Regional localisation of left ventricular sheet structure: integration with current models of cardiac fibre, sheet and band structure

Normal cardiac dimensions by magnetic resonance imaging and topographic anatomy of the adult arabian one-humped camel (Camelus dromedarius)

BACKGROUND

Dromedaries' normal heart architecture and size have not been adequately examined utilizing magnetic resonance imaging (MRI) and topographic anatomy.

RESULT

we aimed to investigate the regular appearance of the heart and its dimensions, using MRI and cross-sectional anatomy, in mature Arabian one-humped camels (Camelus dromedarius). We also analyzed hematological and cardiac biochemical markers. MRI scans were conducted on twelve camel heart cadavers using a closed 1.5-Tesla magnet with fast spin echo (FSE) weighted sequences. Subsequently, the hearts were cross-sectionally sliced. Additionally, hematobiochemical studies were conducted on ten mature live camels. The study analyzed standard cardiac dimensions including HL, BW, RA, LA, RV, LV, IVS, LAD, RAD, RVD, AoD, TCVD, and MVD. The results showed a strong positive correlation between the cardiac dimensions obtained from both gross analysis and MR images, with no significant difference between them. On both gross and MRI images, the usual structures of the heart were identified and labeled. Along with the cardiac markers (creatine kinase and troponin), the average hematological values and standard biochemical parameters were also described.

CONCLUSION

According to what we know, this investigation demonstrates, for the first time the typical heart structures and dimensions of the heart in dromedaries, and it could serve as a basis for diagnosing cardiac disorders in these animals.

Influence of Power-Weighted Center of Echo Signal Within Window Function on Local Strain Rate Distribution in Left Ventricular Wall

OBJECTIVE

The deviation of the power-weighted center of the echo signal from the geometric center within the velocity estimation window for calculating strain rate (SR) causes an estimation error. This study aimed to confirm whether an erroneous multilayer pattern in the SR distribution of the left ventricular wall could be corrected by considering the power-weighted center of the echo signal.

METHODS

The SR distributions were measured locally in the transmural direction around the pre-ejection and early diastolic phases in healthy volunteers. The estimation error related to the power-weighted center of the echo signal was corrected using a previously proposed method, and the effectiveness of the correction was confirmed based on the accuracy of the estimated myocardial displacement.

RESULTS

The SR distribution in early diastole was observed as multilayers of low- and high-amplitude negative SRs. However, this multilayer pattern disappeared after correction. In the pre-ejection phase, multilayers of positive and negative SRs were observed in the SR distributions with and without correction. This correction was sufficiently effective in accurately tracking the local peak of the echo signal.

CONCLUSION

The multilayer pattern of low- and high-amplitude positive or negative SRs is caused by estimation errors related to the power-weighted center of the echo signal. The multilayer pattern of positive and negative SRs might not be caused by these errors and might relate to the actual change in myocardial thickness because the estimation errors do not convert the negative (positive) SR to positive (negative) in a homogeneous negative (positive) SR distribution.

Optimal assist strategy exploration for a direct assist device under stress‒strain dynamics

OBJECTIVES

The aim of this paper is to introduce a new assist strategy for a direct assist device that can enhance the heart's pumping efficiency and decrease the chances of myocardial injury in contrast to the conventional assist strategy.

METHODS

We established a finite element model of a biventricular heart, divided the ventricles into several regions, and applied pressure to each region separately in order to identify the primary and secondary assist areas. Then combined and tested these areas to obtain the optimal assist strategy.

RESULTS

The results indicate that our method exhibits an assist efficiency approximately ten times higher than that of the traditional assist method. Additionally, the stress distribution in the ventricles is more uniform after assistance.

CONCLUSIONS

In summary, this approach can result in a more homogenous stress distribution within the heart while also minimizing the contact area with it, which can reduce the incidence of allergic reactions and the likelihood of myocardial injury.

