Structural finite deformation model of the left ventricle during diastole and systole

A model of left ventricular function is developed based on morphological characteristics of the myocardial tissue. The passive response of the three-dimensional collagen network and the active contribution of the muscle fibers are integrated to yield the overall response of the left ventricle which is considered to be a thick wall cylinder. The deformation field and the distributions of stress and pressure are determined at each point in the cardiac cycle by numerically solving three equations of equilibrium. Simulated results in terms of the ventricular deformation during ejection and isovolumic cycles are shown to be in good qualitative agreement with experimental data. It is shown that the collagen network in the heart has considerable effect on the pressure-volume loops. The particular pattern of spatial orientation of the collagen determines the ventricular recoil properties in early diastole. The material properties (myocardial stiffness and contractility) are shown to affect both the pressure-volume loop and the deformation pattern of the ventricle. The results indicate that microstructural consideration offer a realistic representation of the left ventricle mechanics.     

Determinants of the occurrence of vortex rings in the left ventricle during diastole

This study employs classical inviscid fluid dynamics theory to investigate whether LV diastolic inflow volume and the size of the LV play a role in vortex ring formation. Fluid injection across an orifice into a large container results in the generation of a vortex ring having a constant size and speed. Relations between the vortex size and speed and the injection were obtained by applying conservation laws regarding kinetic energy, impulse and vorticity; the initial state was computed using a bolus injection model, and the final state by using the Kelvin vortex model. An important parameter in the equations is the relative injection length, i.e., the ratio of the length of the injected bolus and the radius of the orifice (L/R). Its estimated highest value in man, L/R = 15, produces a rather thick vortex ring (relative thickness 0.77). Comparable results following from the Hill vortex model convinced us that the Kelvin vortex model can be applied in the whole range of injection lengths in the human left ventricle. In an in vitro model it is shown experimentally that vortex rings can be generated for L/R in the range from 2 to 16. The measured traveling speed of the vortex ring is in fair agreement with the theory, as well as the ring radius for large injections. A vortex ring located in a narrow channel cannot reach its proper traveling speed. The method of images is used to estimate the speed reduction of vortex rings within a cylinder. It turns out that propagation of vortex rings is possible when the ratio of orifice to cylinder radius is less than about 0.5.(ABSTRACT TRUNCATED AT 250 WORDS)     

An elongation model of left ventricle deformation in diastole

A numerical method of the left ventricle (LV) deformation, an elongation model, was put forth for the study of LV fluid mechanics in diastole. The LV elongated only along the apical axis, and the motion was controlled by the intraventricular flow rate. Two other LV models, a fixed control volume model and a dilation model, were also used for model comparison and the study of LV fluid mechanics. For clinical sphere indices (SIs, between 1.0 and 2.0), the three models showed little difference in pressure and velocity distributions along the apical axis at E-peak. The energy dissipation was lower at a larger SI in that the jet and vortex development was less limited by the LV cavity in the apical direction. LV deformation of apical elongation may represent the primary feature of LV deformation in comparison with the secondary radial expansion. The elongation model of the LV deformation with an appropriate SI is a reasonable, simple method to study LV fluid mechanics in diastole.     

A modified Holzapfel-Ogden law for a residually stressed finite strain model of the human left ventricle in diastole

In this work, we introduce a modified Holzapfel-Ogden hyperelastic constitutive model for ventricular myocardium that accounts for residual stresses, and we investigate the effects of residual stresses in diastole using a magnetic resonance imaging–derived model of the human left ventricle (LV). We adopt an invariant-based constitutive modelling approach and treat the left ventricular myocardium as a non-homogeneous, fibre-reinforced, incompressible material. Because in vivo images provide the configuration of the LV in a loaded state even in diastole, an inverse analysis is used to determine the corresponding unloaded reference configuration. The residual stress in this unloaded state is estimated by two different methods. One is based on three-dimensional strain measurements in a local region of the canine LV, and the other uses the opening angle method for a cylindrical tube. We find that including residual stress in the model changes the stress distributions across the myocardium and that whereas both methods yield qualitatively similar changes, there are quantitative differences between the two approaches. Although the effects of residual stresses are relatively small in diastole, the model can be extended to explore the full impact of residual stress on LV mechanical behaviour for the whole cardiac cycle as more experimental data become available. In addition, although not considered here, residual stresses may also play a larger role in models that account for tissue growth and remodelling.     

