The influence of wall stress on AAA growth and biomarkers.

OBJECTIVES: This study investigated the relation between abdominal aortic aneurysm (AAA) wall stress, AAA growth rate and biomarker concentrations. With increasing wall stress, more damage may be caused to the AAA wall, possibly leading to progression of the aneurysm and reflection in up- or downregulation of specific circulating biomarkers. Levels of matrix metalloproteinase-9, tissue inhibitor of matrix metalloproteinase-1, C-reactive protein and alpha 1-antitrypsin were therefore evaluated. METHODS: Thirty-seven patients (maximum AAA diameter 41-55mm) with two, three or four consecutive computed tomography angiography (CTA) scans were prospectively included. Diameter growth rate in mm/year was determined between each pair of two sequential CTA scans. AAA wall stress was computed by finite element analysis, based on the first of the two sequential CTA scans only (n=69 pairs). Biomarker information was determined in 46 measurements in 18 patients. The relation between AAA diameter and wall stress was determined and the AAA's were divided into three equally sized groups (relative low, medium and high stress). Growth rate and biomarker concentrations were compared between these groups. Additionally, correlation coefficients were computed between absolute wall stress, AAA growth and biomarker concentrations. RESULTS: A relative low AAA wall stress was associated with a lower aneurysm growth rate. Growth rate was also positively related to MMP-9 plasma concentration (r=0.32). The average MMP-9 and CRP concentrations increased with increasing degrees of relative wall stress, although the absolute and relative wall stress did not correlate with any of the biomarkers. CONCLUSION: Although lower relative wall stress was associated to a lower AAA growth rate, no relation was found between biomarker concentrations and wall stress. Future research may focus on more and extensive biomarker measurements in relation to AAA wall stress.

The influence of model order reduction on the computed fractional flow reserve using parameterized coronary geometries.

Computational fluid dynamics (CFD) models combined with patient-specific imaging data are used to non-invasively predict functional significance of coronary lesions. This approach to predict the fractional flow reserve (FFR) is shown to have a high diagnostic accuracy when comparing against invasively measured FFR. However, one of the main drawbacks is the high computational effort needed for preprocessing and computations. Hence, uncertainty quantification may become unfeasible. Reduction of complexity is desirable, computationally inexpensive models with high diagnostic accuracy are preferred. We present a parametric comparison study for three types of CFD models (2D axisymmetric, Semi-3D and 3D) in which we study the impact of model reduction on three models on the predicted FFR. In total 200 coronary geometries were generated for seven geometrical characteristics e.g. stenosis severity, stenosis length and vessel curvature. The effect of time-averaged flow was investigated using unsteady, mean steady and a root mean square (RMS) steady flow. The 3D unsteady model was regarded as reference model. Results show that when using an unsteady or RMS flow, predicted FFR hardly varies between models contrary to using average flows. The 2D model with RMS flow has a high diagnostic accuracy (0.99), reduces computational time by a factor 162,000 and the introduced model error is well below the clinical relevant differences. Stenosis severity, length, curvature and tapering cause most discrepancies when using a lower order model. An uncertainty analysis showed that this can be explained by the low variability that is caused by variations in stenosis asymmetry.

Patient-specific AAA wall stress analysis: 99-percentile versus peak stress.

OBJECTIVE: Biomechanically, rupture of an Abdominal Aortic Aneurysm (AAA) occurs when the stress acting on the wall due to the blood pressure, exceeds the strength of the wall. Peak wall stress estimations, based on CT reconstruction, may be prone to observer variation. This study focuses on the robustness and reproducibility of AAA wall stress assessment and the relation with geometrical features of the AAA. METHODS: The AAAs of twenty patients were reconstructed by three operators. Both the peak and 99-percentile stress were used for intra- and inter-operator variability using the intraclass correlation coefficient (ICC). A regression analysis was performed to relate the stress parameters with the maximum diameter. Outliers were analyzed by their geometrical characteristics. RESULTS: The intra-operator ICC was 0.73-0.79 for the peak stress and 0.94 for the 99-percentile stress. The inter-operator ICC was 0.71 for the peak stress and 0.95 for the 99-percentile stress. A significant linear relation with the diameter was found only for the 99-percentile stress. CONCLUSIONS: The 99-percentile stress is more reproducible than peak wall stress. A significant relation between wall stress and diameter was found. Other geometrical features had no statistical relation with high stress.

