# Texture Analysis is a Useful Tool to Assess the Complexity Profile of Microcirculatory Blood Flow

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Experimental

#### 2.2. Numerical

^{n}(here in color scale) for each signal scale. The approximate frequency of a component is obtained by dividing the central wavelet frequency by the scale of the component. From a visual inspection, the WT scalogram also presents an oscillatory pattern in pixel distribution on different scales, making it a suitable candidate for TA. The scalogram was then used as a grayscale image, where several regions of interest (ROI) were marked, each per component per phase of the protocol. Each ROI was then converted to a gray-level co-occurrence matrix (GLCM), a matrix where the number of rows and columns is equal to the number of gray levels (G) in the image, from which the TE was calculated as follows [37]:

_{1}=3.2 Hz; f

_{2}=1.6 Hz; f

_{3}=0.7 Hz, f

_{4}=0.26 Hz; f

_{5}=0.1 Hz; f

_{6}=0.045 Hz; f

_{7}=0.015 Hz; f

_{8}=0.007 Hz), where each frequency is close to the ones that define the borders of the PPG components’ detected frequency ranges. The sine wave signal was then deconstructed with the WT, and a reference scalogram was generated (Figure 2).

^{m}(r) is the probability that two sequences will match for m + 1 points and B

^{m}(r) is the probability that two sequences will match for m points. The more regular and predictable a time series is, the lower the value of SampEn. The more random a time series is, the higher the value of SampEn. Plotting the SampEn over the scale factor yields the MSE curve, which gives insight into the integrated complexity of the system over the time scales of interest, which can be of interest when comparing groups where differences in specific time scales are probable. The randomness/unpredictability of the signal can finally be straightforwardly summarized as the complexity index (CI), which corresponds to the area under the MSE curve [38]. The CI and TE were statistically compared between each phase of the protocol with the Wilcoxon signed-rank test, and were compared between feet for each phase with the Mann-Whitney independent sample test, adopting a 95% confidence interval.