Fiber stress profiles in the left ventricle of the heart during diastole: Effects of distension and hypertrophy

Pressure-volume and volume-dimensions relationships, obtained from excised dog left ventricles were used for calculating the stresses acting along the longitudinal axis of the individual myocardial fibers. The calculations were based on a set of empirical and theoretical equations. The pressure-volume relationship as well as the volume-dimensions relationships for the excised left ventricle were expressed in the form of empirical equations; the fiber orientation was written as a function of the fiber location within the left ventricular wall; finally, the fiber stress was determined by means of theoretically derived formulas. Simultaneous solutions for the fibers of a meridian cut through the left ventricular myocardial shell were obtained by means of a digital computer and presented in the form of diagrams. The results showed that at low degrees of distension of the left ventricle there are two zones of higher stresses at the equatorial area, one near the epicardium and one near the endocardium. As the distension proceeds under the effect of progressively increasing intraventricular pressure, these two zones become less well defined, whereas a new zone of higher stresses appears near the apex. At high degrees of distension, the ventricle assumes a more spherical shape and the equatorial zones of higher stresses are replaced by zones of lower stresses. Increase in the myocardial mass results in appearance of the equatorial lower stress zones at lower degrees of distension.     

Dose warping performance in deformable image registration in lung

PurposeIt is unclear that spatial accuracy can reflect the impact of deformed dose distribution. In this study, we used dosimetric parameters to compare an in-house deformable image registration (DIR) system using NiftyReg, with two commercially available systems, MIM Maestro (MIM) and Velocity AI (Velocity).MethodsFor 19 non-small-cell lung cancer patients, the peak inspiration (0%)-4DCT images were deformed to the peak expiration (50%)-4DCT images using each of the three DIR systems, which included computation of the deformation vector fields (DVF). The 0%-gross tumor volume (GTV) and the 0%-dose distribution were also then deformed using the DVFs. The agreement in the dose distributions for the GTVs was evaluated using generalized equivalent uniform dose (gEUD), mean dose (D_mean), and three-dimensional (3D) gamma index (criteria: 3 mm/3%). Additionally, a Dice similarity coefficient (DSC) was used to measure the similarity of the GTV volumes.ResultsD_mean and gEUD demonstrated good agreement between the original and deformed dose distributions (differences were generally less than 3%) in 17 of the patients. In two other patients, the Velocity system resulted in differences in gEUD of 50.1% and 29.7% and in D_mean of 11.8% and 4.78%. The gamma index comparison showed statistically significant differences for the in-house DIR vs. MIM, and MIM vs. Velocity.ConclusionsThe finely tuned in-house DIR system could achieve similar spatial and dose accuracy to the commercial systems. Care must be taken, as we found errors of more than 5% for D_mean and 30% for gEUD, even with a commercially available DIR tool.     

Development of a dynamic deformable thorax phantom for the quality management of deformable image registration

The purpose of this study was to develop a novel dynamic deformable thorax phantom for deformable image registration (DIR) quality assurance (QA) and to verify as a tool for commissioning and DIR QA.The phantom consists of a base phantom, an inner phantom, and a motor-derived piston. The base phantom is an acrylic cylinder phantom with a diameter of 180 mm. The inner phantom consists of deformable, 20 mm thick disk-shaped sponges. To evaluate the physical characteristics of the phantom, we evaluated its image quality and deformation. DIR accuracies were evaluated using the three types of commercially DIR software (MIM, RayStation, and Velocity AI) to test the feasibility of this phantom. We used different DIR parameters to test the impact of parameters on DIR accuracy in various phantom settings. To evaluate DIR accuracy, a target registration error (TRE) was calculated using the anatomical landmark points.The three locations (i.e., distal, middle, and proximal positions) had different displacement amounts. This result indicated that the inner phantom was not moved but deformed. In cases with different phantom settings and marker settings, the ranges of the average TRE were 0.63–15.60 mm (MIM). In cases with different DIR parameters settings, the ranges of the average TRE were as follows: 0.73–7.10 mm (MIM), 8.25–8.66 mm (RayStation), and 8.26–8.43 mm (Velocity). These results suggest that our phantom could evaluate the detailed DIR behaviors with TRE. Therefore, this is indicative of the potential usefulness of our phantom in DIR commissioning and QA.     