Quantifying pressure sore-related muscle damage using high-resolution MRI.

To obtain insight into the etiology of deep pressure sores, understanding of the relationship between prolonged transverse loading and local muscle damage is required. To date, the amount and location of muscle damage have been determined by histological examination. In the present study, we determined whether T2-weighted high-resolution magnetic resonance imaging (MRI) can also be applied to evaluate muscle tissue after prolonged transverse loading. The tibialis anterior muscle and overlying skin in the right hindlimbs of five rats were compressed between an indenter and the tibia. The in vivo magnetic resonance images of the loaded and contralateral hindlimbs were obtained 24 h after load application. The tibialis anterior muscles were then processed for histological examination. In the magnetic resonance images of all five loaded hindlimbs, signal intensity appeared higher in the loaded regions of the muscle compared with the unloaded regions. The location of the higher signal intensity coincided with the location of damage assessed from histology. Also the amount of damage determined with MRI was in good agreement with the amount of damage assessed from histological examination. Because MRI is nondestructive, it is a promising alternative for histology in research on pressure sore etiology, especially in follow-up studies to evaluate the development of muscle damage in time and in clinical studies.

Can loaded interface characteristics influence strain distributions in muscle adjacent to bony prominences?

Pressure distributions at the interface between skin and supporting tissues are used in design of supporting surfaces like beds, wheel chairs, prostheses and in sales brochures to support commercial products. The reasoning behind this is, that equal pressure distributions in the absence of high pressure gradients is assumed to minimise the risk of developing pressure sores. Notwithstanding the difficulty in performing reproducible and accurate pressure measurements, the question arises if the interface pressure distribution is representative of the internal mechanical state of the soft tissues involved. The paper describes a study of the mechanical condition of a supported buttock contact, depending on cushion properties, relative properties of tissue layers and friction. Numerical, mechanical simulations of a buttock on a supporting cushion are described. The ischial tuberosity is modelled as a rigid body, whereas the overlying muscle, fat and skin layers are modelled as a non-linear Ogden material. Material parameters and thickness of the fat layer are varied. Coulomb friction between buttock and cushion is modelled with different values of the friction coefficient. Moreover, the thickness and properties of the cushion are varied. High shear strains are found in the muscle near the bony prominence and the fat layer near the symmetry line. The performed parameter variations lead to large differences in shear strain in the fat layer but relatively small variations in the skeletal muscle. Even with a soft cushion, leading to a high reduction of the interface pressure the deformation of the skeletal muscle near the bone is high enough to form a risk, which is a clear argument that interface pressures alone are not sufficient to evaluate supporting surfaces.

A sensitivity analysis of a personalized pulse wave propagation model for arteriovenous fistula surgery. Part A: Identification of most influential model parameters.

Previously, a pulse wave propagation model was developed that has potential in supporting decision-making in arteriovenous fistula (AVF) surgery for hemodialysis. To adapt the wave propagation model to personalized conditions, patient-specific input parameters should be available. In clinics, the number of measurable input parameters is limited which results in sparse datasets. In addition, patient data are compromised with uncertainty. These uncertain and incomplete input datasets will result in model output uncertainties. By means of a sensitivity analysis the propagation of input uncertainties into output uncertainty can be studied which can give directions for input measurement improvement. In this study, a computational framework has been developed to perform such a sensitivity analysis with a variance-based method and Monte Carlo simulations. The framework was used to determine the influential parameters of our pulse wave propagation model applied to AVF surgery, with respect to parameter prioritization and parameter fixing. With this we were able to determine the model parameters that have the largest influence on the predicted mean brachial flow and systolic radial artery pressure after AVF surgery. Of all 73 parameters 51 could be fixed within their measurement uncertainty interval without significantly influencing the output, while 16 parameters importantly influence the output uncertainty. Measurement accuracy improvement should thus focus on these 16 influential parameters. The most rewarding are measurement improvements of the following parameters: the mean aortic flow, the aortic windkessel resistance, the parameters associated with the smallest arterial or venous diameters of the AVF in- and outflow tract and the radial artery windkessel compliance.