Cardiomyocyte orientation recovery at micrometer scale reveals long-axis fiber continuum in heart walls

Coordinated cardiomyocyte contraction drives the mammalian heart to beat and circulate blood. No consensus model of cardiomyocyte geometrical arrangement exists, due to the limited spatial resolution of whole heart imaging methods and the piecemeal nature of studies based on histological sections. By combining microscopy and computer vision, we produced the first-ever three-dimensional cardiomyocyte orientation reconstruction across mouse ventricular walls at the micrometer scale, representing a gain of three orders of magnitude in spatial resolution. We recovered a cardiomyocyte arrangement aligned to the long-axis direction of the outer ventricular walls. This cellular network lies in a thin shell and forms a continuum with longitudinally arranged cardiomyocytes in the inner walls, with a complex geometry at the apex. Our reconstruction methods can be applied at fine spatial scales to further understanding of heart wall electrical function and mechanics, and set the stage for the study of micron-scale fiber remodeling in heart disease.

Physical model of end-diastolic and end-systolic pressure-volume relationships of a heart

Left ventricular stiffness and contractility, characterized by the end-diastolic pressure-volume relationship (EDPVR) and the end-systolic pressure-volume relationship (ESPVR), are two important indicators of the performance of the human heart. Although much research has been conducted on EDPVR and ESPVR, no model with physically interpretable parameters combining both relationships has been presented, thereby impairing the understanding of cardiac physiology and pathology. Here, we present a model that evaluates both EDPVR and ESPVR with physical interpretations of the parameters in a unified framework. Our physics-based model fits the available experimental data and in silico results very well and outperforms existing models. With prescribed parameters, the new model is used to predict the pressure-volume relationships of the left ventricle. Our model provides a deeper understanding of cardiac mechanics and thus will have applications in cardiac research and clinical medicine.

Oscillation of the orientation of cardiomyocyte aggregates in human left ventricle free wall

Orientation of local cardiomyocyte aggregates in the human left ventricle free wall experiences an oscillation in the laminar structure regions, besides its gradual change trend. We described this oscillation using five transmural samples imaged at the European Synchrotron Radiation Facility with an isotropic voxel size of 3.5 × 3.5 × 3.5 μm³ . In the reconstructed volume of each sample, we manually selected a region containing a regular laminar structure as the region of interest and measured the distribution of the orientation of local cardiomyocyte aggregates inside using a Fourier-based method. Then, we extracted the gradual change part of the orientation of cardiomyocyte aggregates with a three-dimensional centered Gaussian filter and measured the angle between the original orientation vector of local cardiomyocyte aggregates and its gradual change part. Further, we assessed the measured angles in different local coordinates. The results indicate that the oscillation amplitude of the orientation of cardiomyocyte aggregates is regional in the left ventricle wall, which may promote our understanding of the rearrangement mechanism of the cardiomyocyte aggregates and provide a new biomarker to study the heart physiological status.

Geometry Does Impact on the Plane Strain Directions of the Human Left Ventricle, Irrespective of Disease

The directions of primary strain lines of local deformation in Epicardial and Endocardial layers have been the subject of debate in recent years. Different methods led to different conclusions and a complete assessment of strain direction patterns in large and variable (in terms of pathology) cohorts of healthy and diseased patients is still lacking. Here, we use local deformation tensors in order to evaluate the angle of strain lines with respect to the horizontal circumferential direction in both Epi- and Endo-layers. We evaluated this on a large group of 193 subjects including 82 healthy control and 111 patients belonging to a great variety of pathological conditions. We found that Epicardial strain lines obliquely directed while those of Endocardium are almost circumferential. This result occurs irrespective of pathological condition. We propose that the geometric vinculum characterizing Endocardium and Epicardium in terms of different lever arm length and orientation of muscular fibers during contraction inescapably requires Endocardial strain lines to be circumferentially oriented and this is corroborated by experimental results. Further investigations on transmural structure of myocytes could couple results presented here in order to furnish additional experimental explanations.

The basic heart anatomy and physiology from the cardiologist's perspective: Toward a better understanding of left ventricular mechanics, systolic, and diastolic function

A comprehensive understanding of the cardiac structure-function relationship is essential for proper clinical cardiac imaging. This review summarizes the basic heart anatomy and physiology from the perspective of a heart imager focused on myocardial mechanics. The main issues analyzed are the left ventricular (LV) architecture, the LV myocardial deformation through the cardiac cycle, the LV diastolic function basic parameters and the basic parameters of the LV deformation used in clinical practice for the LV function assessment.