Measurement of intracellular strain on deformable substrates with texture correlation

Mechanical stimuli are important factors that regulate cell proliferation, survival, metabolism and motility in a variety of cell types. The relationship between mechanical deformation of the extracellular matrix and intracellular deformation of cellular sub-regions and organelles has not been fully elucidated, but may provide new insight into the mechanisms involved in transducing mechanical stimuli to biological responses. In this study, a novel fluorescence microscopy and image analysis method was applied to examine the hypothesis that mechanical strains are fully transferred from a planar, deformable substrate to cytoplasmic and intranuclear regions within attached cells. Intracellular strains were measured in cells derived from the anulus fibrosus of the intervertebral disc when attached to an elastic silicone membrane that was subjected to tensile stretch. Measurements indicated cytoplasmic strains were similar to those of the underlying substrate, with a strain transfer ratio (STR) of 0.79. In contrast, nuclear strains were much smaller than those of the substrate, with an STR of 0.17. These findings are consistent with previous studies indicating nuclear stiffness is significantly greater than cytoplasmic stiffness, as measured using other methods. This study provides a novel method for the study of cellular mechanics, including a new technique for measuring intranuclear deformations, with evidence of differential magnitudes and patterns of strain transferred from the substrate to cell cytoplasm and nucleus.     

Commissioning and validation of commercial deformable image registration software for adaptive contouring

PurposeTo report the commissioning and validation of deformable image registration(DIR) software for adaptive contouring.MethodsDIR (SmartAdapt®v13.6) was validated using two methods namely contour propagation accuracy and landmark tracking, using physical phantoms and clinical images of various disease sites. Five in-house made phantoms with various known deformations and a set of 10 virtual phantoms were used. Displacement in lateral, anterio-posterior (AP) and superior-inferior (SI) direction were evaluated for various organs and compared with the ground truth. Four clinical sites namely, brain (n = 5), HN (n = 9), cervix (n = 18) and prostate (n = 23) were used. Organs were manually delineated by a radiation oncologist, compared with the deformable image registration (DIR) generated contours. 3D slicer v4.5.0.1 was used to analyze Dice Similarity Co-efficient (DSC), shift in centre of mass (COM) and Hausdorff distances Hf_95%/avg.ResultsMean (SD) DSC, Hf_95% (mm), Hf_avg (mm) and COM of all the phantoms 1–5 were 0.84 (0.2) mm, 5.1 (7.4) mm, 1.6 (2.2) mm, and 1.6 (0.2) mm respectively. Phantom-5 had the largest deformation as compared to phantoms 1–4, and hence had suboptimal indices. The virtual phantom resulted in consistent results for all the ROIs investigated. Contours propagated for brain patients were better with a high DSC score (0.91 (0.04)) as compared to other sites (HN: 0.84, prostate: 0.81 and cervix 0.77). A similar trend was seen in other indices too. The accuracy of propagated contours is limited for complex deformations that include large volume and shape change of bladder and rectum respectively. Visual validation of the propagated contours is recommended for clinical implementation.ConclusionThe DIR algorithm was commissioned and validated for adaptive contouring.     

Stress and strain adaptation in load-dependent remodeling of the embryonic left ventricle

Altered pressure in the developing left ventricle (LV) results in altered morphology and tissue material properties. Mechanical stress and strain may play a role in the regulating process. This study showed that confocal microscopy, three-dimensional reconstruction, and finite element analysis can provide a detailed model of stress and strain in the trabeculated embryonic heart. The method was used to test the hypothesis that end-diastolic strains are normalized after altered loading of the LV during the stages of trabecular compaction and chamber formation. Stage-29 chick LVs subjected to pressure overload and underload at stage 21 were reconstructed with full trabecular morphology from confocal images and analyzed with finite element techniques. Measured material properties and intraventricular pressures were specified in the models. The results show volume-weighted end-diastolic von Mises stress and strain averaging 50–82 % higher in the trabecular tissue than in the compact wall. The volume-weighted-average stresses for the entire LV were 115, 64, and 147 Pa in control, underloaded, and overloaded models, while strains were 11, 7, and 4 %; thus, neither was normalized in a volume-weighted sense. Localized epicardial strains at mid-longitudinal level were similar among the three groups and to strains measured from high-resolution ultrasound images. Sensitivity analysis showed changes in material properties are more significant than changes in geometry in the overloaded strain adaptation, although resulting stress was similar in both types of adaptation. These results emphasize the importance of appropriate metrics and the role of trabecular tissue in evaluating the evolution of stress and strain in relation to pressure-induced adaptation.     