## 3. Results

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Ethics Statement

## References

- Stefanovska, A. Coupled Oscillators: Complex but Not Complicated Cardiovascular and Brain Interactions. IEEE Eng. Med. Biol.
**2007**, 26, 25–29. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Stefanovska, A.; Lotric, M.B.; Strle, S.; Haken, H. The cardiovascular system as coupled oscillators? Physiol. Meas.
**2001**, 22, 535–550. [Google Scholar] [CrossRef] - Bernjak, A.; Stefanovska, A. Importance of wavelet analysis in laser Doppler flowmetry time series. In Proceedings of the 29th Annual International Conference of the IEEE Engeniring in Medicine and Biology Society, Lyon, France, 22–26 August 2007; pp. 4064–4067. [Google Scholar]
- Silva, H.; Ferreira, H.A.; Da Silva, H.P.; Rodrigues, L.M. The Venoarteriolar Reflex Significantly Reduces Contralateral Perfusion as Part of the Lower Limb Circulatory Homeostasis in vivo. Front. Physiol.
**2018**, 9, 1–9. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Silva, H.; Bento, M.; Vieira, H.; Rodrigues, L.M. Comparing the spectral components of laser Doppler flowmetry and photoplethysmography signals for the assessment of the vascular response to hyperoxia. J. Biomed. Biopharm. Res.
**2017**, 14, 187–194. [Google Scholar] [CrossRef] - Silva, H.; Ferreira, H.; Rodrigues, L.M. Studying the Oscillatory Components of Human Skin Microcirculation. In Measuring the Skin; Springer Science and Business Media LLC: Berlin, Germany, 2015; pp. 1–15. [Google Scholar]
- Mizeva, I.; Di Maria, C.; Frick, P.; Podtaev, S.; Allen, J. Quantifying the correlation between photoplethysmography and laser Doppler flowmetry microvascular low-frequency oscillations. J. Biomed. Opt.
**2015**, 20, 37007. [Google Scholar] [CrossRef] [PubMed] - Costa, M.; Goldberger, A.L.; Peng, C.-K. Multiscale entropy analysis of biological signals. Phys. Rev. E
**2005**, 71, 021906. [Google Scholar] [CrossRef] [Green Version] - Rangel, J.A.O. The Systemic Theory of Living Systems and Relevance to CAM Part I: The Theory. Evid-Based Compl. Alt.
**2005**, 2, 13–18. [Google Scholar] [CrossRef] - Zhang, Y.; Wei, S.; Long, Y.; Liu, C. Performance Analysis of Multiscale Entropy for the Assessment of ECG Signal Quality. J. Electr. Comput. Eng.
**2015**, 2015, 1–9. [Google Scholar] [CrossRef] [Green Version] - Chung, C.-C.; Kang, J.-H.; Yuan, R.-Y.; Wu, D.; Chen, C.-C.; Chi, N.-F.; Chen, P.-C.; Hu, C.-J. Multiscale Entropy Analysis of Electroencephalography During Sleep in Patients With Parkinson Disease. Clin. EEG Neurosci.
**2013**, 44, 221–226. [Google Scholar] [CrossRef] - Trunkvalterova, Z.; Javorka, M.; Tonhajzerova, I.; Javorkova, J.; Lazárová, Z.; Javorka, K.; Baumert, M. Reduced short-term complexity of heart rate and blood pressure dynamics in patients with diabetes mellitus type 1: multiscale entropy analysis. Physiol. Meas.
**2008**, 29, 817–828. [Google Scholar] [CrossRef] - Humeau, A.; Buard, B.; Mahé, G.; Rousseau, D.; Chapeau-Blondeau, F.; Abraham, P. Multiscale entropy of laser Doppler flowmetry signals in healthy human subjects. Med. Phys.
**2010**, 37, 6142. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Schack, T.; Harb, Y.S.; Muma, M.; Zoubir, A.M. Computationally efficient algorithm for photoplethysmography-based atrial fibrillation detection using smartphones. In 2017 39th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC); Institute of Electrical and Electronics Engineers (IEEE): Piscataway, NJ, USA, 2017; pp. 104–108. [Google Scholar]
- Zhang, X.D.; Shen, B. Entropy for the Complexity of Physiological Signal Dynamics. Adv. Exp. Med. Biol.
**2017**, 1028, 39–53. [Google Scholar] [PubMed] - Yang, D.; Luo, Z.; Ma, S.; Wong, W.T.; Ma, L.; Zhong, J.; He, H.; Zhao, Z.; Cao, T.; Yan, Z.; et al. Activation of TRPV1 by dietary capsaicin improves endothelium-dependent vasorelaxation and prevents hypertension. Cell Metab.
**2010**, 12, 130–141. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Liu, Y.; Lin, Y.; Wang, J.; Shang, P. Refined generalized multiscale entropy analysis for physiological signals. Phys. A: Stat. Mech. its Appl.
**2018**, 490, 975–985. [Google Scholar] [CrossRef] - Vargas, B.; Cuesta-Frau, D.; Ruiz-Esteban, R.; Cirugeda, E.; Varela, M. What Can Biosignal Entropy Tell Us About Health and Disease? Applications in Some Clinical Fields. Nonlinear Dyn. Psychol. Life Sci.
**2015**, 19, 419–436. [Google Scholar] - Costa, M.; Goldberger, A.L.; Peng, C.-K. Multiscale Entropy Analysis of Complex Physiologic Time Series. Phys. Rev. Lett.