Myocardial mesostructure and mesofunction

The complex and highly organized structural arrangement of some five billion cardiomyocytes directs the coordinated electrical activity and mechanical contraction of the human heart. The characteristic transmural change in cardiomyocyte orientation underlies base-to-apex shortening, circumferential shortening, and left ventricular torsion during contraction. Individual cardiomyocytes shorten ∼15% and increase in diameter ∼8%. Remarkably, however, the left ventricular wall thickens by up to 30-40%. To accommodate this, the myocardium must undergo significant structural rearrangement during contraction. At the mesoscale, collections of cardiomyocytes are organized into sheetlets, and sheetlet shear is the fundamental mechanism of rearrangement that produces wall thickening. Herein, we review the histological and physiological studies of myocardial mesostructure that have established the sheetlet shear model of wall thickening. Recent developments in tissue clearing techniques allow for imaging of whole hearts at the cellular scale, whereas magnetic resonance imaging (MRI) and computed tomography (CT) can image the myocardium at the mesoscale (100 µm to 1 mm) to resolve cardiomyocyte orientation and organization. Through histology, cardiac diffusion tensor imaging (DTI), and other modalities, mesostructural sheetlets have been confirmed in both animal and human hearts. Recent in vivo cardiac DTI methods have measured reorientation of sheetlets during the cardiac cycle. We also examine the role of pathological cardiac remodeling on sheetlet organization and reorientation, and the impact this has on ventricular function and dysfunction. We also review the unresolved mesostructural questions and challenges that may direct future work in the field.

Comparison of interpolation methods of predominant cardiomyocyte orientation from in vivo and ex vivo cardiac diffusion tensor imaging data

Cardiac electrophysiology and cardiac mechanics both depend on the average cardiomyocyte long-axis orientation. In the realm of personalized medicine, knowledge of the patient-specific changes in cardiac microstructure plays a crucial role. Patient-specific computational modelling has emerged as a tool to better understand disease progression. In vivo cardiac diffusion tensor imaging (cDTI) is a vital tool to non-destructively measure the average cardiomyocyte long-axis orientation in the heart. However, cDTI suffers from long scan times, rendering volumetric, high-resolution acquisitions challenging. Consequently, interpolation techniques are needed to populate bio-mechanical models with patient-specific average cardiomyocyte long-axis orientations. In this work, we compare five interpolation techniques applied to in vivo and ex vivo porcine input data. We compare two tensor interpolation approaches, one rule-based approximation, and two data-driven, low-rank models. We demonstrate the advantage of tensor interpolation techniques, resulting in lower interpolation errors than do low-rank models and rule-based methods adapted to cDTI data. In an ex vivo comparison, we study the influence of three imaging parameters that can be traded off against acquisition time: in-plane resolution, signal to noise ratio, and number of acquired short-axis imaging slices.

Personalization of biomechanical simulations of the left ventricle by in-vivo cardiac DTI data: Impact of fiber interpolation methods

Simulations of cardiac electrophysiology and mechanics have been reported to be sensitive to the microstructural anisotropy of the myocardium. Consequently, a personalized representation of cardiac microstructure is a crucial component of accurate, personalized cardiac biomechanical models. In-vivo cardiac Diffusion Tensor Imaging (cDTI) is a non-invasive magnetic resonance imaging technique capable of probing the heart's microstructure. Being a rather novel technique, issues such as low resolution, signal-to noise ratio, and spatial coverage are currently limiting factors. We outline four interpolation techniques with varying degrees of data fidelity, different amounts of smoothing strength, and varying representation error to bridge the gap between the sparse in-vivo data and the model, requiring a 3D representation of microstructure across the myocardium. We provide a workflow to incorporate in-vivo myofiber orientation into a left ventricular model and demonstrate that personalized modelling based on fiber orientations from in-vivo cDTI data is feasible. The interpolation error is correlated with a trend in personalized parameters and simulated physiological parameters, strains, and ventricular twist. This trend in simulation results is consistent across material parameter settings and therefore corresponds to a bias introduced by the interpolation method. This study suggests that using a tensor interpolation approach to personalize microstructure with in-vivo cDTI data, reduces the fiber uncertainty and thereby the bias in the simulation results.

