Abstract
Manual ultrasound (US)-based methods are adapted for lumen diameter (LD) measurement to estimate the risk of stroke but they are tedious, error prone, and subjective causing variability. We propose an automated deep learning (DL)-based system for lumen detection. The system consists of a combination of two DL systems: encoder and decoder for lumen segmentation. The encoder employs a 13-layer convolution neural network model (CNN) for rich feature extraction. The decoder employs three up-sample layers of fully convolution network (FCN) for lumen segmentation. Three sets of manual tracings were used during the training paradigm leading to the design of three DL systems. Cross-validation protocol was implemented for all three DL systems. Using the polyline distance metric, the precision of merit for three DL systems over 407 US scans was 99.61%, 97.75%, and 99.89%, respectively. The Jaccard index and Dice similarity of DL lumen segmented region against three ground truth (GT) regions were 0.94, 0.94, and 0.93 and 0.97, 0.97, and 0.97, respectively. The corresponding AUC for three DL systems was 0.95, 0.91, and 0.93. The experimental results demonstrated superior performance of proposed deep learning system over conventional methods in literature.
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The authors at the National Institute of Technology, Goa, India, would like to acknowledge MediaLab Asia, Ministry of Electronics and Information Technology, and the Government of India for their kind support.
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The ethics approval was granted by Toho University IRB, Japan. Informed consent was obtained from all the patients.
Appendices
Appendix 1 Statistical test results
Appendix 2 Polyline distance method
1.1 Polyline distance metric
Polyline distance metric (PDM) [40] is used to measure the lumen diameter (LD), LI-far error, and LI-near error. In here, we focus on deriving the PDM given two border contours. Let the first and second contours be denoted as I1 and I2. Let the reference point on I1 be vertex A1 and the segment in I2 be defined by vertices A2 and A3. Let the distance between A1 and A2 be d1and the distance between A1 and A3 be denoted as d2. Let D(A1, L) be the polyline distance between vertex A1 : (x1, y1) on I1 and line segment L formed by two points A2 : (x2, y2)and A3 : (x3, y3). Let phi (φ) be the distance of the reference point, A1 towards the line segment L. The perpendicular distance between the line segment L and the reference point, A1, is given by dP. Then, the polyline distance D(A1, L) can be defined as:
where,
and
The process to obtain D(A1, L) is repeated for the rest of the points of the contour Ij and is given by:
where, N is the total number of points on I1 and \( {S}_{I_2} \) is the segment on contour I2. This algorithm is repeated in reverse, where I2 becomes the reference contour and I1 becomes the segment contour. The reverse is represented as D(I2, I1). Finally, by combining both D(I1, I2) and D(I2, I1), we obtain the PDM which is given by:
Appendix 3 Figure-of-merit and precision-of-merit
1.1 LD and mean LD computation
The LD error is computed as PDM between the ground truth LD (LDgt) and deep learning LD (LDdl). The LD for a patient i is computed as a PDM between LI-far ( LIfar(i)) and LI-near ( LInear(i)) wall of the patient. The ground truth LD (LDgt(i)) for patient i is given as:
Similarly, deep learning LD (LDdl(i)) for image i is given as:
The mean LD can therefore be computed as:
1.2 LD error and mean LD error
The LD error (εLD(i)) for an image i is computed as the absolute difference between LDgt(i) and LDdl(i) and is mathematically represented as:
If εLD(i) represents the LD error for an image i, then the mean LD error (\( {\overline{\varepsilon}}_{\mathrm{LD}} \)) for all N patients is given by:
1.3 Precision-of-merit
Using Eqs. (C.1) and (C.2), one can therefore define mathematically the precision-of-merit (POM) and is given as:
1.4 Figure-of-merit
The central tendency of the LD distribution can also be used to tell the difference between the DL-based LD and GT-based LD. Using (C.3) and (C.4), one can therefore compute figure-of-merit (FoM) and can be expressed mathematically as:
Appendix 4 LI-far and LI-near position errors
1.1 LI-far error
The LI-far error (εfar(i)) for patient i is computed as the PDM between the GT LI-far wall (\( {\mathrm{LI}}_{\mathrm{far}(i)}^{\mathrm{gt}} \)) and DL LI-far (\( {\mathrm{LI}}_{\mathrm{far}(i)}^{\mathrm{dl}} \)) wall for the patient, which is given by:
If εfar(i) represents the LI-far error for the patient i, then, the mean LI-far error (\( {\overline{\varepsilon}}_{\mathrm{far}} \)) for all N patients is given by:
1.2 LI-near error
Similarly, the LI-near error (εnear(i)) is computed as the PDM between the GT LI-near wall (\( {\mathrm{LI}}_{\mathrm{near}(i)}^{\mathrm{gt}} \)) and DL LI-near (\( {\mathrm{LI}}_{\mathrm{near}(i)}^{\mathrm{dl}} \)) wall for patient i is given by:
The mean LI-near error (\( {\overline{\varepsilon}}_{\mathrm{near}} \)) for all N patients is given by:
The corresponding symbol table is given in Appendix 5, Table 8.
Appendix 5 Symbol table
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Biswas, M., Kuppili, V., Saba, L. et al. Deep learning fully convolution network for lumen characterization in diabetic patients using carotid ultrasound: a tool for stroke risk. Med Biol Eng Comput 57, 543–564 (2019). https://doi.org/10.1007/s11517-018-1897-x
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DOI: https://doi.org/10.1007/s11517-018-1897-x