2

Convert into

(raw data) (new orthogonal principal component)

Zi=principle component score(PC score) -Composed of the coefficient which measure the contribution of the principle component to each individualOriginal waveform data.-analyzed for group difference using Student’s t-tests.

PCA 1 V.S. PCA 2PCA 1 V.S. PCA 2

Model 1: Capture information of each parameter

independent of time and show some principle components that can represent the main profile of these input

useful for observing power coordinationModel 2: Differentiate difference in each frame of input

data and show these differences by degrees with principal components.

Sensitive in time domain

Mechanical energy modelMechanical energy model

Energy analysis of lower Energy analysis of lower extremityextremity2 methods to determine segment power

◦ Forward dynamic model-based method◦ Inverse dynamics

Segmental power analysis could not track directly the work done by calf muscle on the trunk during push off.

Instead, compared ankle joint power to energy passively transferred through the hip into the trunk via the proximal linear power term

(Meinders, 2001)

Forward dynamic model combined with segmental power analysis in lower limb

quantify the mechanical energy transferred through the leg by the net joint moments

Neptune et al: examine the effect of individual ankle plantar flexor muscle contributions to support and forward progression.

Kepple et al: showed pairs of joint moment with opposite energetic effect work together to balance flow through the segment(ankle plantar/hip flexor)

eg: hip moment remove energy from leg and simultaneously ankle moment supplies energy to leg during push-off. Therefore, it suggested compensation between hip and ankle for muscle weakness.

Energy flow is a complicate and time-dependent data.

Gait data is temporal waveforms including time-dependence informaiton.

PCA is an useful tool for capturing time-direction information and give insight into the dominate performance in power coordination.

Future work of thesisFuture work of thesisUse PCA model to find the component of

elderly fallers in gait pattern.◦Find motor deficit(eg. Muscle weakness

but peripheral n. intact )elderly fallers to be sujects.

◦ the lower extremity is treated as 3 segament linked system.(hip/knee/ankle; proximal/distal)

◦Muscular data would come from saggital motion(hip flexor/extensor; knee flexor extensor/ ankle dorsi/plantar flexion)

Thank you for Thank you for listening!listening!

To be continued~