A 3D personalized cardiac myocyte aggregate orientation model using MRI data-driven low-rank basis functions

Cardiac myocyte aggregate orientation has a strong impact on cardiac electrophysiology and mechanics. Studying the link between structural characteristics, strain, and stresses over the cardiac cycle and cardiac function requires a full volumetric representation of the microstructure. In this work, we exploit the structural similarity across hearts to extract a low-rank representation of predominant myocyte orientation in the left ventricle from high-resolution magnetic resonance ex-vivo cardiac diffusion tensor imaging (cDTI) in porcine hearts. We compared two reduction methods, Proper Generalized Decomposition combined with Singular Value Decomposition and Proper Orthogonal Decomposition. We demonstrate the existence of a general set of basis functions of aggregated myocyte orientation which defines a data-driven, personalizable, parametric model featuring higher flexibility than existing atlas and rule-based approaches. A more detailed representation of microstructure matching the available patient data can improve the accuracy of personalized computational models. Additionally, we approximate the myocyte orientation of one ex-vivo human heart and demonstrate the feasibility of transferring the basis functions to humans.

The Future of Direct Cardiac Reprogramming: Any GMT Cocktail Variety?

Direct cardiac reprogramming has emerged as a novel therapeutic approach to treat and regenerate injured hearts through the direct conversion of fibroblasts into cardiac cells. Most studies have focused on the reprogramming of fibroblasts into induced cardiomyocytes (iCMs). The first study in which this technology was described, showed that at least a combination of three transcription factors, GATA4, MEF2C and TBX5 (GMT cocktail), was required for the reprogramming into iCMs in vitro using mouse cells. However, this was later demonstrated to be insufficient for the reprogramming of human cells and additional factors were required. Thereafter, most studies have focused on implementing reprogramming efficiency and obtaining fully reprogrammed and functional iCMs, by the incorporation of other transcription factors, microRNAs or small molecules to the original GMT cocktail. In this respect, great advances have been made in recent years. However, there is still no consensus on which of these GMT-based varieties is best, and robust and highly reproducible protocols are still urgently required, especially in the case of human cells. On the other hand, apart from CMs, other cells such as endothelial and smooth muscle cells to form new blood vessels will be fundamental for the correct reconstruction of damaged cardiac tissue. With this aim, several studies have centered on the direct reprogramming of fibroblasts into induced cardiac progenitor cells (iCPCs) able to give rise to all myocardial cell lineages. Especially interesting are reports in which multipotent and highly expandable mouse iCPCs have been obtained, suggesting that clinically relevant amounts of these cells could be created. However, as of yet, this has not been achieved with human iCPCs, and exactly what stage of maturity is appropriate for a cell therapy product remains an open question. Nonetheless, the major concern in regenerative medicine is the poor retention, survival, and engraftment of transplanted cells in the cardiac tissue. To circumvent this issue, several cell pre-conditioning approaches are currently being explored. As an alternative to cell injection, in vivo reprogramming may face fewer barriers for its translation to the clinic. This approach has achieved better results in terms of efficiency and iCMs maturity in mouse models, indicating that the heart environment can favor this process. In this context, in recent years some studies have focused on the development of safer delivery systems such as Sendai virus, Adenovirus, chemical cocktails or nanoparticles. This article provides an in-depth review of the in vitro and in vivo cardiac reprograming technology used in mouse and human cells to obtain iCMs and iCPCs, and discusses what challenges still lie ahead and what hurdles are to be overcome before results from this field can be transferred to the clinical settings.

