# Machine Learning-Based Pulse Wave Analysis for Early Detection of Abdominal Aortic Aneurysms Using In Silico Pulse Waves

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Modelling Pulse Waves in Baseline Subjects with and without AAAs

#### 2.2. Parameter Sensitivity Analysis

_{max}) in clinical practice, with D

_{max}larger than 30 mm being diagnosed as AAA and D

_{max}larger than 50 mm being stratified as a serious AAA [2,40]. Since this study focused on the early detection of AAAs, herein three levels of D

_{max}were considered in the parameter sensitivity analysis: 30, 40 and 50 mm. Besides the maximum diameter, the length of an AAA also shows inter-patient difference [18,41], which was considered in the present study by increasing the length of the reference model from 106 to 120 mm (see Figure 1).

_{1}, k

_{2}, and k

_{3}were taken from a previous study [14]. Variations in AAA local stiffness were described by multiplying the above expression by a cosine function that made the maximum Eh value decrease or increase by 20% (see Figure 1).

#### 2.3. Database of In Silico Pulse Waves

#### 2.3.1. Modelling a Database of Pulse Waves in Subjects with and without an AAA

#### 2.3.2. Extracting Pulse Wave Indexes

_{f}) and backward (P

_{b}) components of the pressure PW in the ascending aorta were calculated from the pressure (P), flow (Q), and local characteristic impedance (Z

_{c}, herein the average value of the modulus of the 3rd to 10th harmonics of the input impedance [55]):

_{b}to the amplitude of P

_{f}. The time delay (ΔT

_{f-b}) between P

_{b}and P

_{f}was obtained using their zero cross-over as reference points. The AIx was calculated as:

_{fb}the pressure at the time when the P

_{b}adds to the P

_{f}(corresponding to the zero cross-over of P

_{b}).

_{1D}is the inflow to the windkessel segment connecting with the arterial outlet, and Q

_{out}is the outflow (see Figure 1).

#### 2.4. Machine Learning-Based Pulse Wave Analysis

#### 2.4.1. Recurrent Neural Network

_{k}

^{j−1}and H

_{k}

^{j}are the input and output, respectively, of the kth LSTM unit in the jth layer, and M

_{k}

^{j}is the memory cell. U and W are the weights, and b is the bias. The subscripts f, i, and o represent the forget gate, input gate, and output gate, respectively. σ and tanh represent the sigmoid function and tanh function, respectively. The parameters of the present machine learning architecture are summarized in Table 3. This architecture was constructed using the open-source library TensorFlow 2.1 together with the high-level application programming interface Keras. The development of this architecture referred to a previous study as well as the corresponding online repository [59].

#### 2.4.2. Training and Testing

## 3. Results

#### 3.1. Parameter Sensitivity Analysis

#### 3.2. Effects of AAA on Pulse Waveforms and Comparison with the Literature

#### 3.3. Comparison of Pulse Wave Indexes Extracted from the Pulse Wave Database

_{b}/P

_{f}) was similar between the IGS and AAA subsets, the wave reflection time (ΔT

_{f-b}) increased significantly in the AAA condition (Figure 7d,e). The AIx did not show a clear trend, though it was considerably higher in the AAA subset with the largest AAA diameters than in the baseline subset (Figure 7f).

