Correlation of four-dimensional ultrasound strain analysis with computed tomography angiography wall stress simulations in abdominal aortic aneurysms.

Objective: Biomechanical modeling of infrarenal aortic aneurysms seeks to predict ruptures in advance, thereby reducing aneurysm-related deaths. As individual methods focusing on strain and stress analysis lack adequate discretization power, this study aims to explore multifactorial characterization for progressive aneurysmal degeneration. The study's objective is to compare stress- and strain-related parameters in infrarenal aortic aneurysms. Methods: Twenty-two patients with abdominal aortic aneurysms (AAAs) (mean maximum diameter, 53.2 ± 7.2 mm) were included in the exploratory study, examined by computed tomography angiography (CTA) and three-dimensional real-time speckle tracking ultrasound (4D-US). The conformity of aneurysm anatomy in 4D-US and CTA was determined with the mean point-to-point distance (MPPD). CTA was employed for each AAA to characterize stress-related indices using the semi-automated A4-clinics RE software. Five segmentations from one 4D-US examination were fused into one averaged model for strain analysis using MATLAB and the Abaqus solver. Results: The mean MPPD between the adjacent points of the 4D-US and CTA-derived geometry was 1.8 ± 0.4 mm. The interclass correlation coefficients for all raters and all measurements for the maximum AAA diameter in 2D, 4D ultrasound, and CTA indicate moderate to good reliability (interclass correlation coefficient1 0.69 with 95% confidence interval [CI], 0.49-0.84; P < .001). The peak wall stress (PWS) correlates fairly with the maximum AAA diameter in 2D-US (r = 0.54; P < .01) and 4D-US (r = 0.53; P < .05) and moderately strongly with the maximum exterior AAA diameter (r = 0.63; P < .01). The peak wall rupture risk index shows a strong correlation with the PWS (ρ > 0.9; P < .001) and is influenced by anatomical parameters with equal strength. Isolated observation of the intraluminal thrombus does not provide significant information in the determination of PWS. The maximum AAA diameter in 2D-US shows a fair negative correlation with the mean circumferential, longitudinal and in-plane shear strain (ρ = -0.46; r = -0.45; ρ = -0.47; P < .05 for all). The circumferential strain ratio as an indicator of wall motion heterogeneity increases with the aneurysm diameter (r = 0.47; P < .05). The direct comparison of wall strain and wall stress indices shows no quantitative correlation. Conclusions: The strain and stress analyses provide independent biomechanical information of AAAs. At the current stage of development, the two methods are considered complementary and may optimize a more patient-specific rupture risk prediction in the future.

Biomechanical characterization of tissue types in murine dissecting aneurysms based on histology and 4D ultrasound-derived strain.

Abdominal aortic aneurysm disease is the local enlargement of the aorta, typically in the infrarenal section, causing up to 200,000 deaths/year. In vivo information to characterize the individual elastic properties of the aneurysm wall in terms of rupture risk is lacking. We used a method that combines 4D ultrasound and direct deformation estimation to compute in vivo 3D Green-Lagrange strain in murine angiotensin II-induced dissecting aortic aneurysms, a commonly used mouse model. After euthanasia, histological staining of cross-sectional sections along the aorta was performed in areas where in vivo strains had previously been measured. The histological sections were segmented into intact and fragmented elastin, thrombus with and without red blood cells, and outer vessel wall including the adventitia. Meshes were then created from the individual contours based on the histological segmentations. The isolated contours of the outer wall and lumen from both imaging modalities were registered individually using a coherent point drift algorithm. 2D finite element models were generated from the meshes, and the displacements from the registration were used as displacement boundaries of the lumen and wall contours. Based on the resulting deformed contours, the strains recorded were grouped according to segmented tissue regions. Strains were highest in areas containing intact elastin without thrombus attachment. Strains in areas with intact elastin and thrombus attachment, as well as areas with disrupted elastin, were significantly lower. Strains in thrombus regions with red blood cells were significantly higher compared to thrombus regions without. We then compared this analysis to statistical distribution indices and found that the results of each aligned, elucidating the relationship between vessel strain and structural changes. This work demonstrates the possibility of advancing in vivo assessments to a microstructural level ultimately improving patient outcomes.