**2002**, 89, 068102. [Google Scholar] [CrossRef] [Green Version] - Tsai, D.-Y.; Lee, Y.; Matsuyama, E. Information Entropy Measure for Evaluation of Image Quality. J. Digit. Imaging.
**2008**, 21, 338–347. [Google Scholar] [CrossRef] [Green Version] - Larroza, A.; Bodí, V.; Moratal, D. Texture Analysis in Magnetic Resonance Imaging: Review and Considerations for Future Applications. In Assessment of Cellular and Organ Function and Dysfunction using Direct and Derived MRI Methodologies; IntechOpen: London, UK, 2016; pp. 75–106. [Google Scholar]
- Pharwaha, A.P.S.; Singh, B. Shannon and Non-Shannon Measures of Entropy for Statistical Texture Feature Extraction in Digitized Mammograms. In Proceedings of the World Congres on Engineering nd Computer Science, San Francisco, CA, USA, 20–22 October 2009. [Google Scholar]
- Al-Kadi, O.; Watson, D. Texture Analysis of Aggressive and Nonaggressive Lung Tumor CE CT Images. IEEE Trans. Biomed. Eng.
**2008**, 55, 1822–1830. [Google Scholar] [CrossRef] - Gibbs, P.; Turnbull, L.W. Textural analysis of contrast-enhanced MR images of the breast. Magn. Reson. Med.
**2003**, 50, 92–98. [Google Scholar] [CrossRef] - Castellano, G.; Bonilha, L.; Li, L.; Cendes, F. Texture analysis of medical images. Clin. Radiol.
**2004**, 59, 1061–1069. [Google Scholar] [CrossRef] - Shrestha, B.; Bishop, J.; Kam, K.; Chen, X.; Moss, R.H.; Stoecker, W.V.; Umbaugh, S.; Stanley, R.J.; Celebi, M.E.; Marghoob, A.A.; et al. Detection of atypical texture features in early malignant melanoma. Skin. Res. Technol.
**2010**, 16, 60–65. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Gao, Y.; Helgeson, M.E. Texture analysis microscopy: quantifying structure in low-fidelity images of dense fluids. Opt. Express
**2014**, 22, 10046–10063. [Google Scholar] [CrossRef] [PubMed] - Pantic, I.; Pantic, S. Germinal Center Texture Entropy as Possible Indicator of Humoral Immune Response: Immunophysiology Viewpoint. Mol. Imaging. Biol.
**2012**, 14, 534–540. [Google Scholar] [CrossRef] [PubMed] - Mir, A.; Hanmandlu, M.; Tandon, S. Texture Analysis of CT. IEEE Eng. Med. Biol.
**1995**, 14, 781–786. [Google Scholar] [CrossRef] - Ng, F.; Ganeshan, B.; Kozarski, R.; Miles, K.A.; Goh, V. Assessment of Primary Colorectal Cancer Heterogeneity by Using Whole-Tumor Texture Analysis: Contrast-enhanced CT Texture as a Biomarker of 5-year Survival. Radiology
**2013**, 266, 177–184. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Ng, F.; Kozarski, R.; Ganeshan, B.; Goh, V. Assessment of tumor heterogeneity by CT texture analysis: Can the largest cross-sectional area be used as an alternative to whole tumor analysis? Eur. J. Radiol.
**2013**, 82, 342–348. [Google Scholar] [CrossRef] - El Hassani, A.; El Hassouni, M.; Jennane, R.; Rziza, M.; Lespessailles, E. Texture Analysis for Trabecular Bone X-Ray Images Using Anisotropic Morlet Wavelet and Rényi Entropy. In Image and Signal Processing, Proceedings of the 5th International Conference on Image and Signal Processing, Agadir, Morocco, 28–30 June 2012; Elmoataz, A., Mammass, D., Lezoray, O., Nouboud, F., Aboutajdine, D., Eds.; Springer: Berlin, Germany, 2012; pp. 290–297. [Google Scholar]
- Kołaciński, M.; Kozakiewicz, M.; Materka, A. Textural entropy as a potential feature for quantitative assessment of jaw bone healing process. Arch. Med. Sci.
**2015**, 11, 78–84. [Google Scholar] [CrossRef] - Shamir, L.; Wolkow, C.A.; Goldberg, I.G. Quantitative measurement of aging using image texture entropy. Bioinformatics
**2009**, 25, 3060–3063. [Google Scholar] [CrossRef] [Green Version] - WMA. World Medical Association Declaration of Helsinki: Ethical principles for medical research involving human subjects. J. Am. Med. Assoc.
**2013**, 310, 2191–2194. [Google Scholar] [CrossRef] [Green Version] - Kvandal, P.; Landsverk, S.A.; Bernjak, A.; Stefanovska, A.; Kvernmo, H.D.; Kirkebøen, K.A. Low-frequency oscillations of the laser Doppler perfusion signal in human skin. Microvasc. Res.
**2006**, 72, 120–127. [Google Scholar] [CrossRef] - Gonzalez, R.; Woods, R.E.; Eddins, S.L. Digital Image Processing Using MATLAB, 2nd ed.; Gatesmark Publishing: USA, 2009. [Google Scholar]
- Ferreira, H.; Rodrigues, F.; Meyer, M.; Santos-Ribeiro, A.; Gonçalves-Pereira, P.; Manaças, R.; Andrade, A. Complexity analysis of resting-state networks. MAGMA
**2013**, 26, 2013. [Google Scholar] - Gabrielsen, A.; Norsk, P. Effect of spaceflight on the subcutaneous venoarteriolar reflex in the human lower leg. J. Appl. Physiol.
**2007**, 103, 959–962. [Google Scholar] [CrossRef] [PubMed]

