Hierarchical Motion Estimation With Bayesian Regularization in Cardiac Elastography: Simulation and In Vivo Validation

Development of a Predictive Statistical Pharmacological Model for Local Anesthetic Agent Effects with Bayesian Hierarchical Model Parameter Estimation

As an alternative to animal use, computer simulations are useful for predicting pharmacokinetics and cardiovascular activities. For this purpose, we constructed a statistical model to simulate the effects of local anesthetic agents. To train the model, animal experiments were performed on 6-week-old male Hartley guinea pigs. Firstly, the guinea pigs' backs were shaved, then local anesthetic agents were subcutaneously injected, with subsequent stimulation of the anesthetized site with a needle six times at regular intervals. The number of reactions (score value) was counted. In this statistical model, the probability of reacting to needle stimulation was calculated using the elapsed time, type of local anesthetic agent, and presence or absence of adrenaline. Score values were assumed to follow a binomial distribution at the calculated probability. Parameters were estimated using the Bayesian hierarchical model and Hamiltonian Monte Carlo method. The predicted curves using the estimated parameters fitted well the observed animal values. When score values were predicted using randomly generated parameters, the median of duration was similar between animal experiments and simulations (Procaine: 55 min vs. 50 min, Lidocaine: both 60 min, and Mepivacaine: both 85 min). This approach effectively modeled the effects of local anesthetic agents. It is possible to create the simulator using the parameter values estimated in this study.

In Vivo Adaptive Bayesian Regularized Lagrangian Carotid Strain Imaging for Murine Carotid Arteries and Its Associations With Histological Findings

OBJECTIVES

Non-invasive methods for monitoring arterial health and identifying early injury to optimize treatment for patients are desirable. The objective of this study was to demonstrate the use of an adaptive Bayesian regularized Lagrangian carotid strain imaging (ABR-LCSI) algorithm for monitoring of atherogenesis in a murine model and examine associations between the ultrasound strain measures and histology.

METHODS

Ultrasound radiofrequency (RF) data were acquired from both the right and left common carotid artery (CCA) of 10 (5 male and 5 female) ApoE tm1Unc/J mice at 6, 16 and 24 wk. Lagrangian accumulated axial, lateral and shear strain images and three strain indices-maximum accumulated strain index (MASI), peak mean strain of full region of interest (ROI) index (PMSRI) and strain at peak axial displacement index (SPADI)-were estimated using the ABR-LCSI algorithm. Mice were euthanized (n = 2 at 6 and 16 wk, n = 6 at 24 wk) for histology examination.

RESULTS

Sex-specific differences in strain indices of mice at 6, 16 and 24 wk were observed. For male mice, axial PMSRI and SPADI changed significantly from 6 to 24 wk (mean axial PMSRI at 6 wk = 14.10 ± 5.33% and that at 24 wk = -3.03 ± 5.61%, p < 0.001). For female mice, lateral MASI increased significantly from 6 to 24 wk (mean lateral MASI at 6 wk = 10.26 ± 3.13% and that at 24 wk = 16.42 ± 7.15%, p = 0.048). Both cohorts exhibited strong associations with ex vivo histological findings (male mice: correlation between number of elastin fibers and axial PMSRI: rs = 0.83, p = 0.01; female mice: correlation between shear MASI and plaque score: rs = 0.77, p = 0.009).

CONCLUSION

The results indicate that ABR-LCSI can be used to measure arterial wall strain in a murine model and that changes in strain are associated with changes in arterial wall structure and plaque formation.

Preliminary Feasibility of Stress Myocardial Elastography for the Detection of Coronary Artery Disease

Myocardial elastography (ME) is a cardiac strain imaging technique that has been found capable of detecting a decrease in radial strain caused by ischemia or infarction in patients with coronary artery disease (CAD) as well as in a canine model. Prior studies have focused on rest imaging, but stress testing can reveal functional deficits caused by stenoses that are asymptomatic at rest. Therefore, it has been proposed that stress ME (S-ME) improves the detection of CAD. A novel strain difference (Δε) metric is presented and investigated in a canine model of induced ischemia, as well as in a study in human patients with CAD validated by myocardial perfusion imaging. In the canine model study, flow-limiting stenosis was induced by partial ligation in n = 2 canines, and stenosis was found to consistently reduce Δε in the affected myocardial regions compared with baseline, as well as compared to myocardial regions that are remote to the induced stenosis. In the clinical study, the median Δε was significantly lower (p < 0.05) in infarcted myocardial regions (-6.29%) than in those with normal perfusion (4.62%), with Δε in ischemic regions falling in between (-2.91%). The same trend was observed when considering radial strain during stress and, to a lesser degree, at rest alone. The results indicate that S-ME may be more sensitive to mild cases of CAD that are functionally asymptomatic at rest.

