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Penile Arterial Waveform Analyzer for Assessing Penile Vascular Function in Young Adults

Abstract

Not only does erectile dysfunction (ED) reflect penile vascular disorder in the majority of patients, but it also implicates their high systemic cardiovascular risk. Based on the principle of reactive hyperemia after a brief period of penile ischemia, in this study, we tested the validity of a new Penile Arterial Waveform Analyzer (PAWA) in assessing the relative increase in post-ischemic penile perfusion. Twenty young adult males (mean age 24.24 ± 2.45) without known history of cardiovascular diseases were recruited, whose anthropometric characteristics were recorded and their serum testosterone levels as well as biochemical profiles were determined. A penile cuff was applied to each subject, with cuff pressure being increased from 80 to 250 mmHg, each for 4 min, followed by reperfusion for 7 min. By dividing the area under waveform contour of hyperemic and baseline signals after Ensemble Empirical Mode Decomposition (EEMD), a Penile Perfusion Index (PPI) was calculated. Penile Brachial Index (PBI) was also obtained for comparison. The results not only showed a significant agreement between PPI and serum testosterone levels, but also a superiority of PPI to PBI in distinguishing the high- and low-risk groups for potential ED (PPI: p = 0.039 vs. PBI: p = 0.147). PPI was also demonstrated to show significant correlations with waist circumference (p < 0.001), body mass index (p = 0.005), body weight, total triglyceride, high-density lipoprotein, and systolic and diastolic pressures (all p < 0.05). In conclusion, we proposed a portable and easy-to-operate system in assessing the relative increase in penile perfusion after brief ischemia. The PPI thus obtained correlated significantly with serum testosterone levels as well as key anthropometric and serum biochemical parameters even in apparently healthy young adults, suggesting its potential as a sensitive tool in monitoring penile vascular function and risk for ED.

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Acknowledgments

The authors would like to thank the Associate Editor, Professor Ioannis A. Kakadiaris, and the anonymous reviewers for their insightful comments and suggestions which have significantly contributed to the improvement of this study. This research was supported in part by grants from the National Science Council (NSC 98-2221-E-259-017 and NSC 99-2221-E-259-001), Taiwan, Republic of China. The authors would also like to thank Miss Shu-Mei Wen, who worked as Acting Head Nurse in the Outpatient Department of Hualien Hospital for her clinical support, and the volunteers involved in this study for allowing us to collect and analyze their data. The authors are also grateful to Texas Instruments, Taiwan, for sponsoring the low-power instrumentation amplifiers and ADC.

Author information Authors and Affiliations
  1. Department of Electrical Engineering, National Dong Hwa University, No. 1, Sec. 2, Da-Hsueh Rd., Shoufeng, Hualien, 97401, Taiwan

    Hsien-Tsai Wu & Chun-Ho Lee

  2. Department of Urology, Hualien Hospital, Department of Health Executive Yuan, Hualien, 97061, Taiwan

    Chin-Jung Chen

  3. Department of Emergency Medicine, E-Da Hospital, I-Shou University, Kaohsiung, 82445, Taiwan

    Cheuk-Kwan Sun

Authors
  1. Hsien-Tsai Wu
  2. Chun-Ho Lee
  3. Chin-Jung Chen
  4. Cheuk-Kwan Sun
Corresponding author

Correspondence to Hsien-Tsai Wu.

Additional information

Associate Editor Ioannis A. Kakadiaris oversaw the review of this article.

Appendix Appendix Ensemble Empirical Mode Decomposition (EEMD)

In general,

$$ x\left( t \right) = s\left( t \right) + n\left( t \right) $$

(A1)

where x(t) is the recorded data, and s(t) and n(t) are the true signal and white noises, respectively.