A sensitivity analysis of a personalized pulse wave propagation model for arteriovenous fistula surgery. Part B: Identification of possible generic model parameters.

Decision-making in vascular access surgery for hemodialysis can be supported by a pulse wave propagation model that is able to simulate pressure and flow changes induced by the creation of a vascular access. To personalize such a model, patient-specific input parameters should be chosen. However, the number of input parameters that can be measured in clinical routine is limited. Besides, patient data are compromised with uncertainty. Incomplete and uncertain input data will result in uncertainties in model predictions. In part A, we analyzed how the measurement uncertainty in the input propagates to the model output by means of a sensitivity analysis. Of all 73 input parameters, 16 parameters were identified to be worthwhile to measure more accurately and 51 could be fixed within their measurement uncertainty range, but these latter parameters still needed to be measured. Here, we present a methodology for assessing the model input parameters that can be taken constant and therefore do not need to be measured. In addition, a method to determine the value of this parameter is presented. For the pulse wave propagation model applied to vascular access surgery, six patient-specific datasets were analyzed and it was found that 47 out of 73 parameters can be fixed on a generic value. These model parameters are not important for personalization of the wave propagation model. Furthermore, we were able to determine a generic value for 37 of the 47 fixable model parameters.

Assisting vascular access surgery planning for hemodialysis by using MR, image segmentation techniques, and computer simulations.

The surgical creation of a vascular access, used for hemodialysis treatment of renal patients, has considerable complication rates (30-50 %). Image-based computational modeling might assist the surgeon in planning by enhanced analysis of preoperative hemodynamics, and in the future might serve as platform for outcome prediction. The objective of this study is to investigate preoperative personalization of the computer model using magnetic resonance (MR). MR-angiography and MR-flow data were obtained for eight patients and eight volunteers. Blood vessels were extracted for model input by a segmentation algorithm. Windkessel elements were added at the ends to represent the peripheral beds. Monte Carlo-based calibration was used to estimate the most influential non-measurable parameters. The predicted flow waveforms were compared with the MR-flow measurements for framework evaluation. The vasculature of all subjects were segmented in on average <5 min. The Monte Carlo-calibrated simulations showed a deviation between measured and simulated flow waveforms of 9 and 10 % for volunteers and patients, respectively. The presented method accurately mimics the preoperative hemodynamic state. Furthermore, the surgeon can interactively explore the hemodynamics at any vascular tree position. This integration of measurements in a modeling approach can provide the surgeon with additional information for preoperative planning.

Experimental validation of a pulse wave propagation model for predicting hemodynamics after vascular access surgery.

Hemodialysis patients require a vascular access that is, preferably, surgically created by connecting an artery and vein in the arm, i.e. an arteriovenous fistula (AVF). The site for AVF creation is chosen by the surgeon based on preoperative diagnostics, but AVFs are still compromised by flow-associated complications. Previously, it was shown that a computational 1D-model is able to describe pressure and flow after AVF surgery. However, predicted flows differed from measurements in 4/10 patients. Differences can be attributed to inaccuracies in Doppler measurements and input data, to neglecting physiological mechanisms or to an incomplete physical description of the pulse wave propagation after AVF surgery. The physical description can be checked by validating against an experimental setup consisting of silicone tubes mimicking the aorta and arm vasculature both before and after AVF surgery, which is the aim of the current study. In such an analysis, the output uncertainty resulting from measurement uncertainty in model input should be quantified. The computational model was fed by geometrical and mechanical properties collected from the setup. Pressure and flow waveforms were simulated and compared with experimental waveforms. The precision of the simulations was determined by performing a Monte Carlo study. It was concluded that the computational model was able to simulate mean pressures and flows accurately, whereas simulated waveforms were less attenuated than experimental ones, likely resulting from neglecting viscoelasticity. Furthermore, it was found that in the analysis output uncertainties, resulting from input uncertainties, cannot be neglected and should thus be considered.

