A Comparative Study of Machine Learning and Algorithmic Approaches to Automatically Identify the Yield Point in Normal and Aneurysmal Human Aortic Tissues

The stress-strain curve of biological soft tissues helps characterize their mechanical behavior. The yield point on this curve is when a specimen breaches its elastic range due to irreversible microstructural damage. The yield point is easily found using the offset yield method in traditional engineering materials. However, correctly identifying the yield point in soft tissues can be subjective due to its nonlinear material behavior. The typical method for yield point identification is visual inspection, which is investigator-dependent and does not lend itself to automation of the analysis pipeline. An automated algorithm to identify the yield point objectively assesses soft tissues' biomechanical properties. This study aimed to analyze data from uniaxial extension testing on biological soft tissue specimens and create a machine learning (ML) model to determine a tissue sample's yield point. We present a trained machine learning model from 279 uniaxial extension curves from testing aneurysmal/nonaneurysmal and longitudinal/circumferential oriented tissue specimens that multiple experts labeled through an adjudication process. The ML model showed a median error of 5% in its estimated yield stress compared to the expert picks. The study found that an ML model could accurately identify the yield point (as defined) in various aortic tissues. Future studies will be performed to validate this approach by visually inspecting when damage occurs and adjusting the model using the ML-based approach.

Flow Monitoring of ECMO Circuit for Detecting Oxygenator Obstructions

Oxygenator thrombosis during extracorporeal membrane oxygenation (ECMO), is a complication that necessitates component replacement. ECMO centers monitor clot burden by intermittent measurement of pressure drop across the oxygenator. An increase in pressure drop at a preset flow rate suggests an increase in resistance/clot formation within the oxygenator. This monitoring method comes with inherent disadvantages such as monitoring gaps, and increased risk of air embolism and infection. We explored utilizing flow measurement, which avoids such risks, as an indicator of ECMO circuit obstructions. The hypothesis that flow rate through a shunt tube in the circuit will increase as distal resistances in the circuit increases was tested. We experimentally simulated controlled levels of oxygenator obstructions using glass microspheres in an ex vivo veno-venous ECMO circuit and measured the change in shunt flow rate using over the tube ultra-sound flow probes. A mathematical model was also used to study the effect of distal resistances in the ECMO circuit on shunt flow. Results of both the mathematical model and the experiments showed a clear and measurable increase in shunt flow with increasing levels of oxygenator obstruction. Therefore, flow monitoring appears to be an effective non-contact and continuous method to monitor for obstruction during ECMO.

Electrochemical Approach to Measure Physiological Fluid Flow Rates

In vivo measurement of the flow rate of physiological fluids such as the blood flow rate in the heart is vital in critically ill patients and for those undergoing surgical procedures. The reliability of these measurements is therefore quite crucial. However, current methods in practice for measuring flow rates of physiological fluids suffer from poor repeatability and reliability. Here, we assessed the feasibility of a flow rate measurement method that leverages time transient electrochemical behavior of a tracer that is injected directly into a medium (the electrochemical signal caused due to the tracer injectate will be diluted by the continued flow of the medium and the time response of the current-the electrodilution curve-will depend on the flow rate of the medium). In an experimental flow loop apparatus equipped with an electrochemical cell, we used the AC voltammetry technique and tested the feasibility of electrodilution-based measurement of the flow rate using two mediums-pure water and anticoagulated blood-with 0.9 wt% saline as the injectate. The electrodilution curve was quantified using three metrics-change in current amplitude, total time, and change in the total charge for a range of AC voltammetry settings (peak voltages and frequencies). All three metrics showed an inverse relationship with the flow rate of water and blood, with the strongest negative correlation obtained for change in current amplitude. The findings are a proof of concept for the electrodilution method of the flow rate measurement and offer the potential for physiological fluid flow rate measurement in vivo.

Non-Invasive Determination of Zero-Pressure Geometry of Arterial Aneurysms

Arterial aneurysms are in a pre-deformed state in vivo under non-zero pressure. The ability to determine their zero pressure geometry may help in improving accuracy of determination of stress distribution and reverse estimation of material properties from dynamic imaging data. An approximate method to recover the zero pressure geometry of the AAA is proposed. This method is motivated by the observation that the patterns in displacement field for a given AAA are strikingly consistent in an AAA under all physiological pressures. The basic principle is to leverage this observation to iteratively identify the geometry that when subjected to the in vivo pressure, will recover the geometry reconstructed from in vivo imaging. The methodology is demonstrated and validated using patient-specific AAA models.

