Statistical shaper modelling lec 10

why do we care about shape?

• It is related to joint function and dysfunction

how do we quantify shape

• 2D measures don’t fully capture geometry

• requires many measurements

• depends on viewing angle

shape

After removing location, scale, and rotational effects,

• Shape is all the geometric information that remains

whar is a 3D shape model?

A mathematical representation that captures the typical shapes and variations within a class of objects

how do we build a 3D shape model

1. 3D meshes

2. Point to point correspondence: points don’t match from generation, must match them (ex: P1 is always the nose in all models)

3. Scale and align points to isolate shape: make them centred aligned and same size

4. reduce to shape modes/variables: From matrix, apply dimension reduction technique (principle component analysis), then to modes (score based on size, big=high score)

Why identify modes of shape variation?

• Understand why bone shape differs person to person

• Inform reconstruction, Design implants+variations (to work for everyone)

• Less shape variables

what is PCA

• Identifies shape models explaining and gives scores of variation + shape

• Makes x and y coordinate into u,v coordinates

• the u coordinate tells us a lot about where a point is

PCA for shape analysis

• Fully describe shape using all points (look at just the 1st few to capture shape of variability)

• Finds shape features and can describe the shape based on a few PCs

• Statistical shape model (SSM): features and scores

How to use morphometrics?

• Define unique anatomy

• Understand shape-function relationships

• Explain human origins

• Guide design

• guide clinical diagnoses

• guide design

• Many others!

how does bone shape differ btwn people

• Ind bone shape

• Joint shape

• Joint shape + alignment

• Bone and cartilage

How does shape vary with size?

• Compressively loaded long bones get disproportionately wider with inc body size

• Articular surfaces on hind foot bones scale alometrically w/size (not at same rate as overall size)

How does shape vary with sex?

• joint function and injury risk dif

• Male and female versions of implant

How does shape change with age?

• Vertebra get wider and flare out

how are other characteristics related to injury/personal characteristics?

injury classification, injury/disease onset (prediction)

how do we Investigate how joint kinematics and

kinetics vary with shape?

Combine node coordinates

and biomechanical measures

into a single matrix. Integration of SSMs and

musculoskeletal models

• patella loading more, shallower groove

example for Patellofemoral Instability – PC2

• Going stable to unstable, unstable have lower score 

• Patella height, shallower trochlear groove, all features

• Get 3d shape features, compare different groups based on shape features