Design of a hybrid deep learning system for discriminating between low- and high-grade colorectal cancer lesions, using microscopy images of IHC stained for AIB1 expression biopsy material

Abstract

To design a hybrid deep learning system (hDL-system) for discriminating low-grade from high-grade colorectal cancer (CRC) lesions, using immunohistochemically stained biopsy specimens for AIB1 expression. AIB1 has oncogenic function in tumour genesis, and it is an important prognostic factor regarding various types of cancers, including CRC. Clinical material consisted of biopsy specimens of sixty-seven patients with verified CRC (26 low-grade, 41 high-grade cases). From each patient, we digitized images, at × 50 and × 200 lens magnifications. We designed the hDL-system, employing the VGG16 pre-trained convolution neural network for generating DL-features, the SVM classifier, and the bootstrap evaluation method for assessing the discrimination accuracy between low-grade and high-grade CRC lesions. Furthermore, we compared the hDL-system’s discrimination accuracy with that of a supervised machine learning system (sML-system). We designed the sML-system by (i) generating sixty-nine (69) textural and colour features from each image, (ii) employing the probabilistic neural network (PNN) classifier, and (iii) using the bootstrapping method for evaluating sML-system performance. The system design was enabled by employing the CUDA platform for programming in parallel the multiprocessors of the Nvidia graphics processing unit card. The hDL-system provided the highest discrimination accuracy of 99.1% using the × 200 lens magnification images as compared to the 92.5.% best accuracy achieved by the sML-system, employing both the × 50 and × 200 lens magnification images. Our results showed that the hDL-system was superior to the sML-system (i) in discriminating low-grade from high-grade CRC-lesions and (ii) by requiring fewer images for its best design, only those at the × 200 lens magnification. The sML-system by employing textural and colour features in its design revealed that high-grade CRC lesions are characterized by (i) loss in the definition of structures, (ii) coarser texture in larger structures, (iii) hazy formless texture, (iv) lower AIB1 uptake, (v) lower local correlation and (vi) slower varying image contrast.

Appendices

Appendix

The mathematical formulations of the eight (8) best-features combination of the sML-system design are presented below.

Α.1 Histogram feature

• (1) Kurtosis (Kurt)

$$ Kurt = \frac{1}{N}\frac{{\sum\nolimits_{i} {\sum\nolimits_{j} {(g(i,j) - m)^{4} } } }}{{std^{4} }} $$

where g(i,j) is the pixel intensity in position (i,j), N the total number of pixels, m is the mean value of the g, and std is the standard deviation of g.

Α.2 Co-occurrence matrix based features

• (2) Sum average (SAV)

$$ SAV = \sum\limits_{i = 2}^{{2N_{g} }} {ip_{x + y} (i)} $$

where N_g is the number of gray levels in the image, i,j = 1,…,N_g, and p(i,j) is the co-occurrence matrix, and p_x+y is $p_{x + y} (k) = \sum\limits_{i = 1}^{{N_{g} }} {\sum\limits_{j = 1}^{{N_{g} }} {p(i,j),i + j = k,k = 2,3,...,2N_{g} } }$.

• (3) Difference variance(DVAR)

$$ DVAR = \sum\limits_{i = 2}^{{2N_{g} }} {(i - SAV)^{2} p_{x - y} (i)} $$

where p_x-y is $p_{x - y} (k) = \sum\limits_{i = 1}^{{N_{g} }} {\sum\limits_{j = 1}^{{N_{g} }} {p(i,j),|i - j| = k,k = 2,3,...,N_{g} - 1} }$.