Three-dimensional finite element analysis of residual stress in arteries

Calculation of residual stress in arteries, using the analytical approach has been quite valuable in our understanding of its critical role in vascular mechanics. Stresses are calculated at the central section of an infinitely long tube by imposing a constant axial stretch while deforming the artery from the stress-free state to its unloaded state. However, segments used to perform opening-angle measurements have finite lengths. Further, the stress-free artery configuration is assumed to be circular. Experiments show that they are slightly noncircular. The numerical approach to residual stress calculation can allow us to study both these issues. Using 3D cylindrical geometries and an isotropic material model, we investigated how segment length can affect residual stress calculations and identified the appropriate segment length for experiments. Further, we recorded and used the true noncircular stress-free state of an artery segment, computed the residual stress distribution, and compared it to that from a similar, but circular segment. Our findings suggest that segment length must be ten times the wall thickness for it to be "long" enough. We also found that the circularity assumption may be a reasonable approximation for typical arteries.

Prediction of rupture risk in abdominal aortic aneurysm during observation: wall stress versus diameter

OBJECTIVES

We previously showed that peak abdominal aortic aneurysm (AAA) wall stress calculated for aneurysms in vivo is higher at rupture than at elective repair. The purpose of this study was to analyze rupture risk over time in patients under observation.

METHODS

Computed tomography (CT) scans were analyzed for patients with AAA when observation was planned for at least 6 months. AAA wall stress distribution was computationally determined in vivo with CT data, three-dimensional computer modeling, finite element analysis (nonlinear hyperelastic model depicting aneurysm wall behavior), and blood pressure during observation.

RESULTS

Analysis included 103 patients and 159 CT scans (mean follow-up, 14 +/- 2 months per CT). Forty-two patients were observed with no intervention for at least 1 year (mean follow-up, 28 +/- 3 months). Elective repair was performed within 1 year in 39 patients, and emergent repair was performed in 22 patients (mean, 6 +/- 1 month after CT) for rupture (n = 14) or acute severe pain. Significant differences were found for initial diameter (observation, 4.9 +/-.1 cm; elective repair, 5.9 +/-.1 cm; emergent repair, 6.1 +/-.2 cm; P <.0001) and initial peak wall stress (38 +/- 1 N/cm(2), 42 +/- 2 n/cm(2), 58 +/- 4 N/cm(2), respectively; P <.0001), but peak wall stress appeared to better differentiate patients who later required emergent repair (elective vs emergent repair: diameter, 3% difference, P =.5; stress, 38% difference, P <.0001). Receiver operating characteristic (ROC) curves for predicting rupture were better for peak wall stress (sensitivity, 94%; specificity,81%; accuracy, 85% [with 44 N/cm(2) threshold]) than for diameter (81%, 70%, 73%, respectively [with optimal 5.5 cm threshold). With proportional hazards analysis, peak wall stress (relative risk, 25x) and gender (relative risk, 3x) were the only significant independent predictors of rupture.

CONCLUSIONS

For AAAs under observation, peak AAA wall stress seems superior to diameter in differentiating patients who will experience catastrophic outcome. Elevated wall stress associated with rupture is not simply an acute event near the time of rupture.

In vivo analysis of mechanical wall stress and abdominal aortic aneurysm rupture risk

OBJECTIVE

The purpose of this study was to calculate abdominal aortic aneurysm (AAA) wall stresses in vivo for ruptured, symptomatic, and electively repaired AAAs with three-dimensional computer modeling techniques, computed tomographic scan data, and blood pressure and to compare wall stress with current clinical indices related to rupture risk.

METHODS

CT scans were analyzed for 48 patients with AAAs: 18 AAAs that ruptured (n = 10) or were urgently repaired for symptoms (n = 8) and 30 AAAs large enough to merit elective repair within 12 weeks of the CT scan. Three-dimensional computer models of AAAs were reconstructed from CT scan data. The stress distribution on the AAA as a result of geometry and blood pressure was computationally determined with finite element analysis with a hyperelastic nonlinear model that depicted the mechanical behavior of the AAA wall.

RESULTS

Peak wall stress (maximal stress on the AAA surface) was significantly different between groups (ruptured, 47.7 +/- 6 N/cm(2); emergent symptomatic, 47.5 +/- 4 N/cm(2); elective repair, 36.9 +/- 2 N/cm(2); P =.03), with no significant difference in blood pressure (P =.2) or AAA diameter (P =.1). Because of trends toward differences in diameter, comparison was made only with diameter-matched subjects. Even with identical mean diameters, ruptured/symptomatic AAAs had a significantly higher peak wall stress (46.8 +/- 4.5 N/cm(2) versus 38.1 +/- 1.3 N/cm(2); P =.05). Maximal wall stress predicted risk of rupture better than the LaPlace equation (20.7 +/- 5.7 N/cm(2) versus 18.8 +/- 2.9 N/cm(2); P =.2) or other proposed indices of rupture risk. The smallest ruptured AAA was 4.8 cm, but this aneurysm had a stress equivalent to the average electively repaired 6.3-cm AAA.