#### 3.4. AAA Early Detection Using Machine Learning

## 4. Discussion

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Sakalihasan, N.; Limet, R.; Defawe, O.D. Abdominal aortic aneurysm. Lancet
**2005**, 365, 1577–1589. [Google Scholar] [CrossRef] - Golledge, J.; Muller, J.; Daugherty, A.; Norman, P. Abdominal aortic aneurysm: Pathogenesis and implications for management. Arterioscler. Thromb. Vasc. Biol.
**2006**, 26, 2605–2613. [Google Scholar] [CrossRef] [Green Version] - Scott, R.A.P.; Ashton, H.A.; Kay, D.N. Abdominal aortic aneurysm in 4237 screened patients: Prevalence, development and management over 6 years. Br. J. Surg.
**1991**, 78, 1122–1125. [Google Scholar] [CrossRef] - Kent, K.C. Abdominal aortic aneurysms. N. Engl. J. Med.
**2014**, 371, 2101–2108. [Google Scholar] [CrossRef] [PubMed] - Upchurch, G.R.; Schaub, T.A. Abdominal aortic aneurysm. Am. Family Physician
**2006**, 73, 1198–1204. [Google Scholar] - Aggarwal, S.; Qamar, A.; Sharma, V.; Sharma, A. Abdominal aortic aneurysm: A comprehensive review. Exp. Clin. Cardiol.
**2011**, 16, 11–15. [Google Scholar] - Wells, C.E.; Pugh, N.D.; Woodcock, J.P. Abdominal aortic aneurysm detection by common femoral artery Doppler ultrasound waveform analysis. J. Med. Eng. Technol.
**2011**, 35, 34–39. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Wood, M.M.; Romine, L.E.; Lee, Y.K.; Richman, K.M.; O’Boyle, M.K.; Paz, D.A.; Chu, P.K.; Pretorius, D.H. Spectral doppler signature waveforms in ultrasonography: A review of normal and abnormal waveforms. Ultrasound Q.
**2010**, 26, 83–99. [Google Scholar] [CrossRef] - Elgendi, M. PPG Signal Analysis: An Introduction Using MATLAB
^{®}; CRC Press: Boca Raton, FL, USA, 2020. [Google Scholar] - Chakshu, N.K.; Sazonov, I.; Nithiarasu, P. Towards Enabling a Cardiovascular Digital Twin for Human Systemic Circulation Using Inverse Analysis. Biomech. Model. Mechanobiol.
**2020**. [Google Scholar] [CrossRef] [PubMed] - Tavallali, P.; Razavi, M.; Pahlevan, N.M. Artifcial intelligence estimation of carotid-femoral pulse wave velocity using carotid waveform. Sci. Rep.
**2018**, 8, 1014. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Biswas, D.; Everson, L.; Liu, M.; Panwar, M.; Verhoef, B.-E.; Patki, S.; Kim, C.H.; Acharyya, A.; Van Hoof, C.; Konijnenburg, M.; et al. CorNET: Deep learning framework for PPG-based heart rate estimation and biometric identification in ambulant environment. IEEE Trans. Biomed. Eng.
**2019**, 13, 282–291. [Google Scholar] [CrossRef] [PubMed] - Jones, G.; Parr, J.; Nithiarasu, P.; Pant, S. Machine learning for detection of stenoses and aneurysms: Application in a physiologically realistic virtual patient database. arXiv
**2021**, arXiv:2103.00599. [Google Scholar] - Charlton, P.H.; Harana, J.M.; Vennin, S.; Li, Y.; Chowienczyk, P.; Alastruey, J. Modelling arterial pulse waves in healthy ageing: A database for in silico evaluation of haemodynamics and pulse wave indexes. Am. J. Physiol. Heart Circulatory Physiol.
**2019**, 317, H1062–H1085. [Google Scholar] [CrossRef] [PubMed] - Jones, G.; Parr, J.; Nithiarasu, P.; Pant, S. A physiologically realistic virtual patient database for the study of arterial haemodynamics. arXiv
**2021**, arXiv:2102.10655. [Google Scholar] - Wang, T.; Liang, F.; Li, L.; Zhang, W.; Wang, G.; Wang, J.; Zhang, C.; Qi, X. A computational model-based study on the exchangeability of hepatic venous pressure gradients measured in multiple hepatic vein. Med. Eng. Phys.
**2020**, 84, 28–35. [Google Scholar] [CrossRef] [PubMed] - Wang, T.; Liang, F.; Zhou, Z.; Qi, X. Global sensitivity analysis of hepatic venous pressure gradient (HVPG) measurement with a stochastic computational model of the hepatic circulation. Comput. Biol. Med.
**2018**, 97, 124–136. [Google Scholar] [CrossRef] [PubMed] - Vilalta, G.; Nieto, F.; Vaquero, C.; Vilalta, J.A. Quantitative indicator of abdominal aortic aneurysm rupture risk based on its geometric parameters. World Acad. Sci. Eng. Technol.