Using averaged models from 4D ultrasound strain imaging allows to significantly differentiate local wall strains in calcified regions of abdominal aortic aneurysms.

Abdominal aortic aneurysms are a degenerative disease of the aorta associated with high mortality. To date, in vivo information to characterize the individual elastic properties of the aneurysm wall in terms of rupture risk is lacking. We have used time-resolved 3D ultrasound strain imaging to calculate spatially resolved in-plane strain distributions characterized by mean and local maximum strains, as well as indices of local variations in strains. Likewise, we here present a method to generate averaged models from multiple segmentations. Strains were then calculated for single segmentations and averaged models. After registration with aneurysm geometries based on CT-A imaging, local strains were divided into two groups with and without calcifications and compared. Geometry comparison from both imaging modalities showed good agreement with a root mean squared error of 1.22 ± 0.15 mm and Hausdorff Distance of 5.45 ± 1.56 mm (mean ± sd, respectively). Using averaged models, circumferential strains in areas with calcifications were 23.2 ± 11.7% (mean ± sd) smaller and significantly distinguishable at the 5% level from areas without calcifications. For single segmentations, this was possible only in 50% of cases. The areas without calcifications showed greater heterogeneity, larger maximum strains, and smaller strain ratios when computed by use of the averaged models. Using these averaged models, reliable conclusions can be made about the local elastic properties of individual aneurysm (and long-term observations of their change), rather than just group comparisons. This is an important prerequisite for clinical application and provides qualitatively new information about the change of an abdominal aortic aneurysm in the course of disease progression compared to the diameter criterion.

Influence of tension-band plates on the mechanical loading of the femoral growth plate during guided growth due to coronal plane deformities.

Introduction: Correction of knee malalignment by guided growth using a tension-band plate is a common therapy to prevent knee osteoarthritis among other things. This approach is based on the Hueter-Volkmann law stating that the length growth of bones is inhibited by compression and stimulated by tension. How the locally varying mechanical loading of the growth plate is influenced by the implant has not yet been investigated. This study combines load cases from the gait cycle with personalized geometry in order to investigate the mechanical influence of the tension-band plates. Methods: Personalized finite element models of four distal femoral epiphyses of three individuals, that had undergone guided growth, were generated. Load cases from the gait cycles and musculoskeletal modelling were simulated with and without implant. Morphological features of the growth plates were obtained from radiographs. 3D geometries were completed using non-individual Magnetic Resonance Images of age-matched individuals. Boundary conditions for the models were obtained from instrumented gait analyses. Results: The stress distribution in the growth plate was heterogenous and depended on the geometry. In the insertion region, the implants locally induced static stress and reduced the cyclic loading and unloading. Both factors that reduce the growth rate. On the contralateral side of the growth plate, increased tension stress was observed, which stimulates growth. Discussion: Personalized finite element models are able to estimate the changes of local static and cyclic loading of the growth plate induced by the implant. In future, this knowledge can help to better control growth modulation and avoid the return of the malalignment after the treatment. However, this requires models that are completely participant-specific in terms of load cases and 3D geometry.

Changes in Aortic Diameter and Wall Strain in Progressing Abdominal Aortic Aneurysms.