Multiscale cardiac imaging spanning the whole heart and its internal cellular architecture in a small animal model

Cardiac pumping depends on the morphological structure of the heart, but also on its subcellular (ultrastructural) architecture, which enables cardiac contraction. In cases of congenital heart defects, localized ultrastructural disruptions that increase the risk of heart failure are only starting to be discovered. This is in part due to a lack of technologies that can image the three-dimensional (3D) heart structure, to assess malformations; and its ultrastructure, to assess organelle disruptions. We present here a multiscale, correlative imaging procedure that achieves high-resolution images of the whole heart, using 3D micro-computed tomography (micro-CT); and its ultrastructure, using 3D scanning electron microscopy (SEM). In a small animal model (chicken embryo), we achieved uniform fixation and staining of the whole heart, without losing ultrastructural preservation on the same sample, enabling correlative multiscale imaging. Our approach enables multiscale studies in models of congenital heart disease and beyond.

Cells, Materials, and Fabrication Processes for Cardiac Tissue Engineering

Cardiovascular disease is the number one killer worldwide, with myocardial infarction (MI) responsible for approximately 1 in 6 deaths. The lack of endogenous regenerative capacity, added to the deleterious remodelling programme set into motion by myocardial necrosis, turns MI into a progressively debilitating disease, which current pharmacological therapy cannot halt. The advent of Regenerative Therapies over 2 decades ago kick-started a whole new scientific field whose aim was to prevent or even reverse the pathological processes of MI. As a highly dynamic organ, the heart displays a tight association between 3D structure and function, with the non-cellular components, mainly the cardiac extracellular matrix (ECM), playing both fundamental active and passive roles. Tissue engineering aims to reproduce this tissue architecture and function in order to fabricate replicas able to mimic or even substitute damaged organs. Recent advances in cell reprogramming and refinement of methods for additive manufacturing have played a critical role in the development of clinically relevant engineered cardiovascular tissues. This review focuses on the generation of human cardiac tissues for therapy, paying special attention to human pluripotent stem cells and their derivatives. We provide a perspective on progress in regenerative medicine from the early stages of cell therapy to the present day, as well as an overview of cellular processes, materials and fabrication strategies currently under investigation. Finally, we summarise current clinical applications and reflect on the most urgent needs and gaps to be filled for efficient translation to the clinical arena.

Decellularized Human Dermal Matrix as a Biological Scaffold for Cardiac Repair and Regeneration

The complex and highly organized environment in which cells reside consists primarily of the extracellular matrix (ECM) that delivers biological signals and physical stimuli to resident cells. In the native myocardium, the ECM contributes to both heart compliance and cardiomyocyte maturation and function. Thus, myocardium regeneration cannot be accomplished if cardiac ECM is not restored. We hypothesize that decellularized human skin might make an easily accessible and viable alternate biological scaffold for cardiac tissue engineering (CTE). To test our hypothesis, we decellularized specimens of both human skin and human myocardium and analyzed and compared their composition by histological methods and quantitative assays. Decellularized dermal matrix was then cut into 600-μm-thick sections and either tested by uniaxial tensile stretching to characterize its mechanical behavior or used as three-dimensional scaffold to assess its capability to support regeneration by resident cardiac progenitor cells (hCPCs) in vitro. Histological and quantitative analyses of the dermal matrix provided evidence of both effective decellularization with preserved tissue architecture and retention of ECM proteins and growth factors typical of cardiac matrix. Further, the elastic modulus of the dermal matrix resulted comparable with that reported in literature for the human myocardium and, when tested in vitro, dermal matrix resulted a comfortable and protective substrate promoting and supporting hCPC engraftment, survival and cardiomyogenic potential. Our study provides compelling evidence that dermal matrix holds promise as a fully autologous and cost-effective biological scaffold for CTE.

High-resolution 3D tractography of fibrous tissue based on polarization-sensitive optical coherence tomography

Fibrous tissues play important roles in many parts of the body. Their highly organized directional structure is essential in achieving their normal biomechanical and physiological functions. Disruption of the typical fiber organization in these tissues is often linked to pathological changes and disease progression. Tractography is a specialized imaging method that can reveal the detailed fiber architecture. Here, we review recent developments in high-resolution optical tractography using Jones matrix polarization-sensitive optical coherence tomography. We also illustrate the use of this new tractography technology for visualizing depth-resolved, three-dimensional fibrous structures and quantifying tissue damages in several major fibrous tissues.