In Vivo Longitudinal Monitoring of Cardiac Remodeling in Murine Ischemia Models With Adaptive Bayesian Regularized Cardiac Strain Imaging: Validation Against Histology

Adaptive Bayesian regularized cardiac strain imaging (ABR-CSI) uses raw radiofrequency signals to estimate myocardial wall contractility as a surrogate measure of relative tissue elasticity incorporating regularization in the Bayesian sense. We determined the feasibility of using ABR-CSI -derived strain for in vivo longitudinal monitoring of cardiac remodeling in a murine ischemic injury model (myocardial infarction [MI] and ischemia-reperfusion [IR]) and validated the findings against ground truth histology. We randomly stratified 30 BALB/CJ mice (17 females, 13 males, median age = 10 wk) into three surgical groups (MI = 10, IR = 12, sham = 8) and imaged pre-surgery (baseline) and 1, 2, 7 and 14 d post-surgery using a pre-clinical high-frequency ultrasound system (VisualSonics Vevo 2100). We then used ABR-CSI to estimate end-systolic and peak radial (er) and longitudinal (el) strain estimates. ABR-CSI was found to have the ability to serially monitor non-uniform cardiac remodeling associated with murine MI and IR non-invasively through temporal variation of strain estimates post-surgery. Furthermore, radial end-systole (ES) strain images and segmental strain curves exhibited improved discrimination among infarct, border and remote regions around the myocardium compared with longitudinal strain results. For example, the MI group had significantly lower (Friedman's with Bonferroni-Dunn test, p = 0.002) ES er values in the anterior middle (infarcted) region at day 14 (n = 9, 9.23 ± 7.39%) compared with the BL group (n = 9, 44.32 ± 5.49). In contrast, anterior basal (remote region) mean ES er values did not differ significantly (non-significant Friedman's test, χ2 = 8.93, p = 0.06) at day 14 (n = 6, 33.05 ± 6.99%) compared with baseline (n = 6, 34.02 ± 6.75%). Histology slides stained with Masson's trichrome (MT) together with a machine learning model (random forest classifier) were used to derive the ground truth cardiac fibrosis parameter termed histology percentage of myocardial fibrosis (PMF). Both radial and longitudinal strain were found to have strong statistically significant correlations with the PMF parameter. However, radial strain had a higher Spearman's correlation value (εresρ = -0.67, n = 172, p < 0.001) compared with longitudinal strain (εlesρ = -0.60, n = 172, p < 0.001). Overall, the results of this study indicate that ABR-CSI can reliably perform non-invasive detection of infarcted and remote myocardium in small animal studies.

Murine cardiac fibrosis localization using adaptive Bayesian cardiac strain imaging in vivo

An adaptive Bayesian regularized cardiac strain imaging (ABR-CSI) algorithm for in vivo murine myocardial function assessment is presented. We report on 31 BALB/CJ mice (n = 17 females, n = 14 males), randomly stratified into three surgical groups: myocardial infarction (MI, n = 10), ischemia–reperfusion (IR, n = 13) and control (sham, n = 8) imaged pre-surgery (baseline- BL), and 1, 2, 7 and 14 days post-surgery using a high frequency ultrasound imaging system (Vevo 2100). End-systole (ES) radial and longitudinal strain images were used to generate cardiac fibrosis maps using binary thresholding. Percentage fibrotic myocardium (PFM) computed from regional fibrosis maps demonstrated statistically significant differences post-surgery in scar regions. For example, the MI group had significantly higher PFM_Radial (%) values in the anterior mid region (p = 0.006) at Day 14 (n = 8, 42.30 ± 14.57) compared to BL (n = 12, 1.32 ± 0.85). A random forest classifier automatically detected fibrotic regions from ground truth Masson’s trichrome stained histopathology whole slide images. Both PFM_Radial (r = 0.70) and PFM_Longitudinal (r = 0.60) results demonstrated strong, positive correlation with PFM_{Histopathology} (p < 0.001).