A pulse wave propagation model to support decision-making in vascular access planning in the clinic.

The preferred vascular access for hemodialysis is an autologous arteriovenous fistula (AVF) in the arm: a surgically created connection between an artery and vein. The surgeon selects the AVF location based on experience and preoperative diagnostics. However, 20-50% of all lower arm AVFs are hampered by a too low access flow, whereas complications associated with too high flows are observed in 20% of all upper arm AVFs. We hypothesize that a pulse wave propagation model fed by patient-specific data has the ability to assist the surgeon in selecting the optimal AVF configuration by predicting direct postoperative flow. Previously, a 1D wave propagation model (spectral elements) was developed in which an approximated velocity profile was assumed based on boundary layer theory. In this study, we derived a distributed lumped parameter implementation of the pulse wave propagation model. The elements of the electrical analog for a segment are based on the approximated velocity profiles and dependent on the Womersley number. We present the application of the lumped parameter pulse wave propagation model to vascular access surgery and show how a patient-specific model is able to predict the hemodynamical impact of AVF creation and might assist in vascular access planning. The lumped parameter pulse wave propagation model was able to select the same AVF configuration as an experienced surgeon in nine out of ten patients. In addition, in six out of ten patients predicted postoperative flows were in the same order of magnitude as measured postoperative flows. Future research should quantify uncertainty in model predictions and measurements.

Global sensitivity analysis of a wave propagation model for arm arteries.

Wave propagation models of blood flow and blood pressure in arteries play an important role in cardiovascular research. For application of these models in patient-specific simulations a number of model parameters, that are inherently subject to uncertainties, are required. The goal of this study is to identify with a global sensitivity analysis the model parameters that influence the output the most. The improvement of the measurement accuracy of these parameters has largest consequences for the output statistics. A patient specific model is set up for the major arteries of the arm. In a Monte-Carlo study, 10 model parameters and the input blood volume flow (BVF) waveform are varied randomly within their uncertainty ranges over 3000 runs. The sensitivity in the output for each system parameter was evaluated with the linear Pearson and ranked Spearman correlation coefficients. The results show that model parameter and input BVF uncertainties induce large variations in output variables and that most output variables are significantly influenced by more than one system parameter. Overall, the Young's modulus appears to have the largest influence and arterial length the smallest. Only small differences were obtained between Spearman's and Pearson's tests, suggesting that a high monotonic association given by Spearman's test is associated with a high linear corelation between the inputs and output parameters given by Pearson's test.

Estimation of distributed arterial mechanical properties using a wave propagation model in a reverse way.

To estimate arterial stiffness, different methods based either on distensibility, pulse wave velocity or a pressure-velocity loop, have been proposed. These methods can be employed to determine the arterial mechanical properties either locally or globally, e.g. averaged over an entire arterial segment. The aim of this study was to investigate the feasibility of a new method that estimates distributed arterial mechanical properties non-invasively. This new method is based on a wave propagation model and several independent ultrasound and pressure measurements. Model parameters (including arterial mechanical properties) are obtained from a reverse method in which differences between modeling results and measurements are minimized using a fitting procedure based on local sensitivity indices. This study evaluates the differences between in vivo measured and simulated blood pressure and volume flow waveforms at the brachial, radial and ulnar arteries of 6 volunteers. The estimated arterial Young's modulus range from 1.0 to 6.0MPa with an average of (3.8±1.7)MPa at the brachial artery and from 1.2 to 7.8MPa with an average of (4.8±2.2)MPa at the radial artery. A good match between measured and simulated waveforms and the realistic stiffness parameters indicate a good in vivo suitability.