A validation framework to assess performance of commercial deformable image registration in lung radiotherapy

IntroductionDeformable image registration (DIR) can play an important role in the context of adaptive radiotherapy. The AAPM Task Group 132 (TG-132) has described several quantitative measures for DIR error assessment but they can only be accurately defined when there is a ground-truth present in high-contrast regions. This work aims to set out a framework to obtain optimal results for CT-CT lung DIR in clinical setting for a commercially available system by quantifying the DIR performance in both low- and high-contrast regions.MethodsFive publicly available thorax datasets were used to assess the DIR quality. A “Ghost fiducial” method was implemented by windowing the contrast in a new feature provided by Varian Velocity v4.1. Target registration error (TRE) of the landmarks and Dice-similarity coefficient of the tumour were calculated at three different contrast settings to assess the algorithm in high- and low-contrast scenarios.ResultsFor the original unedited dataset, higher resolution DIR methods showed best performance acceptable within the recommended limit according to TG-132, when actual displacements were less than 10 mm. The relation of the actual displacement of the landmarks and TRE shows the limited capacity of the algorithm to deal with movements larger than 10 mm.ConclusionThis work found the performance of DIR methods and settings available in Varian Velocity v4.1 to be a function of contrast level as well as extent of motion. This highlights the need for multiple metrics to assess different aspects of DIR performance for various applications related to low-contrast and/or high-contrast regions.     

Validation of a deformable image registration produced by a commercial treatment planning system in head and neck

In recent years one of the areas of interest in radiotherapy has been adaptive radiation therapy (ART), with the most efficient way of performing ART being the use of deformable image registration (DIR). In this paper we use the distances between points of interest (POIs) in the computed tomography (CT) and the cone beam computed tomography (CBCT) acquisition images and the inverse consistence (IC) property to validate the RayStation treatment planning system (TPS) DIR algorithm. This study was divided into two parts: Firstly the distance-accuracy of the TPS DIR algorithm was ascertained by placing POIs on anatomical features in the CT and CBCT images from five head and neck cancer patients. Secondly, a method was developed for studying the implication of these distances on the dose by using the IC. This method compared the dose received by the structures in the CT, and the structures that were quadruply-deformed. The accuracy of the TPS was 1.7 ± 0.8 mm, and the distance obtained with the quadruply-deformed IC method was 1.7 ± 0.9 mm, i.e. the difference between the IC method multiplied by two, and that of the TPS validation method, was negligible. Moreover, the IC method shows very little variation in the dose-volume histograms when comparing the original and quadruply-deformed structures. This indicates that this algorithm is useful for planning adaptive radiation treatments using CBCT in head and neck cancer patients, although these variations must be taken into account when making a clinical decision to adapt a treatment plan.     

MRI-based strain and strain rate analysis of left ventricle: a modified hierarchical transformation model

Background

Different from other indicators of cardiac function, such as ejection fraction and transmitral early diastolic velocity, myocardial strain is promising to capture subtle alterations that result from early diseases of the myocardium. In order to extract the left ventricle (LV) myocardial strain and strain rate from cardiac cine-MRI, a modified hierarchical transformation model was proposed.

Methods

A hierarchical transformation model including the global and local LV deformations was employed to analyze the strain and strain rate of the left ventricle by cine-MRI image registration. The endocardial and epicardial contour information was introduced to enhance the registration accuracy by combining the original hierarchical algorithm with an Iterative Closest Points using Invariant Features algorithm. The hierarchical model was validated by a normal volunteer first and then applied to two clinical cases (i.e., the normal volunteer and a diabetic patient) to evaluate their respective function.

Results

Based on the two clinical cases, by comparing the displacement fields of two selected landmarks in the normal volunteer, the proposed method showed a better performance than the original or unmodified model. Meanwhile, the comparison of the radial strain between the volunteer and patient demonstrated their apparent functional difference.

Conclusions

The present method could be used to estimate the LV myocardial strain and strain rate during a cardiac cycle and thus to quantify the analysis of the LV motion function.