OBJECTIVES: The analysis of wall strain opens new perspectives in the prediction of abdominal aortic aneurysm (AAA) rupture. This study investigates the capability of four-dimensional ultrasound (4D US) to detect and characterize changes in wall strain in the same patients during follow-up observations. METHODS: Eighteen patients were examined by 64 4D US scans during a median follow-up period of 24.5 months. After performing the 4D US and manual aneurysm segmentation, kinematic analysis was performed using a customized interface and evaluation of the mean and peak circumferential strain, as well as spatial heterogeneity. RESULTS: All aneurysms showed a continuous diameter growth with a mean rate of 4% per year (P < .001). The mean circumferential strain (MCS) tends to increase from a median 0.89% by 10.49% per year in follow-up independent of the aneurysm diameter (P = .063). The subgroup analysis reveals a cohort with increasing MCS and decreasing spatial heterogeneity, as well as a cohort with nonincreasing MCS and increasing spatial heterogeneity (P < .05). CONCLUSIONS: The 4D US is able to register the strain changes in AAA follow-up. The MCS tends to increase during the observation time in the entire cohort, but the changes were independent of the maximum aneurysm diameter. The kinematic parameters allow the entire AAA cohort to differentiate into two subgroups and provide additional information about the pathologic behavior of the aneurysm wall.

Intra- and Interobserver Variability of 4D Ultrasound Examination of the Infrarenal Aorta.

OBJECTIVES: The four-dimensional ultrasound (4D-US) enables imaging of the aortic segment and simultaneous determination of the wall expansion. The method shows a high spatial and temporal resolution, but its in vivo reliability is so far unknown for low-measure values. The present study determines the intraobserver repeatability and interobserver reproducibility of 4D-US in the atherosclerotic and non-atherosclerotic infrarenal aorta. METHODS: In all, 22 patients with non-aneurysmal aorta were examined by an experienced examiner and a medical student. After registration of 4D images, both the examiners marked the aortic wall manually before the commercially implemented speckle tracking algorithm was applied. The cyclic changes of the aortic diameter and circumferential strain were determined with the help of custom-made software. The reliability of 4D-US was tested by the intraclass correlation coefficient (ICC). RESULTS: The 4D-US measurements showed very good reliability for the maximum aortic diameter and the circumferential strain for all patients and for the non-atherosclerotic aortae (ICC >0.7), but low reliability for circumferential strain in calcified aortae (ICC = 0.29). The observer- and masking-related variances for both maximum diameter and circumferential strain were close to zero. CONCLUSIONS: Despite the low-measured values, the high spatial and temporal resolution of the 4D-US enables a reliable evaluation of cyclic diameter changes and circumferential strain in non-aneurysmal aortae independent from the observer experience but with some limitations for calcified aortae. The 4D-US opens up a new perspective with regard to noninvasive, in vivo assessment of kinematic properties of the vessel wall in the abdominal aorta.

Comparison of Abdominal Aortic Aneurysm Sac and Neck Wall Motion with 4D Ultrasound Imaging.

OBJECTIVE: The rupture of abdominal aortic aneurysms (AAAs) is associated with high mortality despite surgical developments. The determination of aneurysm diameter allows for follow up of aneurysm growth but fails in precisely predicting aneurysm rupture. In this study, time resolved three dimensional ultrasound (4D ultrasound) based wall motion indices (WMIs) are investigated to see if they are capable of distinguishing between uneven affected regions of the aneurysm wall. METHODS: In a prospective study, 56 patients with an AAA were examined using 4D ultrasound. Local longitudinal, circumferential, and shear strains were computed using custom methods. The deformation of the neck and sac of each aneurysm was characterised by statistical indices of the obtained distributions of local wall strains (WMIs): mean and peak strain, heterogeneity index, and local strain ratio. The locations of regions with highest local peak strain were determined. RESULTS: Compared with the aneurysm neck, the sac is characterised by low mean strain, but highly heterogeneous deformation, described by high local strain ratio and heterogeneity index. Differences were highly significant (p < .001) for all strain components. The regions with the highest circumferential peak strain were found more often in the posterior part of the aneurysm neck (p < .050) and sac (p < .001) regions, compared with other wall regions. No statistically significant correlation was found between the WMIs and maximum AAA diameter, except for longitudinal mean strain, which decreased with the increasing diameter (rho = -.42, p < .010). CONCLUSION: Characterisation of wall kinematics by 4D ultrasound based WMIs provides a new and independent criterion for the distinction of diseased tissue in the AAA sac and the less affected neck region. This is a promising step towards the establishment of new biomarkers to differentiate between the mechanical instability of the AAA and rupture risk.