Spatiotemporal Bayesian Regularization for Cardiac Strain Imaging: Simulation and In Vivo Results

Cardiac strain imaging (CSI) plays a critical role in the detection of myocardial motion abnormalities. Displacement estimation is an important processing step to ensure the accuracy and precision of derived strain tensors. In this paper, we propose and implement Spatiotemporal Bayesian regularization (STBR) algorithms for two-dimensional (2-D) normalized cross-correlation (NCC) based multi-level block matching along with incorporation into a Lagrangian cardiac strain estimation framework. Assuming smooth temporal variation over a short span of time, the proposed STBR algorithm performs displacement estimation using at least four consecutive ultrasound radio-frequency (RF) frames by iteratively regularizing 2-D NCC matrices using information from a local spatiotemporal neighborhood in a Bayesian sense. Two STBR schemes are proposed to construct Bayesian likelihood functions termed as Spatial then Temporal Bayesian (STBR-1) and simultaneous Spatiotemporal Bayesian (STBR-2). Radial and longitudinal strain estimated from a finite-element-analysis (FEA) model of realistic canine myocardial deformation were utilized to quantify strain bias, normalized strain error and total temporal relative error (TTR). Statistical analysis with one-way analysis of variance (ANOVA) showed that all Bayesian regularization methods significantly outperform NCC with lower bias and errors (p < 0.001). However, there was no significant difference among Bayesian methods. For example, mean longitudinal TTR for NCC, SBR, STBR-1 and STBR-2 were 25.41%, 9.27%, 10.38% and 10.13% respectively An in vivo feasibility study using RF data from ten healthy mice hearts were used to compare the elastographic signal-to-noise ratio (SNR_e) calculated using stochastic analysis. STBR-2 had the highest expected SNR_e both for radial and longitudinal strain. The mean expected SNR_e values for accumulated radial strain for NCC, SBR, STBR-1 and STBR-2 were 5.03, 9.43, 9.42 and 10.58, respectively. Overall results suggest that STBR improves CSI in vivo.

Bayesian Regularized Strain Imaging for Assessment of Murine Cardiac Function In vivo

A cardiac strain imaging framework with adaptive Bayesian regularization (ABR) is proposed for in vivo assessment of murine cardiac function. The framework uses ultrasound (US) radio-frequency data collected with a high frequency (f_c = 30MHz) imaging system and a multi-level block matching algorithm with ABR to derive inter-frame cardiac displacements. Lagrangian cardiac strain (radial, e_r and longitudinal, e_l) tensors were derived by segmenting the myocardial wall starting at the ECG R-wave and accumulating interframe deformations over a cardiac cycle. In vivo feasibility was investigated through a longitudinal study with two mice (one ischemia-perfusion (IR) injury and one sham) imaged at five sessions (pre-surgery (BL) and 1,2,7 and 14 days post-surgery). End-systole (ES) strain images and segmental strain curves were derived for quantitative evaluation. Both mice showed periodic variation of e_r and e_l strain at BL with segmental synchroneity. Infarcted regions of IR mouse at Day 14 were associated with reduced or sign reversed ES e_r and e_l values while the sham mouse had similar or higher strain than at BL. Infarcted regions identified in vivo were associated with increased collagen content confirmed with Masson's Trichrome stained ex vivo heart sections.Clinical Relevance-Higher quality cardiac strain images derived with RF data and Bayesian regularization can potentially improve the sensitivity and accuracy of non-invasive assessment of cardiovascular disease models.

Subaperture Processing-Based Adaptive Beamforming for Photoacoustic Imaging

Delay-and-sum (DAS) beamformers, when applied to photoacoustic (PA) image reconstruction, produce strong sidelobes due to the absence of transmit focusing. Consequently, DAS PA images are often severely degraded by strong off-axis clutter. For preclinical in vivo cardiac PA imaging, the presence of these noise artifacts hampers the detectability and interpretation of PA signals from the myocardial wall, crucial for studying blood-dominated cardiac pathological information and to complement functional information derived from ultrasound imaging. In this article, we present PA subaperture processing (PSAP), an adaptive beamforming method, to mitigate these image degrading effects. In PSAP, a pair of DAS reconstructed images is formed by splitting the received channel data into two complementary nonoverlapping subapertures. Then, a weighting matrix is derived by analyzing the correlation between subaperture beamformed images and multiplied with the full-aperture DAS PA image to reduce sidelobes and incoherent clutter. We validated PSAP using numerical simulation studies using point target, diffuse inclusion and microvasculature imaging, and in vivo feasibility studies on five healthy murine models. Qualitative and quantitative analysis demonstrate improvements in PAI image quality with PSAP compared to DAS and coherence factor weighted DAS (DAS _CF ). PSAP demonstrated improved target detectability with a higher generalized contrast-to-noise (gCNR) ratio in vasculature simulations where PSAP produces 19.61% and 19.53% higher gCNRs than DAS and DAS _CF , respectively. Furthermore, PSAP provided higher image contrast quantified using contrast ratio (CR) (e.g., PSAP produces 89.26% and 11.90% higher CR than DAS and DAS _CF in vasculature simulations) and improved clutter suppression.

