Applying limiting entropy to quantify the alignment of collagen fibers by polarized light imaging

Yingjie Qu; Zachary J. Smith; Kelly Tyler; Shufang Chang; Shuwei Shen; Mingzhai Sun; Ronald X. Xu; Yingjie Qu; Zachary J. Smith; Kelly Tyler; Shufang Chang; Shuwei Shen; Mingzhai Sun; Ronald X. Xu

doi:10.3934/mbe.2021118

Mathematical Biosciences and Engineering

2021, Volume 18, Issue 3: 2331-2356. doi: 10.3934/mbe.2021118

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Research article

Applying limiting entropy to quantify the alignment of collagen fibers by polarized light imaging

1.
Department of Precision Machinery and Precision Instrumentation, University of Science and Technology of China, Hefei, China
2.
Department of Dermatology, the Ohio State University, Columbus, USA
3.
Department of Obstetrics and Gynecology, Second Affiliated Hospital of Chongqing Medical University, Chongqing, China
4.
Department of Biomedical Engineering, The Ohio State University, Columbus, USA

Received: 14 November 2020 Accepted: 25 February 2021 Published: 08 March 2021

Collagen alignment has shown clinical significance in a variety of diseases. For instance, vulvar lichen sclerosus (VLS) is characterized by homogenization of collagen fibers with increasing risk of malignant transformation. To date, a variety of imaging techniques have been developed to visualize collagen fibers. However, few works focused on quantifying the alignment quality of collagen fiber. To assess the level of disorder of local fiber orientation, the homogeneity index (HI) based on limiting entropy is proposed as an indicator of disorder. Our proposed methods are validated by verification experiments on Poly Lactic Acid (PLA) filament phantoms with controlled alignment quality of fibers. A case study on 20 VLS tissue biopsies and 14 normal tissue biopsies shows that HI can effectively characterize VLS tissue from normal tissue (P < 0.01). The classification results are very promising with a sensitivity of 93% and a specificity of 95%, which indicated that our method can provide quantitative assessment for the alignment quality of collagen fibers in VLS tissue and aid in improving histopathological examination of VLS.
- linear polarized imaging,
- collagen homogenization,
- fiber alignment,
- VLS,
- entropy
Citation: Yingjie Qu, Zachary J. Smith, Kelly Tyler, Shufang Chang, Shuwei Shen, Mingzhai Sun, Ronald X. Xu. Applying limiting entropy to quantify the alignment of collagen fibers by polarized light imaging[J]. Mathematical Biosciences and Engineering, 2021, 18(3): 2331-2356. doi: 10.3934/mbe.2021118

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Abstract

Collagen alignment has shown clinical significance in a variety of diseases. For instance, vulvar lichen sclerosus (VLS) is characterized by homogenization of collagen fibers with increasing risk of malignant transformation. To date, a variety of imaging techniques have been developed to visualize collagen fibers. However, few works focused on quantifying the alignment quality of collagen fiber. To assess the level of disorder of local fiber orientation, the homogeneity index (HI) based on limiting entropy is proposed as an indicator of disorder. Our proposed methods are validated by verification experiments on Poly Lactic Acid (PLA) filament phantoms with controlled alignment quality of fibers. A case study on 20 VLS tissue biopsies and 14 normal tissue biopsies shows that HI can effectively characterize VLS tissue from normal tissue (P < 0.01). The classification results are very promising with a sensitivity of 93% and a specificity of 95%, which indicated that our method can provide quantitative assessment for the alignment quality of collagen fibers in VLS tissue and aid in improving histopathological examination of VLS.

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