### Application of statistical

### shape analysis to the

### classification of renal tumours

### appearing in childhood

M.A./Dipl. Math. /Cand. Soz. päd.

Université du Luxembourg Campus Limpertsberg

Dr. J.P.-Schenk Uniklinikum Heidelberg Prof. Dr. J. Schiltz, Uni Luxembourg

**Stefan Markus Giebel**

**Overview**

### 1) Survey

### 2) Shape

### 3) Mean Shape

### 4) Tests

### 5)

### Differences

### between tumours

### shown in an optical way

**Renal tumours appearing in **

**early childhood**

**•**

Wilms- tumours growing in the near to the kidney
*Genetic cause*

*The majority of renal tumours in the childhood is diagnosed as *
*“Wilms” (80%)*

*There are four types of tissue (a, b, c, d) and three stages of *
*development (I, II, III)*

### •

Renal cell carcinoma*growing also in the near to the kidney*
*Are very rare in the childhood*

**•**

Neuroblastoma
*Growing in the near to nerve tissue *
*Also very rare*

### •

Clear cell carcinoma*Growing in the near to the bones .*
*Are also rare*

### •

etc.**The therapy depends on the diagnosis.**

**Dicom Data**

**Three-dimensional object**

**Explorative* survey of **

**landmarks**

### 1.Determining of three dimensional mass point

### 2.Taking two dimensional image therein the mass point

**Data process**

### 1.Standardisation (using Euclidean norm)

### 2.Centring on two-dimensional centre

**Determining of **

**„mean shape“**

### Determining the expected “mean shape” of a group

### of objects.

### That mean's: smallest distance in the average to all shapes in the group

**Determining of **

**“mean shape” **

### Algorithm for „mean shape“ (Ziezold 1994)

Using the following algorithm

if if

**Determining of **

**„mean shape“**

### Statement: Patient No. 3 is very far from the “mean shape”.

### Patient No. 16 is very near to the “mean shape“.

**Distance from the**

** “mean shape” (Wilms)**

**Description of the test **

**(Ziezold, 1994)**

### The group of m objects is an indepent realisation of the distribution P and the other group

### of k objects an independent realisation of the distribution Q

### Determining of p-value according to the test

### H P=Q

o### 1. step: Determining of “mean shape”

### 2.step: Detemining of distances to the “mean shape” and the u according to the Mann

_{0 }

### Whitney-U-Test

### 3.step: Determining all possible u-values separating the group (k+m) in two groups with

### m and k objects

### 4.step: Determining the rank of u in the group of all u-values

_{0}

### 5.step: p-value = r/N

### 6.step: Determining the p-values in the other direction. Determining “mean shape” in the

### group of m objects

**Description of the test **

**(Ziezold 1994)**

**High u -values means: A lot of cases - not used for the “mean shape”- has a smaller **

_{o}

### distance to the “mean shape” than the cases used for the “mean shape”

**Low u -values means: Only a small number of cases - not used for the “mean shape”- **

_{o}

### has a smaller distance to the “mean shape” than the cases used for the “mean shape”

**Determining of all possible permutations**

**possibilities**

### bbrr

### rrbb ...

### rbbr ...

### brrb ...

### brbr ...

### rbrb

### 4!/ (2! 2!) = 6 possibilities

**Checking of differences between **

**types of „Wilms“- tumours**

### Subsets

### Differentiation

### m= …: Number of cases with the same u-value

### m<…: Number of cases with a lower u-value

**Checking of differences between **

**different tumours **

### Subsets

### Differentiation

### m= …: Number of cases with the same u-value

### m<…: Number of cases with a lower u-value

### The interval is a result of the smallest and the highest rank of u

_{o}

### N1:neuroblastoma

**Conclusions **

### „Typ c“ and clear cell carcinoma have a

### tendency for differentiation

### Independence (Influence) of Landmarks of Shapes

Ziezold •Mathematische Schriften Kassel, Heft 03/2003

*The k th landmark of X is independent (influenced by) of the*

### other landmarks with respect to the distance

**The k th landmark of X is not independent (influenced by) of the**

**The k th landmark of X is not independent (influenced by) of the**

### other landmarks with respect to the distance

### H

_{0}

### H

_{1}

### Step 2.

### Step 3.

### Step 1.

Distance between Landmarks Distance between Objects without kth landmark Random selected N: 100 possibilities n: all cases n p: all possibilities for 2 in n cases p: only a part of the sample (p-quantille)### Explanation of test

### Constellation

### Possibilities

### numerator

### denumerator

_{numerator}

_{denumerator}

### Results

### for

### p-quantile= 65%

### N=100

### Wilcoxon - Test

*Also it is interesting to test the distance of landmarks to the*

*mean shape for differentiating nephroblastoma to neuroblastoma.*

*For that test we use the Wilcoxon-Test and calculate according to the *

*Mann-Whitney-U-Test all possibilities.*

*We assume that the average of difference to the mean shape for every*

*landmark can be used for differentiating the tumors.*

### p0

### [0,1887; 0,1917]

### p0

### [0,7586; 0,763]

### Wilms / Neuroblastome

### Neuroblastome / Wilms

### No results for

### %

### = 0,1

### Wilms Mean shape

### Landmark Landmark

### d

### Neuro Mean shape

### Landmark Landmark

### d

### Explorative take k=5 landmarks from 24

### 1. One sample for best configuration (Test Ziezold 1994)

**Forecast **

### First results

### Sample:

### 5 neuroblastoma - 14 wilms

### Test Ziezold (1994)

### p0

### [0,157; 0,187]

### p0

### [0,069; 0,108]

### Wilms / Neuroblastoma

### Neuroblastoma / Wilms

Three dimensional case

### Application of statistical

### shape analysis to the

### classification of renal tumours

### appearing in early childhood

(M.A./Dipl. Math. /Cand. Soz. päd.)

Université du Luxembourg Campus Limpertsberg

Dr. J.P.-Schenk Uniklinikum Heidelberg Prof. Dr. J. Schiltz, Uni Luxembourg

**Stefan Markus Giebel**