**2010**, 70, 181–185. [Google Scholar] - Giannoglou, G.; Giannakoulas, G.; Soulis, J.; Chatzizisis, Y.; Perdikides, T.; Melas, N.; Parcharidis, G.; Louridas, G. Predicting the risk of rupture of abdominal aortic aneurysms by utilizing various geometrical parameters revisiting the diameter criterion. Angiology
**2006**, 57, 487–494. [Google Scholar] [CrossRef] - Li, Z.; Kleinstreuer, C. A new wall stress equation for aneurysm-rupture prediction. Ann. Biomed. Eng.
**2005**, 33, 209–213. [Google Scholar] [CrossRef] - Venkatasubramaniam, A.K.; Fagan, M.J.; Mehta, T.; Mylankal, K.J.; Ray, B.; Kuhan, G.; Chetter, I.C.; McCollum, P.T. A comparative study of aortic wall stress using finite element analysis for ruptured and non-ruptured abdominal aortic aneurysms. Eur. J. Vasc. Endovasc. Surg.
**2004**, 28, 168–176. [Google Scholar] - Lindquist Liljeqvist, M.; Hultgren, R.; Siika, A.; Gasser, T.C.; Roy, J. Gender, smoking, body size, and aneurysm geometry influence the biomechanical rupture risk of abdominal aortic aneurysms as estimated by finite element analysis. J. Vasc. Surg.
**2017**, 65, 1014–1022. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Volokh, K.Y.; Vorp, D.A. A model of growth and rupture of abdominal aortic aneurysm. J. Biomech.
**2008**, 41, 1015–1021. [Google Scholar] [CrossRef] [PubMed] - Grytsan, A.; Watton, P.N.; Holzapfel, G.A. A thick-walled fluid–solid-growth model of abdominal aortic aneurysm evolution: Application to a patient-specific geometry. J. Biomech. Eng.
**2015**, 137, 031008. [Google Scholar] [CrossRef] [PubMed] - Humphrey, J.D.; Holzapfel, G.A. Mechanics, mechanobiology, and modeling of human abdominal aorta and aneurysms. J. Biomech.
**2012**, 45, 805–814. [Google Scholar] [CrossRef] [Green Version] - Figueroa, C.A.; Taylor, C.A.; Yeh, V.; Chiou, A.J.; Zarins, C.K. Effect of curvature on displacement forces acting on aortic endografts: A 3-dimensional computational analysis. J. Endovasc. Ther.
**2009**, 16, 284–294. [Google Scholar] [CrossRef] [Green Version] - Gindre, J.; Bel-Brunon, A.; Kaladji, A.; Duménil, A.; Rochette, M.; Lucas, A.; Haigron, P.; Combescure, A. Finite element simulation of the insertion of guidewires during an EVAR procedure: Example of a complex patient case, a first steptoward patient-specific parameterized models. Int. J. Numer. Method Biomed. Eng.
**2015**, 31, e02716. [Google Scholar] [CrossRef] - Casciaro, M.E.; Alfonso, M.A.; Craiem, D.; Alsac, J.M.; El-Batti, S.; Armentano, R.L. Predicting the effect on pulse wave reflection of different endovascular repair techniques in abdominal aortic aneurysm using 1D patient-specific models. Health Technol.
**2016**, 6, 173–179. [Google Scholar] [CrossRef] - Fraser, K.H.; Meagher, S.; Blake, J.R.; Easson, W.J.; Hoskins, P.R. Characterization of an abdominal aortic velocity waveform in patients with abdominal aortic aneurysm. Ultrasound Med. Biol.
**2008**, 34, 73–80. [Google Scholar] [CrossRef] - Taylor, C.A.; Cheng, C.P.; Espinosa, L.A.; Tang, B.T.; Parker, D.; Herfkens, R.J. In vivo quantification of blood flow and wall shear stress in the human abdominal aorta during lower limb exercise. Ann. Biomed. Eng.
**2002**, 30, 402–408. [Google Scholar] [CrossRef] - Les, A.S.; Yeung, J.J.; Schultz, G.M.; Herfkens, R.J.; Dalman, R.L.; Taylor, C.A. Supraceliac and infrarenal aortic flow in patients with abdominal aortic aneurysms: Mean flows, waveforms, and allometric scaling relationships. Cardiovasc. Eng. Technol.
**2010**, 1, 39–51. [Google Scholar] [CrossRef] - Wang, T.; Alastruey, J.; Liang, F. A computational model-based study on the effect of abdominal aortic aneurysm on pulse wave morphology. Artery Res.