     

The utility of deformable image registration for small artery visualisation in contrast-enhanced whole body MR angiography

PurposeAn investigation was carried out into the effect of three image registration techniques on the diagnostic image quality of contrast-enhanced magnetic resonance angiography (CE-MRA) images.MethodsWhole-body CE-MRA data from the lower legs of 27 patients recruited onto a study of asymptomatic atherosclerosis were processed using three deformable image registration algorithms. The resultant diagnostic image quality was evaluated qualitatively in a clinical evaluation by four expert observers, and quantitatively by measuring contrast-to-noise ratios and volumes of blood vessels, and assessing the techniques' ability to correct for varying degrees of motion.ResultsThe first registration algorithm (‘AIR’) introduced significant stenosis-mimicking artefacts into the blood vessels' appearance, observed both qualitatively (clinical evaluation) and quantitatively (vessel volume measurements). The two other algorithms (‘Slicer’ and ‘SEMI’), based on the normalised mutual information (NMI) concept and designed specifically to deal with variations in signal intensity as found in contrast-enhanced image data, did not suffer from this serious issue but were rather found to significantly improve the diagnostic image quality both qualitatively and quantitatively, and demonstrated a significantly improved ability to deal with the common problem of patient motion.ConclusionsThis work highlights both the significant benefits to be gained through the use of suitable registration algorithms and the deleterious effects of an inappropriate choice of algorithm for contrast-enhanced MRI data. The maximum benefit was found in the lower legs, where the small arterial vessel diameters and propensity for leg movement during image acquisitions posed considerable problems in making accurate diagnoses from the un-registered images.     

Importance of material parameters and strain energy function on the wall stresses in the left ventricle

Patient-specific estimates of the stress distribution in the left ventricles (LV) may have important applications for therapy planning, but computing the stress generally requires knowledge of the material behaviour. The passive stress-strain relation of myocardial tissue has been characterized by a number of models, but material parameters (MPs) remain difficult to estimate. The aim of this study is to implement a zero-pressure algorithm to reconstruct numerically the stress distribution in the LV without precise knowledge of MPs. We investigate the sensitivity of the stress distribution to variations in the different sets of constitutive parameters. We show that the sensitivity of the LV stresses to MPs can be marginal for an isotropic constitutive model. However, when using a transversely isotropic exponential strain energy function, the LV stresses become sensitive to MPs, especially to the linear elastic coefficient before the exponential function. This indicates that in-vivo identification efforts should focus mostly on this MP for the development of patient-specific finite-element analysis.     

A quantitative evaluation of deformable image registration based on MV cone beam CT images: Impact of deformation magnitudes and image modalities

Background and purposeTo evaluate the impact of deformation magnitude and image modality on deformable-image-registration (DIR) accuracy using Halcyon megavoltage cone beam CT images (MVCBCT).Materials and methodsPlanning CT images of an anthropomorphic Head phantom were aligned rigidly with MVCBCT and re-sampled to achieve the same resolution, denoted as pCT. MVCBCT was warped with twenty simulated pre-known virtual deformation fields (T_i, i = 1–20) with increasing deformation magnitudes, yielding warped CBCT (wCBCT). The pCT and MVCBCT were registered to wCBCT respectively (Multi-modality and Uni-modality DIR), generating deformation vector fields V_i and V_i′ (i = 1–20). V_i and V_i′ were compared with T_i respectively to assess the DIR accuracy geometrically. In addition, V_i, T_i, and V_i′ were applied to pCT, generating deformed CT (dCT_i), ground-truth CT (G_i) and deformed CT′ (dCT_i′) respectively. The Hounsfield Unit (HU) on these virtual CT images were also compared.ResultsThe mean errors of vector displacement increased with the deformation magnitude. For deformation magnitudes between 2.82 mm and 7.71 mm, the errors of uni-modality DIR were 1.16 mm ~ 1.73 mm smaller than that of multi-modality (p = 0.0001, Wilcoxon signed rank test). DIR could reduce the maximum signed and absolute HU deviations from 70.8 HU to 11.4 HU and 208 HU to 46.2 HU respectively.ConclusionsAs deformation magnitude increases, DIR accuracy continues to deteriorate and uni-modality DIR consistently outperformed multi-modality DIR. DIR-based adaptive radiotherapy utilizing the noisy MVCBCT images is only conditionally applicable with caution.