CONCLUSION

Peak wall stresses calculated in vivo for AAAs near the time of rupture were significantly higher than peak stresses for electively repaired AAAs, even when matched for maximal diameter. Calculation of wall stress with computer modeling of three-dimensional AAA geometry appears to assess rupture risk more accurately than AAA diameter or other previously proposed clinical indices. Stress analysis is practical and feasible and may become an important clinical tool for evaluation of AAA rupture risk.

Wall stress distribution on three-dimensionally reconstructed models of human abdominal aortic aneurysm

PURPOSE

Abdominal aortic aneurysm (AAA) rupture is believed to occur when the mechanical stress acting on the wall exceeds the strength of the wall tissue. Therefore, knowledge of the stress distribution in an intact AAA wall could be useful in assessing its risk of rupture. We developed a methodology to noninvasively estimate the in vivo wall stress distribution for actual AAAs on a patient-to-patient basis.

METHODS

Six patients with AAAs and one control patient with a nonaneurysmal aorta were the study subjects. Data from spiral computed tomography scans were used as a means of three-dimensionally reconstructing the in situ geometry of the intact AAAs and the control aorta. We used a nonlinear biomechanical model developed specifically for AAA wall tissue. By means of the finite element method, the stress distribution on the aortic wall of all subjects under systolic blood pressure was determined and studied.

RESULTS

In all the AAA cases, the wall stress was complexly distributed, with distinct regions of high and low stress. Peak wall stress among AAA patients varied from 29 N/cm(2) to 45 N/cm(2) and was found on the posterior surface in all cases studied. The wall stress on the nonaneurysmal aorta in the control subject was relatively low and uniformly distributed, with a peak wall stress of 12 N/cm(2). AAA volume, rather than AAA diameter, was shown by means of statistical analysis to be a better indicator of high wall stresses and possibly rupture.

CONCLUSION

The approach taken to estimate AAA wall stress distribution is completely noninvasive and does not require any additional involvement or expense by the AAA patient. We believe that this methodology may allow for the evaluation of an individual AAA's rupture risk on a more biophysically sound basis than the widely used 5-cm AAA diameter criterion.

Toward a biomechanical tool to evaluate rupture potential of abdominal aortic aneurysm: identification of a finite strain constitutive model and evaluation of its applicability

Knowledge of the wall stresses in an abdominal aortic aneurysm (AAA) may be helpful in evaluating the need for surgical intervention to avoid rupture. This must be preceded by the development of a more suitable finite strain constitutive model for AAA, as none currently exists. Additionally, reliable stress analysis of in vivo AAA for the purposes of clinical diagnostics requires patient-specific values of the material parameters, which are difficult to determine noninvasively. The purpose of this work, therefore, was three-fold: (1) to develop a finite strain constitutive model for AAA; (2) to estimate the variation of model parameters within a sample population; and (3) to evaluate the sensitivity of computed stress distribution in AAA due to this biologic variation. We propose here a two parameter, hyperelastic, isotropic, incompressible material model and utilize experimental data from 69 freshly excised AAA specimens to both develop the functional form of the model and estimate its material parameters. Parametric analyses were performed via repeated finite element computations to determine the effect of varying each of the two model parameters on the stress distribution in a three-dimensional AAA model. The agreement between experimental data and the proposed functional form of the constitutive law was very good (R2 > 0.9). Our finite element simulations showed that the computed AAA wall stresses changed by only 4% or less when both the parameters were varied within the 95% confidence intervals for the patient population studied. This observation indicates that in lieu of the patient-specific material parameters, which are difficult to determine the use of population mean values is sufficiently accurate for the model to be reasonably employed in a clinical setting. We believe that this is an important advancement toward the development of a computational tool for the estimation of rupture potential for individual AAA, for which there is great clinical need.

In vivo three-dimensional surface geometry of abdominal aortic aneurysms

Abdominal aortic aneurysm (AAA) is a local, progressive dilation of the distal aorta that risks rupture until treated. Using the law of Laplace, in vivo assessment of AAA surface geometry could identify regions of high wall tensions as well as provide critical dimensional and shape data for customized endoluminal stent grafts. In this study, six patients with AAA underwent spiral computed tomography imaging and the inner wall of each AAA was identified, digitized, and reconstructed. A biquadric surface patch technique was used to compute the local principal curvatures, which required no assumptions regarding axisymmetry or other shape characteristics of the AAA surface. The spatial distribution of AAA principal curvatures demonstrated substantial axial asymmetry, and included adjacent elliptical and hyperbolic regions. To determine how much the curvature spatial distributions were dependent on tortuosity versus bulging, the effects of AAA tortuosity were removed from the three-dimensional (3D) reconstructions by aligning the centroids of each digitized contour to the z axis. The spatial distribution of principal curvatures of the modified 3D reconstructions were found to be largely axisymmetric, suggesting that much of the surface geometric asymmetry is due to AAA bending. On average, AAA surface area increased by 56% and abdominal aortic length increased by 27% over those for the normal aorta. Our results indicate that AAA surface geometry is highly complex and cannot be simulated by simple axisymmetric models, and suggests an equally complex wall stress distribution.