Detailed Measurement of Wall Strain with 3D Speckle Tracking in the Aortic Root: A Case of Bionic Support for Clinical Decision Making.

Three-dimensional (3D) wall motion tracking (WMT) based on ultrasound imaging enables estimation of aortic wall motion and deformation. It provides insights into changes in vascular compliance and vessel wall properties essential for understanding the pathogenesis and progression of aortic diseases. In this report, we employed the novel 3D WMT analysis on the ascending aorta aneurysm (AA) to estimate local aortic wall motion and strain in case of a patient scheduled for replacement of the aortic root. Although progression of the diameter indicates surgical therapy, at present we addressed the question for optimal surgical time point. According to the data, AA in our case has enlarged diameter and subsequent reduced circumferential wall strain, but area tracking data reveals almost normal elastic properties. Virtual remodeling of the aortic root opens a play list for different loading conditions to determine optimal surgical intervention in time.

Cyclic three-dimensional wall motion of the human ascending and abdominal aorta characterized by time-resolved three-dimensional ultrasound speckle tracking.

The aim of this study was to measure, characterize, and compare the time-resolved three-dimensional wall kinematics of the ascending and the abdominal aorta. Comprehensive description of aortic wall kinematics is an important issue for understanding its physiological functioning and early detection of adverse changes. Data on the three-dimensional, dynamic cyclic deformation of the aorta in vivo are scarce. Either most imaging techniques available are too slow to capture aortic wall motion (CT, MRI) or they do not provide three-dimensional geometry data. Three-dimensional volume data sets of ascending and abdominal aortae of male healthy subjects (25.5 [24.5, 27.5] years) were acquired by use of a commercial echocardiography system with a temporal resolution of 11-25 Hz. Longitudinal and circumferential strain, twist, and relative volume change were determined by use of a commercial speckle tracking algorithm and in-house software. The kinematics of the abdominal aorta is characterized by diameter change, almost constant length and unidirectional, either clockwise or counter clockwise twist. In contrast, the ascending aorta undergoes a complex deformation with alternating clockwise and counterclockwise twist. Length and diameter changes were in the same order of magnitude with a phase shift between both. Longitudinal strain and its phase shift to circumferential strain contribute to the proximal aorta's Windkessel function. Complex cyclic deformations are known to be highly fatiguing. This may account for increased degradation of components of the aortic wall and therefore promote aortic dissection or aneurysm formation.

A finite element updating approach for identification of the anisotropic hyperelastic properties of normal and diseased aortic walls from 4D ultrasound strain imaging.

Computational analysis of the biomechanics of the vascular system aims at a better understanding of its physiology and pathophysiology and eventually at diagnostic clinical use. Because of great inter-individual variations, such computational models have to be patient-specific with regard to geometry, material properties and applied loads and boundary conditions. Full-field measurements of heterogeneous displacement or strain fields can be used to improve the reliability of parameter identification based on a reduced number of observed load cases as is usually given in an in vivo setting. Time resolved 3D ultrasound combined with speckle tracking (4D US) is an imaging technique that provides full field information of heterogeneous aortic wall strain distributions in vivo. In a numerical verification experiment, we have shown the feasibility of identifying nonlinear and orthotropic constitutive behaviour based on the observation of just two load cases, even though the load free geometry is unknown, if heterogeneous strain fields are available. Only clinically available 4D US measurements of wall motion and diastolic and systolic blood pressure are required as input for the inverse FE updating approach. Application of the developed inverse approach to 4D US data sets of three aortic wall segments from volunteers of different age and pathology resulted in the reproducible identification of three distinct and (patho-) physiologically reasonable constitutive behaviours. The use of patient-individual material properties in biomechanical modelling of AAAs is a step towards more personalized rupture risk assessment.