**Figure 1.**WT scalogram of the PPG signal from the control (top) and test (bottom) feet from a representative subject (20 y.o.).

**Figure 2.**WT scalogram of the reference sine wave signal. The region corresponding to each component frequency interval is shown (1—first harmonic of the cardiac component; 2—cardiac; 3—respiratory; 4—myogenic; 5—sympathetic; 6—endothelial NO-dependent; 7—endothelial NO-independent).

**Figure 3.**PPG 3D frequency spectrum (period vs. sample vs. amplitude) for the test foot of a representative subject (20 y.o.). Signals were acquired at a 100 Hz sampling rate, which translates to a total of 180,000 signal samples for a 30 minute acquisition period. Period is a natural logarithmic representation of the wavelet scale.

**Figure 4.**Time evolution of the PPG signal components’ amplitude ratio for the control (blue) and test (red) feet throughout the protocol (baseline: signal samples 0–60,000; challenge: signal samples 60,000–120,000; recovery: signal samples 120,000–180,000) for a representative subject (20 y.o.).

**Table 1.**Mean and standard deviation (SD) of the MSE complexity index for each foot on each phase of the protocol (card—cardiac, resp—respiratory, myo—myogenic, sym—sympathetic, NOd—endothelial NO-dependent, NOi—endothelial NO-independent). Statistical comparison to Phase I is shown (*—p < 0.05).

Complexity Index | Test Foot | Control Foot | p-Value (T vs. C) | |||
---|---|---|---|---|---|---|