**2020**, 26, S10–S11. [Google Scholar] [CrossRef] - Sazonov, I.; Khir, A.W.; Hacham, W.S.; Boileau, E.; Carson, J.M.; van Loon, R.; Ferguson, C.; Nithiarasu, P. A novel method for non-invasively detecting the severity and location of aortic aneurysms. Biomech. Model. Mechanobiol.
**2017**, 16, 1225–1242. [Google Scholar] [CrossRef] [Green Version] - Safaei, S. Simulating Blood Flow in an Anatomical Arterial Network; University of Auckland: Auckland, New Zealand, 2015. [Google Scholar]
- Low, K.; van Loon, R.; Sazonov, I.; Bevan, R.L.T.; Nithiarasu, P. An improved baseline model for a human arterial network to study the impact of aneurysms on pressure-flow waveforms. Int. J. Numer. Methods Biomed. Eng.
**2012**, 28, 1224–1246. [Google Scholar] [CrossRef] [PubMed] - Swillens, A.; Lanoye, L.; De Backer, J.; Stergiopulos, N.; Verdonck, P.R.; Vermassen, F.; Segers, P. Effect of an abdominal aortic aneurysm on wave reflection in the aorta. IEEE Trans. Biomed. Eng.
**2008**, 55, 1602–1611. [Google Scholar] [CrossRef] [PubMed] - Tong, J.; Cohnert, T.; Holzapfel, G.A. Diameter-related variations of geometrical, mechanical, and mass fraction data in the anterior portion of abdominal aortic aneurysms. Eur. J. Vasc. Endovasc. Surg.
**2015**, 49, 262–270. [Google Scholar] [CrossRef] [Green Version] - Martufi, G.; Di Martino, E.S.; Amon, C.H.; Muluk, S.C.; Finol, E.A. Three-dimensional geometrical characterization of abdominal aortic aneurysms: Image-based wall thickness distribution. J. Biomech. Eng.
**2009**, 131, 061015. [Google Scholar] [CrossRef] [PubMed] - Rodríguez, J.F.; Ruiz, C.; Doblaré, M.; Holzapfel, G.A. Mechanical stresses in abdominal aortic aneurysms influence of diameter, asymmetry, and material anisotropy. J. Biomech. Eng.
**2008**, 130, 021023. [Google Scholar] [CrossRef] [Green Version] - Doyle, B.J.; Morris, L.G.; Callanan, A.; Kelly, P.; Vorp, D.A.; McGloughlin, T.M. 3D reconstruction and manufacture of real abdominal aortic aneurysms: From CT scan to silicone model. J. Biomech. Eng.
**2008**, 130, 034501. [Google Scholar] [CrossRef] [PubMed] - Shum, J.; Martufi, G.; Di Martino, E.; Washington, C.B.; Grisafi, J.; Muluk, S.C.; Finol, E.A. Quantitative assessment of abdominal aortic aneurysm geometry. Ann. Biomed. Eng.
**2011**, 39, 277–286. [Google Scholar] [CrossRef] [Green Version] - Kolipaka, A.; Illapani, V.S.P.; Kenyhercz, W.; Dowell, J.D.; Go, M.R.; Starr, J.E.; Vaccaro, P.S.; White, R.D. Quantification of abdominal aortic aneurysm stiffness using magnetic resonance elastography and its comparison to aneurysm diameter. J. Vasc. Surg.
**2016**, 64, 966–974. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Durmus, I.; Kazaz, Z.; Altun, G.; Cansu, A. Augmentation index and aortic pulse wave velocity in patients with abdominal aortic aneurysms. Int. J. Clin. Exp. Med.
**2014**, 7, 421–425. [Google Scholar] - Kadoglou, N.P.E.; Papadakis, I.; Moulakakis, K.G.; Ikonomidis, I.; Alepaki, M.; Moustardas, P.; Lampropoulos, S.; Karakitsos, P.; Lekakis, J.; Liapis, C.D. Arterial stiffness and novel biomarkers in patients with abdominal aortic aneurysms. Regul. Pept.
**2012**, 179, 50–54. [Google Scholar] [CrossRef] - Kadoglou, N.P.E.; Moulakakis, K.G.; Papadakis, I.; Ikonomidis, I.; Alepaki, M.; Lekakis, J.; Liapis, C.D. Changes in aortic pulse wave velocity of patients undergoing endovascular repair of abdominal aortic aneurysms. J. Endovasc. Ther.
**2012**, 19, 661–666. [Google Scholar] [CrossRef] - Länne, T.; Sonesson, B.; Bergqvist, D.; Bengtsson, H.; Gustafsson, D. Diameter and compliance in the male human abdominal aorta: Influence of age and aortic aneurysm. Eur. J. Vasc. Surg.