Mechanical wall stress in abdominal aortic aneurysm: influence of diameter and asymmetry

PURPOSE

Risk for rupture of an abdominal aortic aneurysm is widely believed to be related to its maximum diameter. From a biomechanical standpoint, however, risk is probably more precisely related to mechanical wall stress. Many abdominal aortic aneurysms are asymmetric (for example because of anterior bulging with posterior expansion limited by the vertebral column). The purpose of this work was to investigate the effect of maximum diameter and asymmetric bulge on wall stress.

METHODS

Three-dimensional computer models of abdominal aortic aneurysms were generated. In one protocol, maximum diameter was held constant while bulge shape factor was varied. The shape factor took into account the asymmetric shape of the bulge. In a second protocol, the shape of the aneurysmal wall was held constant while maximum diameter was varied. Wall stress was computed in each instance with a commercial software package and assumption of physiologic intraluminal pressure.

RESULTS

Both maximum diameter and the shape factor were found to have substantial influence on the distribution of wall stress within the aneurysm. In some instances the maximum stress occurred at the midsection, and in others it occurred elsewhere. The magnitude of peak stress acting on the aneurysm increased nonlinearly with increasing maximum diameter or increasing asymmetry.

CONCLUSIONS

Our computer models showed that the stress within the wall of an abdominal aortic aneurysm and possibly the potential for rupture are as dependent on aneurysm shape as they are on maximum diameter. This information may be important in determining severity of individual abdominal aortic aneurysms and in improving understanding of the natural history of the disease.

Ex vivo biomechanical behavior of abdominal aortic aneurysm: assessment using a new mathematical model

Knowledge of the biomechanical behavior of abdominal aortic aneurysm (AAA) as compared to nonaneurysmal aorta may provide information on the natural history of this disease. We have performed uniaxial tensile testing of excised human aneurysmal and nonaneurysmal abdominal aortic specimens. A new mathematical model that conforms to the fibrous structure of the vascular tissue was used to quantify the measured elastic response. We determined for each specimen the yield (sigma y) and ultimate (sigma u) strengths, the separate contribution to total tissue stiffness by elastin (EE) and collagen (EC) fibers, and a collagen recruitment parameter (A), which is a measure of the tortuosity of the collagen fibers. There was no significant difference in any of these mechanical properties between longitudinal and circumferential AAA specimens, nor in EE and EC between longitudinally oriented aneurysmal and normal specimens. A, sigma y, and sigma u were all significantly higher for the normal than for the aneurysmal group: A = 0.223 +/- 0.046 versus A = 0.091 +/- 0.009 (mean +/- SEM; p < 0.0005), sigma y = 121.0 +/- 32.8 N/cm2 versus sigma y = 65.2 +/- 9.5 N/cm2 (p < 0.05), and sigma u = 201.4 +/- 39.4 N/cm2 versus sigma u = 86.4 +/- 10.2 N/cm2 (p < 0.0005), respectively. Our findings suggest that the AAA tissue is isotropic with respect to these mechanical properties. The observed difference in A between aneurysmal and normal aorta may be due to the complete recruitment and loading of collagen fibers at lower extensions in the former. Our data indicate that AAA rupture may be related to a reduction in tensile strength and that the biomechanical properties of AAA should be considered in assessing the severity of an individual aneurysm.

Modeling the transmural stress distribution during healing of bioresorbable vascular prostheses

Little attention has been given to the stresses within the wall of bioresorbable vascular prostheses and how they might affect the resorption process. We modeled the graft "complex" (inner tissue capsule, residual graft, and outer tissue capsule) as a three-layered compound tube under internal pressure. Using this biomechanical model, we studied the effects of alterations in the geometry (i.e., radius and thickness) and mechanical properties of each stratum on the overall transmural stress distribution. Hypothetical simulations were performed to investigate the possible sequence of and alterations in the radial and circumferential stresses during the resorption process. Our results suggest that early in the resorption phase, the inner tissue capsule is subjected to compressive hoop stresses and concentrated, large-magnitude compressive radial stresses. This distribution gives way to the more typical distribution for a thick-walled tube when equilibration (i.e., complete resorption) is approached. The prediction of the compressive stresses in the pseudo-intima during early resorption parallels findings of an elevated mitotic index in that region at that time. This leads to a new hypothesis, namely, that compressive stresses, both in-plane and out-of-plane with respect to the regenerated vascular cells, participate in the resorption process of bioresorbable vascular grafts by modulating elevated cellular proliferative activity and may play an important role in other aspects of vascular cell biology. Results of recent experimentation support this hypothesis.