Multi-scale approaches for the simulation of cardiac electrophysiology: II - Tissue-level structure and function

Computational models of the heart, from cell-level models, through one-, two- and three-dimensional tissue-level simplifications, to biophysically-detailed three-dimensional models of the ventricles, atria or whole heart, allow the simulation of excitation and propagation of this excitation, and have provided remarkable insight into the normal and pathological functioning of the heart. In this article we present equations for modelling cellular excitation (i.e. the cell action potential) from both a phenomenological and a biophysical perspective. Hodgkin-Huxley formalism is discussed, along with the current generation of biophysically-detailed cardiac cell models. Alternative Markovian formulations for modelling ionic currents are also presented. Equations describing propagation of this cellular excitation, through one-, two- and three-dimensional idealised or realistic tissues, are then presented. For all types of model, from cell to tissue, methods for discretisation and integration of the underlying equations are discussed. The article finishes with a discussion of two tissue-level experimental imaging techniques - diffusion tensor magnetic resonance imaging and optical imaging - that can be used to provide data for parameterisation and validation of cell- and tissue-level cardiac models.

Biomechanical assessment of remote and postinfarction scar remodeling following myocardial infarction

The importance of collagen remodeling following myocardial infarction (MI) is extensively investigated, but little is known on the biomechanical impact of fibrillar collagen on left ventricle post-MI. We aim to identify the significant effects of the biomechanics of types I, III, and V collagen on physio-pathological changes of murine hearts leading to heart failure. Immediately post-MI, heart reduces its function (EF = 40.94 ± 2.12%) while sarcomeres' dimensions are unchanged. Strikingly, as determined by immunohistochemistry staining, type V collagen fraction significantly grows in remote and scar for sustaining de novo-types I and III collagen fibers' assembly while hindering their enzymatic degradation. Thereafter, the compensatory heart function (EF = 63.04 ± 3.16%) associates with steady development of types I and III collagen in a stiff remote (12.79 ± 1.09 MPa) and scar (22.40 ± 1.08 MPa). In remote, the soft de novo-type III collagen uncoils preventing further expansion of elongated sarcomeres (2.7 ± 0.3 mm). Once the compensatory mechanisms are surpassed, the increased turnover of stiff type I collagen (>50%) lead to a pseudo-stable biomechanical regime of the heart (≅9 MPa) with reduced EF (50.55 ± 3.25%). These end-characteristics represent the common scenario evidenced in patients suffering from heart failure after MI. Our pre-clinical data advances the understanding of the cause of heart failure induced in patients with extended MI.

Imaging technologies for cardiac fiber and heart failure: a review

There has been an increasing interest in studying cardiac fibers in order to improve the current knowledge regarding the mechanical and physiological properties of the heart during heart failure (HF), particularly early HF. Having a thorough understanding of the changes in cardiac fiber orientation may provide new insight into the mechanisms behind the progression of left ventricular (LV) remodeling and HF. We conducted a systematic review on various technologies for imaging cardiac fibers and its link to HF. This review covers literature reports from 1900 to 2017. PubMed and Google Scholar databases were searched using the keywords "cardiac fiber" and "heart failure" or "myofiber" and "heart failure." This review highlights imaging methodologies, including magnetic resonance diffusion tensor imaging (MR-DTI), ultrasound, and other imaging technologies as well as their potential applications in basic and translational research on the development and progression of HF. MR-DTI and ultrasound have been most useful and significant in evaluating cardiac fibers and HF. New imaging technologies that have the ability to measure cardiac fiber orientations and identify structural and functional information of the heart will advance basic research and clinical diagnoses of HF.

Will the real ventricular architecture please stand up?

Ventricular twisting, essential for cardiac function, is attributed to the contraction of myocardial helical fibers. The exact relationship between ventricular anatomy and function remains to be determined, but one commonly used explanatory model is the helical ventricular myocardial band (HVMB) model of Torrent‐Guasp. This model has been successful in explaining many aspects of ventricular function, (Torrent‐Guasp et al. Eur. J. Cardiothorac. Surg., 25, 376, 2004; Buckberg et al. Eur. J. Cardiothorac. Surg., 47, 587, 2015; Buckberg et al. Eur. J. Cardiothorac. Surg. 47, 778, 2015) but the model ignores important aspects of ventricular anatomy and should probably be replaced. The purpose of this review is to compare the HVMB model with a different model (nested layers). A complication when interpreting experimental observations that relate anatomy to function is that, in the myocardium, shortening does not always imply activation and lengthening does not always imply inactivation.