Assessment of blood volume flow in slightly curved arteries from a single velocity profile.

Non-invasive estimation of arterial blood volume flow (BVF) has become a central issue in assessment of cardiovascular risk. Poiseuille and Womersley approaches are commonly used to assess the BVF from centerline velocity, but both methods neglect the influence of curvature. Based on the assumption that the velocity in curved tubes as function of the circumferential position for a given radial position can be approximated by a cosine, the BVF can also be estimated by averaging velocities at opposite radial positions, referred to as the cosine theta model (CTM). This study investigates the accuracy of BVF estimation in slightly curved arteries for BVF waveforms obtained in the brachial artery of 6 volunteers. Computational fluid dynamics simulations were used to compute the influence of curvature on velocity profiles. The BVF was then estimated from the simulation results with the CTM and methods based on Poiseuille, Womersley and using the center stream velocity and the velocity waveform at the position where the maximum velocity is observed, and compared to the prescribed BVF. The simulations show that the influence of curvature is strongest when the flow decelerates. For Poiseuille and Womersley, the time average BVF was underestimated by maximally 10.4% and 7.8% for a radius of curvature of 50 and 100 mm, respectively. The estimation error is lower for the CTM and equals 4.2% and 1.2% for a radius of curvature of 50 and 100mm, respectively. From this study, we can conclude that the velocity waveform at the position of the maximum rather than the center stream velocity waveform combined with the Womersley method should be chosen. The CTM improves current estimation techniques if in-vivo velocity distributions are available.

Model-based assessment of dynamic arterial blood volume flow from ultrasound measurements.

To assess in clinical practice arterial blood volume flow (BVF) from ultrasound measurements, the assumption is commonly made that the velocity profile can be approximated by a quasi-static Poiseuille model. However, pulsatile flow behaviour is more accurately described by a Womersley model. No clinical studies have addressed the consequences on the estimated dynamics of the BVF when Poiseuille rather than Womersley models are used. The aim of this study is to determine the influence of assumed Poiseuille profile instead of Womersley profile on the estimation and intrasubject variability of dynamical parameters of the BVF. For this purpose, a low number of volunteers sufficed. Brachial artery centerline velocity waveform and vessel diameter were measured with ultrasound within a small group of six volunteers. Within subjects, the intra- and inter-registration variability of BVF parameters estimates did not significantly differ. Poiseuille profiles compared to Womersley underestimates the maximum BVF by 19%, the maximum retrograde volume flow by 32% and the rise time by 18%. It can be concluded that when estimating in a straight vessel the dynamic properties of the BVF, Womersley profiles should preferably be chosen.

Initial stress and nonlinear material behavior in patient-specific AAA wall stress analysis.

Rupture risk estimation of abdominal aortic aneurysms (AAA) is currently based on the maximum diameter of the AAA. A more critical approach is based on AAA wall stress analysis. For that, in most cases, the AAA geometry is obtained from CT-data and treated as a stress free geometry. However, during CT imaging, the AAA is subjected to a time-averaged blood pressure and is therefore not stress free. The aim of this study is to evaluate the effect of neglecting these initial stresses (IS) on the patient-specific AAA wall stress as computed by finite element analysis. Additionally, the contribution of the nonlinear material behavior of the AAA wall is evaluated. Thirty patients with maximum AAA diameters below the current surgery criterion were scanned with contrast-enhanced CT and the AAA's were segmented from the image data. The mean arterial blood pressure (MAP) was measured immediately after the CT-scan and used to compute the IS corresponding with the CT geometry and MAP. Comparisons were made between wall stress obtained with and without IS and with linear and nonlinear material properties. On average, AAA wall stresses as computed with IS were higher than without IS. This was also the case for the stresses computed with the nonlinear material model compared to the linear material model. However, omitting initial stress and material nonlinearity in AAA wall stress computations leads to different effects in the resulting wall stress for each AAA. Therefore, provided that other assumptions made are not predominant, IS cannot be discarded and a nonlinear material model should be used in future patient-specific AAA wall stress analyses.