Contrast detection in fluid-saturated media with magnetic resonance poroelastography.

PURPOSE: Recent interest in the poroelastic behavior of tissues has led to the development of magnetic resonance poroelastography (MRPE) as an alternative to single-phase MR elastographic image reconstruction. In addition to the elastic parameters (i.e., Lamé's constants) commonly associated with magnetic resonance elastography (MRE), MRPE enables estimation of the time-harmonic pore-pressure field induced by external mechanical vibration. METHODS: This study presents numerical simulations that demonstrate the sensitivity of the computed displacement and pore-pressure fields to a priori estimates of the experimentally derived model parameters. In addition, experimental data collected in three poroelastic phantoms are used to assess the quantitative accuracy of MR poroelastographic imaging through comparisons with both quasistatic and dynamic mechanical tests. RESULTS: The results indicate hydraulic conductivity to be the dominant parameter influencing the deformation behavior of poroelastic media under conditions applied during MRE. MRPE estimation of the matrix shear modulus was bracketed by the values determined from independent quasistatic and dynamic mechanical measurements as expected, whereas the contrast ratios for embedded inclusions were quantitatively similar (10%-15% difference between the reconstructed images and the mechanical tests). CONCLUSIONS: The findings suggest that the addition of hydraulic conductivity and a viscoelastic solid component as parameters in the reconstruction may be warranted.

Magnetic resonance poroelastography: an algorithm for estimating the mechanical properties of fluid-saturated soft tissues.

Magnetic resonance poroelastography (MRPE) is introduced as an alternative to single-phase model-based elastographic reconstruction methods. A 3-D finite element poroelastic inversion algorithm was developed to recover the mechanical properties of fluid-saturated tissues. The performance of this algorithm was assessed through a variety of numerical experiments, using synthetic data to probe its stability and sensitivity to the relevant model parameters. Preliminary results suggest the algorithm is robust in the presence of noise and capable of producing accurate assessments of the underlying mechanical properties in simulated phantoms. Furthermore, a 3-D time-harmonic motion field was recorded for a poroelastic phantom containing a single cylindrical inclusion and used to assess the feasibility of MRPE image reconstruction from experimental data. The elastograms obtained from the proposed poroelastic algorithm demonstrate significant improvement over linearly elastic MRE images generated using the same data. In addition, MRPE offers the opportunity to estimate the time-harmonic pressure field resulting from tissue excitation, highlighting the potential for its application in the diagnosis and monitoring of disease processes associated with changes in interstitial pressure.

Modeling of soft poroelastic tissue in time-harmonic MR elastography.

Elastography is an emerging imaging technique that focuses on assessing the resistance to deformation of soft biological tissues in vivo. Magnetic resonance elastography (MRE) uses measured displacement fields resulting from low-amplitude, low-frequency (10 Hz-1 kHz) time-harmonic vibration to recover images of the elastic property distribution of tissues including breast, liver, muscle, prostate, and brain. While many soft tissues display complex time-dependent behavior not described by linear elasticity, the models most commonly employed in MRE parameter reconstructions are based on elastic assumptions. Further, elasticity models fail to include the interstitial fluid phase present in vivo. Alternative continuum models, such as consolidation theory, are able to represent tissue and other materials comprising two distinct phases, generally consisting of a porous elastic solid and penetrating fluid. MRE reconstructions of simulated elastic and poroelastic phantoms were performed to investigate the limitations of current-elasticity-based methods in producing accurate elastic parameter estimates in poroelastic media. The results indicate that linearly elastic reconstructions of fluid-saturated porous media at amplitudes and frequencies relevant to steady-state MRE can yield misleading effective property distributions resulting from the complex interaction between their solid and fluid phases.

Optimized motion estimation for MRE data with reduced motion encodes.