Investigating the Role of Interventricular Interdependence in Development of Right Heart Dysfunction During LVAD Support: A Patient-Specific Methods-Based Approach

Predictive computation models offer the potential to uncover the mechanisms of treatments whose actions cannot be easily determined by experimental or imaging techniques. This is particularly relevant for investigating left ventricular mechanical assistance, a therapy for end-stage heart failure, which is increasingly used as more than just a bridge-to-transplant therapy. The high incidence of right ventricular failure following left ventricular assistance reflects an undesired consequence of treatment, which has been hypothesized to be related to the mechanical interdependence between the two ventricles. To investigate the implication of this interdependence specifically in the setting of left ventricular assistance device (LVAD) support, we introduce a patient-specific finite-element model of dilated chronic heart failure. The model geometry and material parameters were calibrated using patient-specific clinical data, producing a mechanical surrogate of the failing in vivo heart that models its dynamic strain and stress throughout the cardiac cycle. The model of the heart was coupled to lumped-parameter circulatory systems to simulate realistic ventricular loading conditions. Finally, the impact of ventricular assistance was investigated by incorporating a pump with pressure-flow characteristics of an LVAD (HeartMate II™ operating between 8 and 12 k RPM) in parallel to the left ventricle. This allowed us to investigate the mechanical impact of acute left ventricular assistance at multiple operating-speeds on right ventricular mechanics and septal wall motion. Our findings show that left ventricular assistance reduces myofiber stress in the left ventricle and, to a lesser extent, right ventricle free wall, while increasing leftward septal-shift with increased operating-speeds. These effects were achieved with secondary, potentially negative effects on the interventricular septum which showed that support from LVADs, introduces unnatural bending of the septum and with it, increased localized stress regions. Left ventricular assistance unloads the left ventricle significantly and shifts the right ventricular pressure-volume-loop toward larger volumes and higher pressures; a consequence of left-to-right ventricular interactions and a leftward septal shift. The methods and results described in the present study are a meaningful advancement of computational efforts to investigate heart-failure therapies in silico and illustrate the potential of computational models to aid understanding of complex mechanical and hemodynamic effects of new therapies.

Automatic quantification of microscopic heart damage in a mouse model of Duchenne muscular dystrophy using optical polarization tractography

Quantification of microscopic myocardium damage in a diseased heart is important in studying disease progression and evaluating treatment outcome. However, it is challenging to use traditional histology and existing medical imaging modalities to quantify all microscopic damages in a small animal heart. Here, a method was developed for fast visualization and quantification of focal tissue damage in the mouse heart based on the fiber alignment index of the local myofiber organization obtained in optical polarization tractography (OPT). This method was tested in freshly excised hearts of the mdx4cv mouse, a commonly used mouse model for studying Duchenne cardiomyopathy. The hearts of age-matched C57BL/6 mice were also imaged as the normal controls. The results revealed a significant amount of damage in the mdx4cv hearts. Histology comparisons confirmed the damage identified by OPT. This fast and automatic method may greatly enhance preclinical studies in murine models of heart diseases.

Personalised computational cardiology: Patient-specific modelling in cardiac mechanics and biomaterial injection therapies for myocardial infarction

Predictive computational modelling in biomedical research offers the potential to integrate diverse data, uncover biological mechanisms that are not easily accessible through experimental methods and expose gaps in knowledge requiring further research. Recent developments in computing and diagnostic technologies have initiated the advancement of computational models in terms of complexity and specificity. Consequently, computational modelling can increasingly be utilised as enabling and complementing modality in the clinic—with medical decisions and interventions being personalised. Myocardial infarction and heart failure are amongst the leading causes of death globally despite optimal modern treatment. The development of novel MI therapies is challenging and may be greatly facilitated through predictive modelling. Here, we review the advances in patient-specific modelling of cardiac mechanics, distinguishing specificity in cardiac geometry, myofibre architecture and mechanical tissue properties. Thereafter, the focus narrows to the mechanics of the infarcted heart and treatment of myocardial infarction with particular attention on intramyocardial biomaterial delivery.