Method for aortic wall strain measurement with three-dimensional ultrasound speckle tracking and fitted finite element analysis.

BACKGROUND: Aortic wall strains are indicators of biomechanical changes of the aorta due to aging or progressing pathologies such as aortic aneurysm. We investigated the potential of time-resolved three-dimensional ultrasonography coupled with speckle-tracking algorithms and finite element analysis as a novel method for noninvasive in vivo assessment of aortic wall strain. METHODS: Three-dimensional volume datasets of 6 subjects without cardiovascular risk factors and 2 abdominal aortic aneurysms were acquired with a commercial real time three-dimensional echocardiography system. Longitudinal and circumferential strains were computed offline with high spatial resolution using a customized commercial speckle-tracking software and finite element analysis. Indices for spatial heterogeneity and systolic dyssynchrony were determined for healthy abdominal aortas and abdominal aneurysms. RESULTS: All examined aortic wall segments exhibited considerable heterogenous in-plane strain distributions. Higher spatial resolution of strain imaging resulted in the detection of significantly higher local peak strains (p ≤ 0.01). In comparison with healthy abdominal aortas, aneurysms showed reduced mean strains and increased spatial heterogeneity and more pronounced temporal dyssynchrony as well as delayed systole. CONCLUSIONS: Three-dimensional ultrasound speckle tracking enables the analysis of spatially highly resolved strain fields of the aortic wall and offers the potential to detect local aortic wall motion deformations and abnormalities. These data allow the definition of new indices by which the different biomechanical properties of healthy aortas and aortic aneurysms can be characterized.

In vivo determination of elastic properties of the human aorta based on 4D ultrasound data.

Computational analysis of the biomechanics of the vascular system aims at a better understanding of its physiology and pathophysiology. To be of clinical use, however, these models and thus their predictions, have to be patient specific regarding geometry, boundary conditions and material. In this paper we present an approach to determine individual material properties of human aortae based on a new type of in vivo full field displacement data acquired by dimensional time resolved three dimensional ultrasound (4D-US) imaging. We developed a nested iterative Finite Element Updating method to solve two coupled inverse problems: The prestrains that are present in the imaged diastolic configuration of the aortic wall are determined. The solution of this problem is integrated in an iterative method to identify the nonlinear hyperelastic anisotropic material response of the aorta to physiologic deformation states. The method was applied to 4D-US data sets of the abdominal aorta of five healthy volunteers and verified by a numerical experiment. This non-invasive in vivo technique can be regarded as a first step to determine patient individual material properties of the human aorta.

A two-parameter study of the extent of chaos in a billiard system.

The billiard system of Benettin and Strelcyn [Phys. Rev. A 17, 773-785 (1978)] is generalized to a two-parameter family of different shapes. Its boundaries are composed of circular segments. The family includes the integrable limit of a circular boundary, convex boundaries of various shapes with mixed dynamics, stadiums, and a variety of nonconvex boundaries, partially with ergodic behavior. The extent of chaos has been measured in two ways: (i) in terms of phase space volume occupied by the main chaotic band; and (ii) in terms of the Lyapunov exponent of that same region. The results are represented as a kind of phase diagram of chaos. We observe complex regularities, related to the bifurcation scheme of the most prominent resonances. A detailed stability analysis of these resonances up to period six explains most of these features. The phenomenon of breathing chaos [Nonlinearity 3, 45-67 (1990)]-that is, the nonmonotonicity of the amount of chaos as a function of the parameters-observed earlier in a one-parameter study of the gravitational wedge billiard, is part of the picture, giving support to the conjecture that this is a fairly common global scenario. (c) 1996 American Institute of Physics.