Motion estimation is an essential step common to all magnetic resonance elastography (MRE) methods. For dynamic techniques, the motion is obtained from a sinusoidal fit of the image phase at multiple, uniformly spaced relative phase offsets, phi, between the motion and the motion encoding gradients (MEGs). Generally, eight values of phi sampled at the Nyquist interval pi/4 over [0, 2pi). We introduce a method, termed reduced motion encoding (RME), that reduces the number of phi required, thereby reducing the imaging time for an MRE acquisition. A frequency-domain algorithm was implemented using the discrete Fourier transform (DFT) to derive the general least-squares solution for the motion amplitude and phase given an arbitrary number of phi. A closed form representation of the condition number of the transformation matrix which is used for estimating motion was introduced to determine the sensitivity to noise for different sampling patterns of phi. Simulation results confirmed the minimum error sampling patterns suggested from the condition number maps. The minimum noise in the motion estimate is obtained when the sampled phi are essentially evenly distributed over the range [0, pi) with an interval pi/n, where n is the number of phi sampled, or alternatively with an interval 2pi/n over the range [0, 2pi) which represents the Nyquist interval. Simulations also show that the noise level decreases as n increases as expected. The decrease in noise is the largest when n is small and it becomes less significant as n increases. The algorithm also makes it possible to estimate the motion from only two values of phi, which cannot be accomplished with traditional methods because sampling at the Nyquist interval is indeterminate. Finally, noise levels in motion estimated from phantom studies and in vivo results taken with different n agreed with that predicted by simulation and condition number calculations.

Clinical wear measurement on low contact stress rotating platform knee bearings.

Whereas fixed-bearing total knee arthroplasty (TKA) designs secure the polyethylene bearing to the tibial tray, mobile-bearing TKAs allow the bearing to move relative to the tray. This study evaluated wear performance of the rotational articulation of the Low Contact Stress Rotating Platform mobile-bearing TKA (DePuy, Warsaw, Ind) by analyzing 100 retrievals. All retrieved bearings showed rotation surface damage, but severity of the damage did not correlate with duration. Rotation surface damage appeared to be caused by contaminant particles, which produced curvilinear scratches that were longer than the normal rotational excursion of the knee. Wear measurement indicated that wear was relatively uniform, long-term wear rates were low (mean, 54 mm(3)/y for durations >2 years) and decreased with longer duration, and damaged appearance did not correspond to high wear.

Elastic and rupture properties of porcine aortic tissue measured using inflation testing.

A new inflation test device was developed to study the mechanical properties of aortic tissue. The device was used to measure failure (rupture) strength and to determine the nonlinear, anisotropic elastic properties of porcine thoracic aorta. The tester was designed to stretch initially flat, circular tissue specimens to rupture under uniform biaxial loading. Water was chosen as the pressurizing fluid. Mechanical stretch and radius of curvature during inflation were measured optically in two orthogonal directions, and the Cauchy stress components were calculated from the deformation and the applied pressure. All porcine samples that ruptured successfully did so via a tear in the circumferential direction. Thus, the failure strength was taken to be the stress in the axial direction immediately prior to rupture. The mean failure strength was 1.75 MPa and mean axial stretch at failure was 1.52. These values agree well with published data for other arterial tissues. The nonlinearly elastic deformation behavior was modeled using a hyperelastic constitutive law of the type proposed by Holzapfel et al. [Holzapfel GA, Gasser TC, Ogden RW. J Elasticity 2000;61:1-48]. The results showed that the dominant directions of anisotropy in the porcine aortas were approximately 45 degrees to the axial and circumferential directions, and that the isotropic contribution to the constitutive model was insignificant.

Data-guided brain deformation modeling: evaluation of a 3-D adjoint inversion method in porcine studies.

