Figure 1.
Examples of different tissue types and states as well as their representations as cell-graphs.
Figure 2.
Analysis of histology and in vitro data sets using coupled matrix and tensor factorization (CMTF).
Time mode is slotted as 0, 1, 2, 4, 6, 10, 16, 24, 72, 120, 168 in hours. Features mode contains the cell graph features: average degree, clustering coefficient C, clustering coefficient D, clustering coefficient E, average eccentricity, diameter, radius, average eccentricity 90, diameter 90, radius 90, average path length, effective hop diameter, hop plot exponent, giant connected component ratio, # connected components, average connected component size, % isolated points, % end points, # central points, % central points, mean, std, skewness, kurtosis, # nodes, # edges. These features are defined in Table S1.
Figure 3.
Singular Value Decomposition and R-component CP model.
Figure 4.
Three-way and Two-way analysis of in vitro brain tissue data.
(a) CP factorization of the tensor with modes: features, samples and time. The 1st component separates the 2 different functional states: cancer (red-triangle sign) from normal (green-plus sign) tissue samples; (b) SVD of matrix of type: features by samples (across all times); (c) features projected over the 1st component of the CP model. Cell-graph features such as % of end points, number of connected components, average connected component size, average path length, average eccentricity are identified as influential in the analysis since their coefficients diverge the most from zero. (Note that we have 23 features on the plot since three features have been identified as outliers and excluded).
Figure 5.
Coupled matrix and tensor factorization (CMTF) on in vitro brain samples represented by tensor
and histology samples represented by matrix Y (see Figure 2). (a) The first column of matrix B, that is the factor matrix corresponding to the in vitro samples mode extracted using CMTF, separates cancer (blue-square signs) from normal (light blue-plus signs) tissue samples; (b) The first column of matrix D, that is the factor matrix corresponding to the histology samples mode extracted using CMTF, can separate cancer (red-triangle sign) from healthy (green-star sign) samples; (c) features captured by the common component extracted by CMTF.
Figure 6.
Three-way and two-way analysis of in vitro bone tissue data.
(a) CP factorization of the tensor with modes: features, samples and time. Both the 1st and the 2nd components separate the two different functional states: cancer (red-triangle sign) from normal (green-plus sign) tissue samples; (b) SVD of matrix of type: features by samples (across all times); (c) features projected over the 1st component of CP model. Cell-graph features such as % of end points, number of connected components, giant connected component ratio, average path length, average eccentricity are identified as influential in the analysis since their coefficients diverge the most from zero; (d) since the 2nd component can also distinguish between two functional states we also show the 2nd CP component in features mode. Note that the influential features are different in the 2nd component, e.g., while the number of connected components has a high coefficient in the 1st component, its coefficient in the 2nd component is close to 0.
Figure 7.
Coupled factorization of in vitro bone samples represented by tensor
and histology samples represented by matrix Y. (a) Both the 1st and the 2nd column of matrix B extracted by a CMTF model separate cancer (blue-square sign) from normal (light blue-plus sign) samples; (b) Matrix D corresponding to the histology samples mode extracted using a CMTF model is useful to narrow the coupled analysis since only the 1st component can separate cancer (red-triangle sign) from healthy (green-star sign) samples; (c) features captured by the 1st CMTF component.
Figure 8.
Three-way and two-way analysis of in vitro breast tissue data.
(a) CP factorization of the tensor with modes: features, samples and time. Only the 2nd component can separate the two different functional states: cancer (red-triangle sign) from normal (green-plus sign) tissue samples; (b) SVD of matrix of type: features by samples (across all times); (c) features projected over the 2nd CP component. Cell-graph features such as % of end points, number of connected components, average connected component size, average path length, average eccentricity are identified as influential in the analysis.
Figure 9.
Coupled matrix and tensor factorization on in vitro breast samples represented by tensor
and histology samples represented by matrix Y (Figure 2). (a) The 1st column of matrix B corresponding to the in vitro samples mode extracted by a CMTF model can separate cancer (blue-square sign) from normal (light blue-plus sign) tissue samples; (b) Unlike for brain and bone tissues, matrix D corresponding to the histology samples mode extracted using a CMTF model cannot separate cancer samples (red-triangle sign) from healthy (green-star sign) samples; (c) features captured by the common component extracted by CMTF. Cell-graph features identified as influential in the coupled analysis are similar to the features in Figure 5c and 7c with some minor differences.
Figure 10.
In vitro vs. histology samples of cancerous tissue (10a Brain, 10b Bone, and 10c Breast samples).
The first two components of SVD analysis explain 72.4%, 65.9%, 66.5% of the variance for each tissue type, respectively. SVD yields a linear separation between in vitro and histology cancerous tissue samples. Two clusters (red and green) are very well separated, with few outliers. This defines and quantifies a structural difference between engineered tissues and the native tissues.
Figure 11.
In vitro vs. histology samples of normal tissue (11a Brain, 11b Bone, and 11c Breast samples).
The first two components of SVD analysis explain 76.5%, 75%, 62.8% of the variance for each tissue type respectively and shows that there is a linear separation of in vitro and native healthy tissue samples. The separation confirms that recreating the complex structural organization of native tissue samples in vitro is difficult.
Figure 12.
In vitro tissue samples remain structurally different from histology samples (blue) over time.
We identified no time point in the development of the in vitro samples that is mathematically similar to histology data. (a) Brain cancer cultures vary considerably over time getting very close to the histology samples, demonstrating they best resemble the histology samples. In vitro bone cancer (b) and breast cancer (c) samples remain clustered over all time points and exhibit no mixing of data points with histology data.