**1992**, 6, 178–184. [Google Scholar] [CrossRef] - Schriefl, A.J.; Zeindlinger, G.; Pierce, D.M.; Regitnig, P.; Holzapfel, G.A. Determination of the layer-specific distributed collagen fibre orientations in human thoracic and abdominal aortas and common iliac arteries. J. R. Soc. Interface
**2012**, 9, 1275–1286. [Google Scholar] [CrossRef] - Shum, J.; Dimartino, E.S.; Goldhammer, A.; Goldman, D.H.; Acker, L.C.; Patel, G.; Ng, J.H.; Martufi, G.; Finol, E.A. Semiautomatic vessel wall detection and quantification of wall thickness in computed tomography images of human abdominal aortic aneurysms. Med. Phys.
**2010**, 37, 638–648. [Google Scholar] [CrossRef] - Raghavan, M.L.; Kratzberg, J.; de Tolosa, E.M.C.; Hanaoka, M.M.; Walker, P.; da Silva, E.S. Regional distribution of wall thickness and failure properties of human abdominal aortic aneurysm. J. Biomech.
**2006**, 39, 3010–3016. [Google Scholar] [CrossRef] - Martufi, G.; Satriano, A.; Moore, R.D.; Vorp, D.A.; Di Martino, E.S. Local quantification of wall thickness and intraluminal thrombus offer insight into the mechanical properties of the aneurysmal aorta. Ann. Biomed. Eng.
**2015**, 43, 1759–1771. [Google Scholar] [CrossRef] [PubMed] - Di Martino, E.S.; Bohra, A.; Vande Geest, J.P.; Gupta, N.; Makaroun, M.S.; Vorp, D.A. Biomechanical properties of ruptured versus electively repaired abdominal aortic aneurysm wall tissue. J. Vasc. Surg.
**2006**, 43, 570–576. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Shum, J.; Xu, A.; Chatnuntawech, I.; Finol, E.A. A framework for the automatic generation of surface topologies for abdominal aortic aneurysm models. Ann. Biomed. Eng.
**2011**, 39, 249–259. [Google Scholar] [CrossRef] [PubMed] - Gaddum, N.R.; Alastruey, J.; Beerbaum, P.; Chowienczyk, P.; Schaeffter, T. A technical assessment of pulse wave velocity algorithms applied to Non-invasive arterial waveforms. Ann. Biomed. Eng.
**2013**, 41, 2617–2629. [Google Scholar] [CrossRef] - Segers, P.; Rietzschel, E.R.; De Buyzere, M.L.; De Bacquer, D.; Van Bortel, L.M.; De Backer, G.; Gillebert, T.C.; Verdonck, P.R. Assessment of pressure wave reflection: Getting the timing right! Physiol. Meas.
**2007**, 28, 1045–1056. [Google Scholar] [CrossRef] [PubMed] - Westerhof, N.; Sipkema, P.; van den Bos, G.C.; Elzinga, G. Forward and backward waves in the arterial system. Cardiovasc. Res.
**1972**, 6, 648–656. [Google Scholar] [CrossRef] - Schmidhuber, J. Deep learning in neural networks: An overview. Neural Netw.
**2015**, 61, 85–117. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Lipton, Z.C.; Berkowitz, J.; Elkan, C. A critical review of recurrent neural networks for sequence learning. Comput. Sci.
**2015**. Available online: http://arxiv.org/abs/1506.00019 (accessed on 4 May 2021). - Hochreiter, S.; Schmidhuber, J. Long short-term memory. Neural Comput.
**1997**, 9, 1735–1780. [Google Scholar] [CrossRef] [PubMed] - Jin, W.; Chowienczyk, P.; Alastruey, J. Estimating pulse wave velocity from the radial pressure wave using machine learning algorithms. medRxiv
**2020**. [Google Scholar] [CrossRef] - Jin, W.; Alastruey, J. Arterial pulse wave propagation across stenoses and aneurysms: Assessment of one-dimensional simulations against three-dimensional simulations and in vitro measurements. J. R. Soc. Interface
**2021**, 18, 20200881. [Google Scholar] [CrossRef] - Li, Z.-Y.; U-King-Im, J.; Tang, T.Y.; Soh, E.; See, T.C.; Gillard, J.H. Impact of calcification and intraluminal thrombus on the computed wall stresses of abdominal aortic aneurysm. J. Vasc. Surg.
**2008**, 47, 928–935. [Google Scholar] [CrossRef] - Di Martino, E.S.; Vorp, D.A. Effect of variation in intraluminal thrombus constitutive properties on abdominal aortic aneurysm wall stress. Ann. Biomed. Eng.
**2003**, 31, 804–809. [Google Scholar] [CrossRef] - Tong, J.; Cohnert, T.; Regitnig, P.; Holzapfel, G.A. Effects of age on the elastic properties of the intraluminal thrombus and the thrombus-covered wall in abdominal aortic aneurysms: Biaxial extension behaviour and material modelling. Eur. J. Vasc. Endovasc. Surg.
**2011**, 42, 207–219. [Google Scholar] [CrossRef] [Green Version]