Biomechanical models of brain deformation are useful tools for estimating parenchymal shift that results during open cranial procedures. Intraoperative data is likely to improve model estimates, but incorporation of such data into the model is not trivial. This study tests the adjoint equations method (AEM) for data assimilation as a viable approach for integrating displacement data into a brain deformation model. AEM was applied to two porcine experiments. AEM-based estimates were compared both to measured displacement data [from computed tomography (CT) scans] and to model solutions obtained without the guidance of sparse data, which we term the best prior estimate (BPE). Additionally, the sensitivity of the AEM solution to inverse parameter selection was investigated. The results suggest that it is most important to estimate the size of the variance in the measurement error correctly, make the correlation length long and estimate displacement (over stress) boundary conditions. Application of AEM shows an average 33% improvement over BPE. This paper represents the first evidence of successful use of the AEM technique in three dimensions with experimental data validation. The guidelines established for selection of model parameters are starting points for further optimization of the method under clinical conditions.

Elemental composition, morphology and mechanical properties of calcified deposits obtained from abdominal aortic aneurysms.

Calcified deposits exist in almost all abdominal aortic aneurysms (AAAs). The significant difference in stiffness between these hard deposits and the compliant arterial wall may result in local stress concentrations and increase the risk of aneurysm rupture. Calcium deposits may also complicate AAA repair by hindering the attachment of a graft or stent-graft to the arterial wall or cause vessel wall injury at the site of balloon dilation or vascular clamp placement. Knowledge of the composition and properties of calcified deposits helps in understanding the risks associated with their presence. This work presents results of elemental composition, microscopic morphology, and mechanical property measurements of human calcified deposits obtained from within AAAs. The elemental analyses indicate the deposits are composed primarily of calcium phosphate with other assorted constituents. Microscopy investigations show a variety of microstructures within the deposits. The mechanical property measurements indicate an average elastic modulus in the range of cortical bone and an average hardness similar to nickel and iron.

Automated methodology for determination of stress distribution in human abdominal aortic aneurysm.

Knowledge of impending abdominal aortic aneurysm (AAA) rupture can help in surgical planning. Typically, aneurysm diameter is used as the indicator of rupture, but recent studies have hypothesized that pressure-induced biomechanical stress may be a better predictor Verification of this hypothesis on a large study population with ruptured and unruptured AAA is vital if stress is to be reliably used as a clinical prognosticator for AAA rupture risk. We have developed an automated algorithm to calculate the peak stress in patient-specific AAA models. The algorithm contains a mesh refinement module, finite element analysis module, and a postprocessing visualization module. Several aspects of the methodology used are an improvement over past reported approaches. The entire analysis may be run from a single command and is completed in less than 1 h with the peak wall stress recorded for statistical analysis. We have used our algorithm for stress analysis of numerous ruptured and unruptured AAA models and report some of our results here. By current estimates, peak stress in the aortic wall appears to be a better predictor of rupture than AAA diameter. Further use of our algorithm is ongoing on larger study populations to convincingly verify these findings.

Assimilating intraoperative data with brain shift modeling using the adjoint equations.

Biomechanical models of brain deformation are increasingly being used to nonrigidly register preoperative MR (pMR) images of the brain to the surgical scene. These model estimates can potentially be improved by incorporating sparse displacement data available in the operating room (OR), but integrating the intraoperative information with model calculations is a nontrivial problem. We present an inverse method to estimate the unknown boundary and volumetric forces necessary to achieve a least-squares fit between the model and the data that is formulated in terms of the adjoint equations, which are solved directly by the method of representers. The scheme is illustrated in a 2D simulation and in a 2D approximation based on a patient case using actual OR data.

A three-parameter mechanical property reconstruction method for MR-based elastic property imaging.

A reconstruction process featuring full parameterization of the three dimensional, time-harmonic equations of linear elasticity is developed and reconstructed property images are presented from simulation-based investigation. While interesting in its own right through the potential for increased adaptability of these reconstructive elastic imaging techniques, this study also presents a set of analysis tools used to study the poor convergence behavior found in the case of tissue like conditions (i.e. nearly incompressible materials). The choice of elastic properties for imaging in elastography research remains an open question at this point; the use of the stability and sensitivity-based analytical methods described here will help to predict and understand the value and reliability of different parameterizations of elasticity imaging. Additionally, though results indicate significant work needs to be done to achieve effective multiparameter reconstructive imaging, the methods detailed here offer the promise of increased flexibility and sophistication in elastographic imaging techniques.

