Table 1.
Collection of Mice
Figure 1.
Presented is a volume rendering of skull forms of C57BL/6 wild-type mice of different sexes and ages (left panel) and DDR2−/−, DDR1−/−, and DDR2+/− mice (right panel). Displayed are distances and representative features of the skeleton of the head viewed from the right side. D1 represents the maximal distance between the external occipital protuberance and the incisor teeth. The distance between the center of the inner ear and the incisor teeth is labeled D2, whereas D3 delineates the distance between the center of the inner ear and the external occipital protuberance. C1 depicts the bend of parietal, interparietal, and occipital bone and is measured as sum of the local contour curvature. The landmark F1 symbolizes the nasal bone.
Figure 2.
Statistical Evaluation of Various Metrical Skull Features
(A, B) Progression of the cumulative local contour curvatures C1 follows the contour positions of knockout mice and their controls. Shown are the mean values and the local standard deviations for each mice strain.
(C–E) Box plots for C1, D*2, and D*3 values are shown. p-Values for the paired Student's t-test for each feature of every strain are indicated in comparison to wild-type controls. Differences with p < 0.05 were considered to be significant. Note, that parameters C1 and D*3 in DDR2-deficient mice, D*3 in heterozygous DDR2-deficient mice, and D*2 in DDR1-deficient mice differ significantly in comparison to wild-type controls.
Figure 3.
Statistical Evaluation of the Generated 34-D Skull-Shape Features
(A) A scatter plot is demonstrated for the two main components of the PCA-transformed 34-D feature space of all skull-shape features. The samples for each mice strain are interconnected with lines. The clusters are strongly overlapping, and in this case the two dimensional subspaces are not linearly separable.
(B) A further cluster analysis for DDR2−/− and DDR1/2+/+ mice based on the Euclidean distance between the feature vectors does not separate the two groups.
(C) PCA-transformed skull-shape features of a subset of age-matched DDR1/2+/+ and DDR2−/− mice with different sex are well clustered according to their sex for DDR1/2+/+ and the female DDR2−/− mice. The male DDR2−/− mice are widely separated resulting in overlaps with their females.
(D) PCA of DDR2−/− and DDR1/2+/+ mice that were separated in male and female are illustrated. Sample points of each group are connected with arrows in the direction of increasing age. No correlation between age and feature vector was depicted.
Figure 4.
Architectures of the ANNs 1 to 3 to Discriminate DDR2−/−, DDR2+/−, DDR1−/−, DDR1/2+/+, and SCID Mice between Different Mouse Populations
(A) Network 1 for paired classification classifies DDR2-deficient mice against their wild-type littermates. It consists of one input layer with 34 neurons for the skull-shape features and two additional input neurons for age and sex. The image shows the network response for a DDR1/2+/+ mouse (pattern 4, Table 2)
(B) Neuronal network 2 applied for classification of all five mice strains in a mixed collective consists of one input layer with 34 neurons, two hidden layers with five and three neurons, and one output layer with five neurons N1 − N5. In network 2 the taught output identifies each output neuron as one mouse population. The output neuron with the highest activation is called the “winning” neuron and indicates with which class of mice the input pattern is associated. The network response for input pattern 4, the input of skull-shape features of a DDR2−/− mouse is displayed. This is demonstrated by high activation of the output neuron N2 (green, high activation; blue, low activation).
(C) Neuronal network 3 applied for classification of DDR2+/− mice, which were incorrectly identified in network 2 as C57BL/6 control mice, consists of one input layer with 34 skull-based features, one hidden layer with five neurons, and one output layer with the neurons N1 and N2. The output of an output unit is a value between 0 and 1. The combination of the taught output that represents a distinct phenotype of DDR2+/− and SCID or C57BL/6 wild-type mice is shown below. High activation of output neuron N1 with simultaneous low activation of N2 represents C57BL/6 wild-type mice, low activation of both N1 and N2 represents a SCID mouse, and low activation of N1 by simultaneous high activation of N2 represents a DDR2+/− mouse. The network response for input pattern 4, the input of skull-shape features of a heterozygous DDR2 mouse, is displayed. This is demonstrated by high activation of N1 and N2 (green, high activation; blue, low activation).
Table 2.
Phenotypic Assessment of DDR2-Deficient Mice Using fpVCT Datasets and ANN 1
Table 3.
Discrimination of DDR1/2+/+, DDR2−/−, DDR2+/−, DDR1−/−, and SCID Mice between Different Mouse Populations Using fpVCT Datasets and ANN 2
Table 4.
Identification of DDR2+/−, C57BL/6 Wild-Type, and SCID Mice Using fpVCT Datasets and ANN 3
Table 5.
Identification of DDR1/2−/− Double Knockout Mice with ANN 2 That Is Only Trained for Single Knockout Mice