Step 1: Identify local extrema in the experimental data x(t). All the local maxima are connected by a cubic spline line x up(t), which forms the upper envelope of the data. Repeat the same procedure for the local minima to produce the lower envelope x low(t). Both envelopes will cover all the data between them. The mean of upper envelope and lower envelope m 1(t) is given by

$$ m_{1} \left( t \right) = \frac{{\left( {x_{\text{up}} \left( t \right) + x_{\text{low}} \left( t \right)} \right)}}{2}. $$

(A2)

Subtracting the running mean m 1(t) from the original time series x(t), we get the first component h 1(t);

$$ h_{1} \left( t \right) = x\left( t \right) - m_{1} \left( t \right). $$

(A3)

If h 1(t) is not an IMF, then the sifting process has to be repeated as many times as required to reduce the extracted signal to an IMF. Subsequently

$$ h_{11} \left( t \right) = h_{1} \left( t \right) - m_{11} \left( t \right). $$

(A4)

Through the iteration process (for a total of k times), the difference within the signal and the mean envelope values, which is denoted as h 1k (t), is obtained as

$$ h_{1k} \left( t \right) = h_{{1\left( {k - 1} \right)}} \left( t \right) - m_{1k} \left( t \right). $$

(A5)

Step 2: If the resulting time series is an IMF, then it is designated as c 1 = h 1k (t). The first IMF is then subtracted from the original data, and the difference r 1 given by

$$ r_{1} \left( t \right) = x\left( t \right) - c_{1} \left( t \right). $$

(A6)

The residue r 1(t) is taken as the original data, and we apply to it again the sifting process of Step 1. Adopting the same procedures for Step 1 and Step 2, we continue the process to find more intrinsic modes c i until the last one. The final residue will be a constant or a monotonic function which represents the general trend of the time series. Finally, we obtain

$$ x\left( t \right) = \sum\limits_{i = 1}^{n} {c_{i} \left( t \right) + r_{n} } $$

(A7)

$$ x\left( t \right) = IMF1 + IMF2 + \cdots + IMFn + r_{n}, $$

(A8)

$$ r_{i - 1} \left( t \right) - c_{i} \left( t \right) = r_{i} \left( t \right),\quad i = 2, \ldots ,n. $$

(A9)

The result of EEMD is obtained when the number in the ensemble approaches infinity:

$$ c_{i} \left( t \right) = \mathop {\lim }\limits_{N \to \infty } \frac{1}{N}\sum\limits_{k = 1}^{n} {\left\{ {c_{i} \left( t \right) + \alpha r_{k} \left( t \right)} \right\}} , $$

(A10)

where

$$ c_{i} \left( t \right) + \alpha r_{k} \left( t \right) $$

(A11)

is the kth realization of the ith IMF in the noise-added signal, α is the standard deviation of the added noise, and r k (t) is the residual after extracting the first k IMF components. The iteration time in the ensemble, N, has to be large. In this study, α is set to be 0.2, and N is equal to 200 for fast computing.20,36,38

The Hilbert Spectrum

Having obtained the IMF components, it is easy to apply the Hilbert transform to each component, and the instantaneous frequency can be computed. Therefore, the Hilbert spectrum of the signal x(t) can be expressed in the following form:

$$ H\left( {\omega ,t} \right) = \text{Re} \sum\limits_{i = 1}^{n} {a\left( t \right)e^{{j\int {\omega \left( t \right)dt} }} } $$

(A12)

where Re means taking the real part of the sum, a(t) indicates the ith instantaneous amplitude of the analysis signal, and ω(t) represents the ith instantaneous frequency. With the Hilbert spectrum defined, we can also define the marginal spectrum, h(ω), as

$$ h\left( \omega \right) = \int\limits_{0}^{T} {H\left( {\omega ,t} \right)dt.} $$

(A13)

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Wu, HT., Lee, CH., Chen, CJ. et al. Penile Arterial Waveform Analyzer for Assessing Penile Vascular Function in Young Adults. Ann Biomed Eng 39, 2857–2868 (2011). https://doi.org/10.1007/s10439-011-0342-1

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