Displacement estimation with co-registered ultrasound for image guided neurosurgery: a quantitative in vivo porcine study.

Brain shift during open cranial surgery presents a challenge for maintaining registration with image-guidance systems. Ultrasound (US) is a convenient intraoperative imaging modality that may be a useful tool in detecting tissue shift and updating preoperative images based on intraoperative measurements of brain deformation. We have quantitatively evaluated the ability of spatially tracked freehand US to detect displacement of implanted markers in a series of three in vivo porcine experiments, where both US and computed tomography (CT) image acquisitions were obtained before and after deforming the brain. Marker displacements ranged from 0.5 to 8.5 mm. Comparisons between CT and US measurements showed a mean target localization error of 1.5 mm, and a mean vector error for displacement of 1.1 mm. Mean error in the magnitude of displacement was 0.6 mm. For one of the animals studied, the US data was used in conjunction with a biomechanical model to nonrigidly re-register a baseline CT to the deformed brain. The mean error between the actual and deformed CT's was found to be on average 1.2 and 1.9 mm at the marker locations depending on the extent of the deformation induced. These findings indicate the potential accuracy in coregistered freehand US displacement tracking in brain tissue and suggest that the resulting information can be used to drive a modeling re-registration strategy to comparable levels of agreement.

Comparison of cross-linked polyethylene materials for orthopaedic applications.

Cross-linked polyethylenes are being marketed by orthopaedic manufacturers to address the problem of osteolysis caused by polyethylene particulate wear debris. Wear testing of these cross-linked polyethylenes in hip simulators has shown dramatic reduction in wear rate compared with standard ultrahigh molecular weight polyethylene, either gamma irradiated in air or nitrogen - or ethylene oxide-sterilized. However, this reduction in wear rate is not without cost. The cross-linking processes can result in materials with lower mechanical properties than standard ultrahigh molecular weight polyethylene. To evaluate the effect of the various cross-linking processes on physical and mechanical properties of ultrahigh molecular weight polyethylene, commercially available cross-linked polyethylenes from six orthopaedic manufacturers were tested. This study was the culmination of collaboration with these manufacturers, who provided cross-linked polyethylene for this study, wear characteristics of the material they provided, and review of the physical and mechanical properties measure for their polyethylene. Cross-linked materials were evaluated as received and after an accelerated aging protocol. Free radical identity and concentration, oxidation, crystallinity, melt temperature, ultimate tensile strength, elongation at break, tensile stress at yield, and toughness are reported for each material. By comparing these physical and mechanical properties, surgeons can evaluate the trade-off that results from developing materials with substantially lower wear rates.

Thresholds for detecting and characterizing focal lesions using steady-state MR elastography.

An objective contrast-detail analysis was performed in this study to assess the low contrast detectability of a clinical prototype harmonic magnetic resonance elastographic imaging system. Elastographic imaging was performed on gelatin phantoms containing spherical inclusions of varying size and modulus contrast. The results demonstrate that lesions as small as 5 mm can be detected with a minimum modulus contrast of 14 dB. However, the shear modulus of such small lesions was not accurately recovered. In general, the shear modulus of larger focal lesions was accurately (i.e., within 25% of the true value) recovered. The minimum modulus contrast needed to detect focal lesions was observed to decrease with increasing lesion size.

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.

Initial in vivo experience with steady-state subzone-based MR elastography of the human breast.

