# Lesson 3: Scaling using segmental scaling vectors

This tutorial presumes that you have completed {doc}`Scaling tutorial

Lesson 1: Joint to joint scaling methods <lesson1>` and {doc}`Scaling tutorial

Lesson 2: Scaling based on External Body Measurements <lesson2>`. It

covered all the methods based on distance measurements and estimations.

This lesson introduces the last scaling method, which differs from the previous

ones by the input parameterse and, therefore, allows another set of

solutions when it comes to anthropometric scaling

## Scaling XYZ

The scaling laws discussed in the previous measurements rely on standard

measurements and distance estimates such as joint-to-joint distances or

predefined external measurements, e.g. manual palpations and so on. This is a

good approach, when a corresponding measurement study can be designed in

advance, or a particular measurement protocol can be adjusted to fit the model

requirements. However, sometimes this is not feasible and the modeller needs to

rely on available data, such as an anthopometric database, or data coming from

an old study with measurements different to the standard ones. In this case

individual segmental scaling can be constructed by establishing a correspondence

between available data and virtual measurements on the model. Let us consider

the following example: For `_SCALING_UNIFORM_` the head is scaled by a single

factor (`HeadHeight`), and in case of the `_SCALING_LENGTHMASSFAT_` it would

also depend on the corresponding mass of the head segment. But we could actually

know even more accurate dimensions of our subject's head. And these measurements

should be used by the model. Let's say that our subject corresponds to the 50th

percentile male and the measurements will be taken from DIN 1986 (Deutsches

Institut fur Normung) anthropometric dataset.

| HEAD HEIGHT, mm | HEAD LENGTH, mm | HEAD BREADTH, mm |

| --------------- | --------------- | ---------------- |

| 228             | 193             | 156              |

The head height represent the vertical size of the head, measured from the

chin to the top of the head, head length represents the depth of the skull

from the most anterior point on the forehead to the most posterior point on

the back of the head, and, finally, head breadth correspond to the width of

the head.

We have prepared some code to visualize points used to measure these distances.

As well as that a couple of measures were added to see the result of scaling.

Please enable this code by uncommenting the following code:

```AnyScriptDoc

// Head scaling visualization and measurements

§#define HEAD_SCALING_XYZ§

#ifdef HEAD_SCALING_XYZ

  #include "Model\HeadScalingXYZ.any"

#endif

```

```{image} _static/lesson3/HeadMarkersFrontView.jpg

:width: 49%

```

```{image} _static/lesson3/HeadMarkersLateralView.jpg

:width: 49%

```

Let us use the last scaling law: `_SCALING_XYZ_`. For this purpose please

switch it on like shown below:

```AnyScriptDoc

// Scaling laws using joint to joint measures

//  #define BM_SCALING _SCALING_UNIFORM_

//  #define BM_SCALING _SCALING_LENGTHMASS_

//  #define BM_SCALING _SCALING_LENGTHMASSFAT_

§   #define BM_SCALING _SCALING_XYZ_§

```

Let us inspect what segment dimension are available for this scaling law. Go to

`Main.HumanModel.Anthropometrics.SegmentDimensions` in the model tree:

```{image} _static/lesson3/XYZ_segment_dimensions.jpg

```

We could see that the first section containing overall body parameters and the

SegmentMasses folder are identical to any other scaling law. But instead of only

having a folder called SegmentDimensions, we now have another called

SegmentScaleFactors. Looking at the content it is clear that this folder

contains invidual scaling factors along main axes. By default all values are set

to be 1, meaning that the cadaveric data will not scale and the law will behave

similarly to the `_SCALING_NONE_`.

Let us define the head scaling factors as expected lengths divided by unscaled

head dimensions. In HeadScalingXYZ.any we have already prepared the

computation of these distances and we just need to check these values in the Model

Tree:

:::{tip}

Right-click on the object and use "Locate in Model Tree" to find it in the Model Tree.

:::

```{image} _static/lesson3/HeadDimensionsModelTree.jpg

```

Now that we know original and desired dimensions the scale factors can be defined as

the following block of code inside the `AnyManXYZ.any`. Please apply this changes and

reload the model:

```AnyScriptDoc

Main.HumanModel.Anthropometrics.SegmentScaleFactors.Head = {

  §// Standard unscaled values

  AnyVar HEAD_BREADTH = 0.19;

  AnyVar HEAD_LENGTH  = 0.239;

  AnyVar HEAD_HEIGHT  = 0.26;

  // Scale factor computation

  LengthScale = 0.228/HEAD_HEIGHT;///< 228mm, DIN 1986

  DepthScale = 0.193/HEAD_LENGTH; ///< 193mm, DIN 1986

  WidthScale = 0.156/HEAD_BREADTH;///< 156mm, DIN 1986 §

};

```

```{image} _static/lesson3/HeadMarkersFrontView.jpg

:width: 49%

```

```{image} _static/lesson3/HeadMarkersAppliedFrontView.jpg

:width: 49%

```

We have succesfully personalized our model to have a head that corresponds to

the German 50th percentile man. We can see that it is slightly smaller than

the default one coming with model. However, we still see that the body does not

match the head size. The same anthropometric dataset suggests that the height

of the 50th percentile man should be 173.3mm. We could mimic `_SCALING_UNIFORM_`

by defining a common scaling factor and applying it to all dimensions like this:

```AnyScriptDoc

Main.HumanModel.Anthropometrics.BodyMass = 75 ;

Main.HumanModel.Anthropometrics.BodyHeight = 180 /100;

§#define STATURE_SCALE_FACTOR 1.733/1.75§

...

Main.HumanModel.Anthropometrics.SegmentScaleFactors.Pelvis = {

  LengthScale = §STATURE_SCALE_FACTOR§;

  DepthScale = §STATURE_SCALE_FACTOR§;

  WidthScale = §STATURE_SCALE_FACTOR§;

};

Main.HumanModel.Anthropometrics.SegmentScaleFactors.Thorax = {

  LengthScale = §STATURE_SCALE_FACTOR§;

  DepthScale = §STATURE_SCALE_FACTOR§;

  WidthScale = §STATURE_SCALE_FACTOR§;

};

...

```

```{image} _static/lesson3/ScalingXYZFinal.jpg

```

By applying these changes we complete this tutorial. Our model looks more natural

and corresponds to the 50th percentile German male as suggested by DIN in 1986.

If you want to learn about more advanced patient specific scaling, take a look at the

AnyBody tutorials. The tutorial on Scaling covers how to do patient-specific scaling based on

geometry data from MRI and CT scans.