Incorporating Multiple Observations in global Ultrasound Elastography

In this paper, we propose a novel framework for time delay estimation in ultrasound elastography. In the presence of high acquisition noise, the state-of-the-art motion tracking techniques suffer from inaccurate estimation of displacement field. To resolve this issue, instead of one, we collect several ultrasound Radio-Frequency (RF) frames from both pre- and post-deformed scan planes to better investigate the data statistics. We formulate a non-linear cost function incorporating all observation frames from both levels of deformations. Beside data similarity, we impose axial and lateral continuity to exploit the prior information of spatial coherence. Most importantly, we consider the continuity among the displacement estimates obtained from different observation RF frames. This novel continuity constraint mainly contributes to the robustness of the proposed technique to high noise power. We efficiently optimize the aforementioned cost function to derive a sparse system of linear equations where we solve for millions of variables to estimate the displacement of all samples of all of the incorporated RF frames simultaneously. We call the proposed algorithm GLobal Ultrasound Elastography using multiple observations (mGLUE). Our primary validation of mGLUE against soft and hard inclusion simulation phantoms proves that mGLUE is capable of obtaining high quality strain map while dealing with noisy ultrasound data. In case of the soft inclusion phantom, Signal-to-Noise Ratio (SNR) and Contrast-to-Noise Ratio (CNR) have improved by 75.37% and 57.08%, respectively. In addition, SNR and CNR improvements of 32.19% and 38.57% have been observed for the hard inclusion case.

Improving Ultrasound Lateral Strain Estimation Accuracy using Log Compression of Regularized Correlation Function

Normalized cross-correlation (NCC) function used in ultrasound strain imaging can get corrupted due to signal decorrelation inducing large displacement errors. Bayesian regularization has been applied in an iterative manner to regularize the NCC function and to reduce estimation variance and peak-hopping errors. However, incorrect choice of the number of iterations can lead to over-regularization errors. In this paper, we propose the use of log compression of regularized NCC function to improve subsample estimation. Performance of parabolic interpolation before and after log compression of the regularized NCC function were compared in numerical simulations of uniform and inclusion phantoms. Significant improvement was achieved with the proposed scheme for lateral estimation results. For example, lateral signal-to-noise ratio (SNR) was 10 dB higher after log compression at 3% strain in a uniform phantom. Lateral contrast-to-noise ratio (CNR) was 1.81 dB higher with proposed method at 3% strain in inclusion phantom. No significant difference was observed in axial estimation due to presence of phase information and high sampling frequency. Our results suggest that this simple approach makes Bayesian regularization robust to over-regularization artifacts.

Locally optimized correlation-guided Bayesian adaptive regularization for ultrasound strain imaging

Ultrasound strain imaging utilizes radio-frequency (RF) ultrasound echo signals to estimate the relative elasticity of tissue under deformation. Due to the diagnostic value inherent in tissue elasticity, ultrasound strain imaging has found widespread clinical and preclinical applications. Accurate displacement estimation using pre and post-deformation RF signals is a crucial first step to derive high quality strain tensor images. Incorporating regularization into the displacement estimation framework is a commonly employed strategy to improve estimation accuracy and precision. In this work, we propose an adaptive variation of the iterative Bayesian regularization scheme utilizing RF similarity metric signal-to-noise ratio previously proposed by our group. The regularization scheme is incorporated into a 2D multi-level block matching (BM) algorithm for motion estimation. Adaptive nature of our algorithm is attributed to the dynamic variation of iteration number based on the normalized cross-correlation (NCC) function quality and a similarity measure between pre-deformation and motion compensated post-deformation RF signals. The proposed method is validated for either quasi-static and cardiac elastography or strain imaging applications using uniform and inclusion phantoms and canine cardiac deformation simulation models. Performance of adaptive Bayesian regularization was compared to conventional NCC and Bayesian regularization with fixed number of iterations. Results from uniform phantom simulation study show significant improvement in lateral displacement and strain estimation accuracy. For instance, at 1.5% lateral strain in a uniform phantom, Bayesian regularization with five iterations incurred a lateral strain error of 104.49%, which was significantly reduced using our adaptive approach to 27.51% (p   <  0.001). Contrast-to-noise (CNR _e ) ratios obtained from inclusion phantom indicate improved lesion detectability for both axial and lateral strain images. For instance, at 1.5% lateral strain, Bayesian regularization with five iterations had lateral CNR _e of  -0.31 dB which was significantly increased using the adaptive approach to 7.42 dB (p   <  0.001). Similar results are seen with cardiac deformation modelling with improvement in myocardial strain images. In vivo feasibility was also demonstrated using data from a healthy murine heart. Overall, the proposed method makes Bayesian regularization robust for clinical and preclinical applications.