Real-time flow impedance evaluation method for ultra-fast early detection of aneurysmal diseases

doi:10.1016/j.bspc.2020.102256

Biomedical Signal Processing and Control

Volume 64, February 2021, 102256

https://doi.org/10.1016/j.bspc.2020.102256 Get rights and content

Highlights

•
Typical Diagnosis of aneurysmal diseases can only be done by routine medical tests.
•
Inexpensive, less time consuming and technical demanding test is in demand.
•
Real-time flow impedance was proposed to detect aneurysm.
•
Features of real-time flow impedance were correlated with the aneurysm formation.

Abstract

Objective

A novel method to measure the real-time input flow impedance of thoracic aorta aneurysm (TAA) was developed.

Methods

The fundamental of real-time input flow impedance was described. The simultaneously measured blood pressure and volumetric flow rate were obtained and used for the calculation. The input flow impedance was then presented in its complexed format: real and imaginary; modulus and phase in the time domain.

Results

Unique features of real-time input flow impedance were extracted to correlate with the TAA formation. It showed that the trough of modulus located at the end of each cardiac cycle has different values, which are proportional to the sizes of TAAs.

Conclusions

A real-time input flow impedance of the cardiovascular system was presented in this paper. We postulate that the proposed fluid mechanics model has the potential to analyze the pathomechanics of aneurysmal diseases in real-time.

Introduction

System modeling has been widely used to study the dynamic behavior of a physical system [1]. In system modeling, lumped elements are used to represent a system. Depending on the energy domain, these elements can be classified as mechanical elements (mass, spring and dashpot); electrical elements (inductor, capacitor and resistor) and fluid elements (mass flow, fluid compliance and flow resistance). The use of lumped elements simplifies the modeling of complex physical systems because the lumped elements produce a finite number of ordinary differential equations which describe the dynamic behavior of a system in either time or frequency domain.

Power conjugate variables are two variables which yield the change of power in a physical system. Therefore, it is possible to develop a logical set of analogies between different energy domains, i.e., force (F) and velocity (V) in a mechanical system; voltage (e) and current (I) in an electrical system; pressure (P) and volumetric flow (Q) in a fluid system. Using this analogy, we are able to calculate the impedance of the system based on Maxwell analogy [2]. As compared with the conventional approach of developing ordinary differential equations, this impedance analogy has advantages such as i) it preserves the analogy between different energy domains; ii) it preserves the analogy between 2 variables. Based on the defined variables in the respective energy domains, it is possible to develop a 1-port with 1 pair of power conjugate or 2-port model with 2 pair of power conjugates separated by input and output channel of the physical system. Therefore, the energy flow of the 1-port or 2-port model is governed by the input or output impedance of the system, which is the quotient of effort variables (F, e, and P) to the flow variables (V, I, and Q).

The input impedance of the 1-port model has an advantage over the lumped elements in characterizing the dynamic behavior of a physical system because the change in input impedance is solely caused by the time variance of lumped elements. Therefore, the input impedance is ideally isolated from the influence of disturbances to the system. However, the drawback of input impedance is that the data can only be presented in the frequency domain. This makes it difficult to evaluate the real-time change of a physical system.

Recently, the Hilbert transform (HT) has been used for the time-frequency analysis of non-stationary and nonlinear signals. Huang et al. [3] developed a Hilbert-Huang transform (HHT) to analyze the intrinsic mode functions of a signal, which is obtained by using the empirical mode decomposition method. It was reported that the time-frequency distribution of the signals can be identified accurately because the Hilbert transform can inherently convert the real-valued signal into complex-valued signal with respect to the instantaneous frequency. The HHT has been applied successfully to investigate structural health condition [4] and bearing vibration problems [5,6].

To further explore the capability of HT in time-frequency analysis, Ling and co-workers developed a real-time input impedance-based health monitoring and diagnosis method for various manufacturing processes such as micro-drilling, wire bonding, ultrasonic welding, resistance spot welding and arc welding [[7], [8], [9], [10], [11]]. Since the real-time input impedance is inherently the system property of a dynamic process, it can be correlated with the change in the physical system, previously described by the lumped elements.

In this study, a novel method to measure the real-time input flow impedance of thoracic aorta aneurysm (TAA) is presented. To demonstrate the capability of the proposed method, four computational fluid dynamic (CFD) models based on patients-specific thoracic aortas were studied and later further examined with an in-vitro experiment to test the feasibility of the proposed method in vitro. This paper is presented as follows: Method to introduce the fundamentals and development of real-time input flow impedance, followed by, Results and Discussion to present the input flow impedance and characterization of thoracic aorta aneurysm. The applications of this proposed method are then summarized.