Mean ± SD | p-Value | Mean ± SD | p-Value | |||

raw signal | Phase I | 34.8 ± 6.1 | - | 34.2 ± 8.2 | - | 0.843 |

Phase II | 15.0 ± 11.5 | 0.005 * | 35.9 ± 8.7 | 0.182 | <0.001 * | |

Phase III | 31.4 ± 7.3 | 0.182 | 37.0 ± 6.7 | 0.239 | 0.089 | |

card | Phase I | 25.9 ± 6.1 | - | 29.3 ± 7.2 | - | 0.347 |

Phase II | 15.6 ± 9.0 | 0.012 * | 28.7 ± 6.5 | 0.754 | <0.001 * | |

Phase III | 23.8 ± 7.3 | 0.224 | 29.7 ± 7.8 | 0.875 | 0.089 | |

resp | Phase I | 25.9 ± 6.1 | - | 29.3 ± 7.2 | - | 0.347 |

Phase II | 6.7 ± 4.2 | 0.002 * | 14.3 ± 4.8 | 0.002 * | 0.001 * | |

Phase III | 10.1 ± 5.5 | 0.002 * | 13.7 ± 4.9 | 0.002 * | 0.160 | |

myo | Phase I | 23.2 ± 8.7 | - | 25.9 ± 7.5 | - | 0.378 |

Phase II | 3.9 ± 3.1 | 0.003 * | 12.0 ± 2.8 | 0.003 * | <0.001 * | |

Phase III | 7.9 ± 5.4 | 0.008 * | 10.9 ± 5.8 | 0.008 * | 0.160 | |

sym | Phase I | 25.9 ± 6.1 | - | 29.3 ± 7.2 | - | 0.347 |

Phase II | 2.6 ± 2.4 | 0.002 * | 10.5 ± 1.9 | 0.002 * | <0.001 * | |

Phase III | 6.8 ± 2.2 | 0.002 * | 10.7 ± 4.0 | 0.002 * | 0.012 * | |

NOd | Phase I | 25.9 ± 6.1 | - | 29.3 ± 7.2 | - | 0.347 |

Phase II | 2.5 ± 3.5 | 0.002 * | 11.5 ± 2.6 | 0.002 * | <0.001 * | |

Phase III | 5.5 ± 2.1 | 0.002 * | 11.0 ± 4.8 | 0.002 * | 0.002 * | |

NOi | Phase I | 25.9 ± 6.1 | - | 29.3 ± 7.2 | - | 0.347 |

Phase II | 1.9 ± 0.9 | 0.002 * | 10.2 ± 3.6 | 0.002 * | <0.001 * | |

Phase III | 6.2 ± 3.4 | 0.002 * | 13.6 ± 5.0 | 0.003 * | <0.001 * |

**Table 2.**Mean and standard deviation (SD) of the texture entropy for each foot on each phase of the protocol (card—cardiac, resp—respiratory, myo—myogenic, sym—sympathetic, NOd—endothelial NO-dependent, NOi—endothelial NO-independent). Statistical comparison to Phase I and between the test and control limbs are shown (*—p < 0.05).

Texture Entropy | Sine Wave Signal | Test Foot | Control Foot | p-Value (T vs. C) | |||
---|---|---|---|---|---|---|---|

Mean ± SD | p-Value | Mean ± SD | p-Value | ||||

card | Phase I | 6.1 | 6.6 ± 0.5 | - | 6.8 ± 0.3 | - | 0.198 |

Phase II | 6.2 ± 0.7 | 0.004 * | 6.9 ± 0.3 | 0.011 * | 0.001 * | ||

Phase III | 7.0 ± 0.2 | 0.563 | 7.0 ± 0.2 | 0.022 * | 0.713 | ||

resp | Phase I | 5.4 | 6.5 ± 0.2 | - | 6.5 ± 0.2 | - | 0.551 |

Phase II | 5.5 ± 1.3 | 0.013 * | 6.3 ± 0.2 | 0.286 | 0.045 * | ||

Phase III | 6.5 ± 0.2 | 0.638 | 6.4 ± 0.2 | 0.530 | 0.478 | ||

myo | Phase I | 5.2 | 6.6 ± 0.3 | - | 6.7 ± 0.1 | - | 0.089 |

Phase II | 6.3 ± 0.4 | 0.008 * | 6.6 ± 0.1 | 0.433 | 0.028 * | ||

Phase III | 6.5 ± 0.2 | 0.289 | 6.7 ± 0.2 | 0.754 | 0.266 | ||

sym | Phase I | 5.3 | 6.2 ± 0.3 | - | 6.2 ± 0.4 | - | 0.671 |

Phase II | 6.2 ± 0.2 | 0.147 | 6.2 ± 0.2 | 0.814 | 0.887 | ||

Phase III | 6.0 ± 0.2 | 0.594 | 6.1 ± 0.3 | 0.239 | 0.630 | ||

NOd | Phase I | 5.3 | 5.8 ± 0.5 | - | 5.9 ± 0.4 | - | 0.630 |

Phase II | 6.4 ± 0.2 | 0.012 * | 5.7 ± 0.5 | 0.272 | 0.001 * | ||

Phase III | 6.1 ± 0.3 | 0.007 * | 5.9 ± 0.3 | 0.307 | 0.060 | ||

NOi | Phase I | 6.2 | 6.0 ± 0.4 | - | 5.9 ± 0.4 | - | 0.551 |

Phase II | 6.2 ± 0.3 | 0.010 * | 5.5 ± 0.7 | 0.753 | 0.001 * | ||

Phase III | 6.2 ± 0.3 | 0.594 | 5.8 ± 0.8 | 0.126 | 0.060 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Silva, H.; Ferreira, H.A.; Rocha, C.; Monteiro Rodrigues, L.
Texture Analysis is a Useful Tool to Assess the Complexity Profile of Microcirculatory Blood Flow. *Appl. Sci.* **2020**, *10*, 911.
https://doi.org/10.3390/app10030911

**AMA Style**

Silva H, Ferreira HA, Rocha C, Monteiro Rodrigues L.
Texture Analysis is a Useful Tool to Assess the Complexity Profile of Microcirculatory Blood Flow. *Applied Sciences*. 2020; 10(3):911.
https://doi.org/10.3390/app10030911

**Chicago/Turabian Style**

Silva, Henrique, Hugo A. Ferreira, Clemente Rocha, and Luís Monteiro Rodrigues.
2020. "Texture Analysis is a Useful Tool to Assess the Complexity Profile of Microcirculatory Blood Flow" *Applied Sciences* 10, no. 3: 911.
https://doi.org/10.3390/app10030911