**Figure 1.**The one-dimensional model of pulse wave propagation with a normal infrarenal abdominal aorta (

**left**) and the parameter variations considered to simulate an AAA (

**right**). These include (1) type of AAA shape, (2) AAA maximum diameter (D

_{max}), (3) AAA length (L), (4) AAA local stiffness (Eh; i.e., elastic modulus multiplied by wall thickness), and (5) global stiffness of the larger systemic arteries. The model contains the arterial segments making up the larger systemic arteries, an aortic inflow waveform prescribed at the aortic root, and lumped outflow boundary conditions at each terminal segment representing vascular beds.

**Figure 2.**Variations of model parameters used to construct the new database of in silico pulse waves. Panels (

**a**–

**h**) show the variations of heart rate (HR), stroke volume (SV), left ventricular ejection time (LVET), infrarenal abdominal aortic diameter, mean arterial pressure (MAP), peripheral vascular resistance (PVR), AAA maximum diameter, and carotid-femoral pulse wave velocity (PWV), respectively. The AAA maximum diameter and increased PWV values shown in red were added to the original database [14] (with parameters shown in black) to simulate increased stiffness and AAAs. Panel (

**i**) shows the PWV as a function of the arterial diameter for the baseline model of each age, in the baseline (black) and IGS/AAA (red) subsets.

**Figure 3.**Schematic of the bidirectional recurrent neural network (BRNN) with long short-term memory (LSTM) used for pulse wave analysis. Simulated PPG pulse waves (PWs) in n = 8748 virtual subjects were used as input data for training a BRNN with LSTM (see Equation (8) for the mathematical expressions of a LSTM unit) to predict the presence (output = 1) or not (output = 0) of an AAA. The BRNN contains input, output and hidden layers, each hidden layer consisting of masking, forward, backward, and dense layers. The forward and backward layers include a series of LSTM units. L and L′ represent the LSTM units in the forward and backward layers, respectively. M and M′ are the corresponding memory cells. X is the input data processed by masking layer for the LSTM units, and H is the output data for the dense layer. PPG PWs are described using discrete values p

_{1}, …, p

_{t}. The subscripts 1, …, t represent each time history point. Details about the symbols in the brown boxes describing LSTM units can be found in Equation (8).

**Figure 4.**Simulated pressure waveforms in the ascending aorta (

**left**), infrarenal abdominal aorta (

**middle**), and femoral artery (

**right**) with individual variations in the AAA-related parameters indicated at the start of each row and illustrated in Figure 1.

**Figure 5.**Simulated flow velocity waveforms in the ascending aorta (

**left**), infrarenal abdominal aorta (

**middle**), and femoral artery (

**right**) with individual variations in the AAA-related parameters indicated at the start of each row and illustrated in Figure 1.