• (4) Difference entropy (DENT)

$$ DENT = - \sum\limits_{i = 0}^{{N_{g} - 1}} {p_{x - y} (i)} \log \left( {p_{x - y} (i)} \right) $$

• (5) Information measure of correlation 1 (ICM1)

  $$ ICM1 = \frac{HXY - HXY1}{{\max \left\{ {HX,HY} \right\}}} $$

where $HXY = - \sum\limits_{i = 0}^{{N_{g} - 1}} {\sum\limits_{j = 0}^{{N_{g} - 1}} {p(i,j)\log \left( {p(i,j)} \right)} }$

$$ HXY1 = - \sum\limits_{i = 0}^{{N_{g} - 1}} {\sum\limits_{j = 0}^{{N_{g} - 1}} {p(i,j)\log \left( {p_{x} (i)p_{y} (j)} \right)} } $$

Α.4 Wavelet based feature

• (6) Median Value of the 2nd level discrete wavelet transform in the horizontal direction (dwt2H_MedV).

The discrete wavelet function of an image $f\left(x,y\right)$ of size M x N is defined as:

$$ W_{\varphi } \left( {j_{0} ,m,n} \right) = \frac{1}{{\sqrt {MN} }}\mathop \sum \limits_{x = 0}^{M - 1} \mathop \sum \limits_{y = 0}^{N - 1} f\left( {x,y} \right)\varphi_{{j_{0} ,m,n}} \left( {x,y} \right) $$

$$ W_{\psi }^{i} \left( {j,m,n} \right) = \frac{1}{{\sqrt {MN} }}\mathop \sum \limits_{x = 0}^{M - 1} \mathop \sum \limits_{y = 0}^{N - 1} f\left( {x,y} \right)\psi_{j,m,n}^{i} \left( {x,y} \right) $$

$$ i = \left\{ {H,V,D} \right\} $$

where $\varphi \left( {x,y} \right)$ is a scaling function, with j = 0,1,2…

$W_{\varphi }$ are the coefficients define an approximation of image $f\left( {x,y} \right)$ at level (scale) j₀.

and $W_{\psi }$ are the coefficients that add horizontal, vertical and diagonal details for levels j ≥ j₀.

Α.5 Tamura-based features

• (7) Tamura coarseness 4

$$ F_{crs} = \frac{1}{m \times n}\sum\limits_{i}^{m} {\sum\limits_{j}^{n} {S_{{{\text{best}}}} (i,j)} } $$

where m, n are region dimensions and

$$ S_{best} (i,j) = 2^{k} $$

where k is the best scaling for highest neighborhood average.

_{The particular feature is the value of the 3rd bin histogram of Sbest} .

Α.6 Lab colour transform-based features

• (8) Median Value of colour channel a* (CLR MedV_Ch_a)

According to the CIE, the coordinates of the Lab colour space are derived by a nonlinear transformation of the three primary colours X, Y and Z. The linear transformation of RGB space to X, Y and Z is defined as [57]

$$ \left( {\begin{array}{*{20}c} {\begin{array}{*{20}c} X \\ Y \\ \end{array} } \\ Z \\ \end{array} } \right) = \left( {\begin{array}{*{20}c} {\begin{array}{*{20}c} {0.607} \\ {0.299} \\ \end{array} } \\ {0.000} \\ \end{array} \begin{array}{*{20}c} { \begin{array}{*{20}c} {0.174} \\ {0.587} \\ \end{array} } \\ {0.066} \\ \end{array} \begin{array}{*{20}c} {\begin{array}{*{20}c} {0.200} \\ {0.114} \\ \end{array} } \\ {1.116} \\ \end{array} } \right)\left( {\begin{array}{*{20}c} {\begin{array}{*{20}c} R \\ G \\ \end{array} } \\ B \\ \end{array} } \right) $$

$$ L* = 116\left( {\sqrt[3]{{\frac{Y}{{Y_{0} }}}}} \right) - 16 $$

$$ a* = 500\left[ {\sqrt[3]{{\frac{X}{{X_{0} }}}} - \sqrt[3]{{\frac{Y}{{Y_{0} }}}}} \right] $$

$$ b* = 200\left[ {\sqrt[3]{{\frac{Y}{{Y_{0} }}}} - \sqrt[3]{{\frac{Z}{{Z_{0} }}}}} \right] $$

where Ch_x is the *a channel of L*a*b colour transform.