Section snippets

Hilbert Transform (HT)

As stated in reference [12], the HT of a real-valued function x(t) can be defined as: $\tilde{x} (t) = h [x (t)] = \int_{- \infty}^{\infty} \frac{x (u)}{π (t - u)} d u$ where $\tilde{x} (t)$ is the convolution integral of x(t) and $(\frac{1}{π t})$ . The computation of HT is achieved by taking the Fourier transform of $\tilde{x} (t)$ $\tilde{X} (f) = X (f) \{\begin{array}{c} e^{- j (\frac{π}{2})} f > 0 \\ e^{j (\frac{π}{2})} f < 0 \end{array}$ where the $\tilde{x} (t)$ is the Fourier transform of x(t) shifted by $(\frac{π}{2})$ . To form the complex-valued signal of x(t), or known as analytic signal, it can be expressed as $\hat{x} (t) = x (t) + j \tilde{x} (t) = |X (t)| e^{j θ (t)}$ in which, $|X (t)| = \sqrt{x^{2} (t) + {\tilde{x}}^{2} (t)}$ $θ (t) = \tan^{- 1} [\frac{\tilde{x} (t)}{x (t)}]$

Detail of patient and healthy subject geometries

We adopted the three patient-specific and one healthy subject geometries from our previous study to evaluate our proposed method [13]. Geometrical information of aneurysms in the thoracic aorta was extracted as axial images with images numbers of 864–1000 (in-plane resolution of 512 by 512 pixels slice thickness of 0.6 mm) from three contrast-enhanced CT scan data. As shown in Fig. 2, TAA#01-TAA#03 was extracted from CT images and segmented into 3D geometries using an image processing software

Discussion

The impedance concept in the cardiovascular system has been widely discussed. Nicolas and O’Rourke [15] defined that the input impedance of the cardiovascular system not only describes the changes in local arterial properties, but also the properties of blood inertial forces, arterial distensibility, pulse wave travel and reflection. It has been proposed that the input impedance could be calculated by dividing the Fourier -transformed values of pressure and flow in the frequency domain [16,17]

Conclusions

In conclusion, a real-time input flow impedance of the cardiovascular system is presented in this paper. The time-varying real part, imaginary part, modulus and phase of real-time input flow impedance offer a great potential to be integrated into next generation real-time monitoring medical devices for detection of the onset of aneurysmal diseases.

Credit authorship contribution statement

Yoke Rung Wong, Chi Wei Ong provided conception, design and acquired data; Yoke Rung Wong, Chi Wei Ong, Alyssa LiYu Toh analyzed the data and Yoke Rung Wong, Chi Wei Ong, Alyssa LiYu Toh, Einly Lim, Hwa Liang Leo drafted the manuscript; all authors revised the manuscript for intellectual content and provided administrative support; Yoke Rung Wong and Hwa Liang Leo acquired funding.

Funding

This work was supported by Singapore Ministry of Education Tier 1 Grant (R-397-000-266-114); the Singapore Ministry of Health’s National Medical Research Council under its Centre Grant (NMRC/CG/M011/2017); and the Surgery Academic Clinical Program Grant (Biomechanics Lab Programme).

Declaration of Competing Interest

The authors report no declarations of interest.

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Cited by (0)

View full text

Real-time flow impedance evaluation method for ultra-fast early detection of aneurysmal diseases

Highlights

Abstract

Objective

Methods

Results

Conclusions

Introduction

Section snippets

Hilbert Transform (HT)

Detail of patient and healthy subject geometries

Discussion

Conclusions

Credit authorship contribution statement

Funding

Declaration of Competing Interest

NDT E Int.

NDT E Int.

Eur. J. Obstet. Gynecol. Reprod. Biol.

Curr. Probl. Cardiol.

Electromechanical Sensors and Actuators

A dynamical theory of the electromagnetic field

The Scientific Papers of James Clerk Maxwell

Hilbert-Huang based approach for structural damage detection

J. Eng. Mech.

Dynamic characterization of a damaged beam using empirical mode decomposition and Hilbert spectrum method

Proc. SPIE – Int. Soc. Opt. Eng.

Analysis of bearing vibration signatures using empirical mode decomposition and Hilbert-Huang transform

Proc. SPIE – Int. Soc. Opt. Eng.

Ensemble empirical mode decomposition and Hilbert-Huang transform applied to bearing fault diagnosis

Proc. of the 2010 3rd Int. Congress on Image and Signal Processing

On-line breakage monitoring of small drills with input impedance of driving motor

Mech. Syst. Signal Process.

Sensor-free monitoring and evaluation of wire bonding quality using input impedance of bonder

IEEE Trans. Electron. Packag. Manuf.

Improved measurement of resistance and calculation of arc power in fusion welding

Sci. Technol. Weld. Join.

Random Data: Analysis and Measurement Procedures

Association of hemodynamic behavior in the thoracic aortic aneurysm to the intraluminal Thrombus prediction: a two-way fluid structure coupling investigation

Int. J. Appl. Mech.