**Figure 6.**Simulated pressure and flow velocity pulse waves at the infrarenal abdominal aorta (labelled in red) and other common measurement sites (labelled in black) for the baseline 65-year-old subject in the IGS subset (without AAA) and AAA subset (D

_{max}= 30 mm, D

_{max}= 40 mm, and D

_{max}= 50 mm). The PPG wave is shown in the digital artery in the time and frequency domains (labelled in blue).

**Figure 7.**Comparison of pulse wave indexes obtained in the baseline and increased global stiffness (IGS) subsets (in black) and the AAA subset with different AAA sizes (in red). SBP: systolic blood pressure (

**a**); DBP: diastolic blood pressure (

**b**); MBP: mean blood pressure (

**c**); P

_{b}/P

_{f}: wave reflection magnitude (

**d**); ΔT

_{f-b}: time delay between P

_{b}and P

_{f}(

**e**); AIx: augmentation index (

**f**); cf-PWV: carotid-femoral pulse wave velocity (

**g**); difference between the magnitudes of the 5th and the 6th harmonics of the digital PPG pulse wave (

**h**), and the same difference normalized by the magnitude of the 1st harmonic (

**i**). Dots indicate mean values and error bars represent standard deviations. All indexes were calculated in the ascending aorta except for cf-PWV and digital PPG indexes.

**Figure 8.**Performance of the trained machine learning model for the early detection of AAAs. Test data (

**left**), confusion matrix (

**middle**), and ROC curve (

**right**) when testing in the original (

**top**) and modified (

**bottom**) testing sets. The confusion matrices indicate the number of subjects in each condition together with the proportion of each age and AAA size (if applicable) in brown.

**Table 1.**Carotid-femoral pulse wave velocities measured in control cohorts of healthy subjects and in cohorts of patients with AAA.

Control (Number) | AAA Patient (Number) | Reference |
---|---|---|

10.0 m/s (20) | 14.8 m/s (18) | [43] |

10.03 m/s (42) | 12.99 m/s (108) | [44] |

7.97 m/s (31) | 13.11 m/s (48) | [45] |

9.33 m/s | 13.63 m/s | Mean value |

Source | Value | Reference |
---|---|---|

Growth ratio of elastic modulus from normal to AAA | ||

Measured by magnetic resonance elastography | 96.8% | [42] |

Calculated from the measured pressure and diameter | 49.6% | [46] |

73.2% | Mean value | |

Normal wall thickness | ||

Derived from clinical measurements | 1.4~1.5 mm | [25] |

1.39 mm | [47] | |

1.4 mm | Mean value | |

AAA wall thickness | ||

Derived from clinical measurements | 2 mm | [37] |

1.63 mm | [48] | |

1.48 mm | [49] | |

2.71 mm | [50] | |

2.87 mm | [51] | |

1.64 mm | [52] | |

Used by previous model-based studies | 2 mm | [21,40] |

2 mm | Mean value |

Parameter | Value |
---|---|

Number of LSTM units | 16 |

Batch size | 32 |

Epoch number | 256 |

Optimiser | Adam |

Cost function | Binary cross-entropy |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 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 (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Wang, T.; Jin, W.; Liang, F.; Alastruey, J.
Machine Learning-Based Pulse Wave Analysis for Early Detection of Abdominal Aortic Aneurysms Using In Silico Pulse Waves. *Symmetry* **2021**, *13*, 804.
https://doi.org/10.3390/sym13050804

**AMA Style**

Wang T, Jin W, Liang F, Alastruey J.
Machine Learning-Based Pulse Wave Analysis for Early Detection of Abdominal Aortic Aneurysms Using In Silico Pulse Waves. *Symmetry*. 2021; 13(5):804.
https://doi.org/10.3390/sym13050804

**Chicago/Turabian Style**

Wang, Tianqi, Weiwei Jin, Fuyou Liang, and Jordi Alastruey.
2021. "Machine Learning-Based Pulse Wave Analysis for Early Detection of Abdominal Aortic Aneurysms Using In Silico Pulse Waves" *Symmetry* 13, no. 5: 804.
https://doi.org/10.3390/sym13050804