PURPOSE: To describe initial in vivo experiences with a subzone-based, steady-state MR elastography (MRE) method. This sparse collection of in vivo results is intended to shed light on some of the strengths and weaknesses of existing clinical MRE approaches and to indicate important areas of future research. MATERIALS AND METHODS: Elastic property reconstruction results are compared with data compiled from the limited existing body of published studies in breast elasticity. Mechanical parameter distributions are also investigated in terms of their implications for the nature of biological soft tissue. Additionally, a derivation of the statistical variance of the elastic parameter reconstruction is given and the resulting confidence intervals (CIs) for different parameter solutions are examined. RESULTS: By comparison with existing estimates of the elastic properties of breast tissue, the subzone-based, steady-state MRE method is seen to produce reasonable estimates for the mechanical properties of in vivo tissue. CONCLUSION: MRE shows potential as an effective way to determine the elastic properties of breast tissue, and may be of significant clinical interest.

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.

In vivo quantification of retraction deformation modeling for updated image-guidance during neurosurgery.

The use of coregistered preoperative anatomical scans to provide navigational information in the operating room has greatly benefited the field of neurosurgery. Nonetheless, it has been widely acknowledged that significant errors between the operating field and the preoperative images are generated as surgery progresses. Quantification of tissue shift can be accomplished with volumetric intraoperative imaging; however, more functional, lower cost alternative solutions to this challenge are desirable. We are developing the strategy of exploiting a computational model driven by sparse data obtained from intraoperative ultrasound and cortical surface tracking to warp preoperative images to reflect the current state of the operating field. This paper presents an initial quantification of the predictive capability of the current model to computationally capture tissue deformation during retraction in the porcine brain. Performance validation is achieved through comparisons of displacement and pressure predictions to experimental measurements obtained from computed tomographic images and pressure sensor recordings. Group results are based upon a generalized set of boundary conditions for four subjects that, on average, account for at least 75% of tissue motion generated during interhemispheric retraction. Individualized boundary conditions can improve the degree of data-model match by 10% or more but warrant further study. Overall, the level of quantitative agreement achieved in these experiments is encouraging for updating preoperative images to reflect tissue deformation resulting from retraction, especially since model improvements are likely as a result of the intraoperative constraints that can be applied through sparse data collection.

Model-Updated Image-Guided Neurosurgery: Preliminary Analysis Using Intraoperative MR.

In this paper, initial clinical data from an intraoperative MR system are compared to calculations made by a three-dimensional finite element model of brain deformation. The preoperative and intraoperative MR data was collected on a patient undergoing a resection of an astrocytoma, grade 3 with non-enhancing and enhancing regions. The image volumes were co-registered and cortical displacements as well as subsurface structure movements were measured retrospectively. These data were then compared to model predictions undergoing intraoperative conditions of gravity and simulated tumor decompression. Computed results demonstrate that gravity and decompression effects account for approximately 40% and 30%, respectively, totaling a 70% recovery of shifting structures with the model. The results also suggest that a non-uniform decompressive stress distribution may be present during tumor resection. Based on this preliminary experience, model predictions constrained by intraoperative surface data appear to be a promising avenue for correcting brain shift during surgery. However, additional clinical cases where volumetric intraoperative MR data is available are needed to improve the understanding of tissue mechanics during resection.

In Vivo Analysis of Heterogeneous Brain Deformation Computations for Model-Updated Image Guidance.

Neurosurgical image-guidance has historically relied on the registration of the patient and preoperative imaging series with surgical instruments in the operating room (OR) coordinate space. Recent studies measuring intraoperative tissue motion have suggested that deformation-induced misregistration from surgical loading is a serious concern with such systems. In an effort to improve registration fidelity during surgery, we are pursuing an approach which uses a predictive computational model in conjunction with data available in the OR to update the high resolution preoperative image series. In previous work, we have developed an in vivo experimental system in the porcine brain which has been used to investigate a homogeneous finite element rendering of consolidation theory as a tissue deformation model. In this paper, our computational approach has been extended to include heterogeneous tissue property distributions determined from an image-to-grid segmentation scheme. Results produced under two different loading conditions show that heterogeneity in the stiffness properties and interstitial pressure gradients varied over a range of physiologically reasonable values account for 1-3% and 5-8% of the predicted tissue motion, respectively, while homogeneous linear elasticity is responsible for 60-70% of the surgically-induced motion that has been recoverable with our model-based approach.