The vertebrate heart: an evolutionary perspective

Convergence is the tendency of independent species to evolve similarly when subjected to the same environmental conditions. The primitive blueprint for the circulatory system emerged around 700-600 Mya and exhibits diverse physiological adaptations across the radiations of vertebrates (Subphylum Vertebrata, Phylum Chordata). It has evolved from the early chordate circulatory system with a single layered tube in the tunicate (Subphylum Urchordata) or an amphioxus (Subphylum Cephalochordata), to a vertebrate circulatory system with a two-chambered heart made up of one atrium and one ventricle in gnathostome fish (Infraphylum Gnathostomata), to a system with a three-chambered heart made up of two atria which maybe partially divided or completely separated in amphibian tetrapods (Class Amphibia). Subsequent tetrapods, including crocodiles and alligators (Order Crocodylia, Subclass Crocodylomorpha, Class Reptilia), birds (Subclass Aves, Class Reptilia) and mammals (Class Mammalia) evolved a four-chambered heart. The structure and function of the circulatory system of each individual holds a vital role which benefits each species specifically. The special characteristics of the four-chamber mammalian heart are highlighted by the peculiar structure of the myocardial muscle.

Postnatal myocardium remodelling generates inhomogeneity in the architecture of the ventricular mass

Background

The 3D architecture of the ventricular mass is poorly known, although in vivo imaging techniques show the physiological inhomogeneity of ventricular walls mechanics. Polarized light imaging makes it possible to quantitatively analyse the myosin filament orientation.

Aims

In this paper, we focus on the study the 3D architecture and regional isotropy of myocardial cells.

Methods

Twenty normal human hearts, 10 from the perinatal period and 10 from the post-neonatal period were studied by polarized light microscopy. In each voxel of the ventricular mass (90 × 90 × 500 µm) the principal orientation segment was automatically and unambiguously extracted as well as a regional isotropy index (regional orientation tensor of the voxel neighbourhood).

Results

During the first months of postnatal age, the median regional isotropy values decreased in the ventricular mesh. This global decrease was not homogeneous across the ventricular walls. From the perinatal to the neonatal period, this decrease was more marked in the inner two-third of the lateral left ventricular wall and in the right part of the interventricular septum. There was a progressive post-neonatal appearance of a particularly inhomogeneous secondary arrangement of myocardial cells with alternation of thick low-RI and thin high-RI areas.

Conclusions

This study has shown a postnatal change in ventricular myocardial architecture, which became more inhomogeneous. The cell rearrangements responsible for the inhomogeneity in ventricular myocardial architecture are revealed by a variation of the regional isotropy index. These major changes are probably an adaptive consequence of the major haemodynamic changes occurring after birth during the neonatal period that generates major parietal stress variations and parietal remodelling.

Electronic supplementary material

The online version of this article (10.1007/s00276-017-1945-5) contains supplementary material, which is available to authorized users.

Global Diffusion Tractography by Simulated Annealing

OBJECTIVE

Our goal is to develop a robust global tractography method for cardiac diffusion imaging.

METHODS

A graph is stretched over the whole myocardium to represent the fiber structure, and the solutions are minima of a graph energy measuring the fidelity to the data along with the fiber density and curvature. The optimization is performed by a variant of simulated annealing that offers increased design freedom without sacrificing theoretical convergence guarantees.

RESULTS

Numerical experiments on synthetic and real data demonstrate the capability of our tractography algorithm to deal with low angular resolution, highly noisy data. In particular, our algorithm outperforms the Bayesian model-based algorithm of Reisert et al. (NeuroImage, vol. 54, no. 2, 2011) and the graph-based algorithm of Frindel et al. (Magn. Reson. Med., vol. 64, no. 4, 2010) at the noise levels typical of in vivo imaging.

CONCLUSION

The proposed algorithm avoids the drawbacks of local techniques and is very robust to noise, which makes it a promising tool for in vivo diffusion imaging of moving organs.

SIGNIFICANCE

Our approach is global in terms of both the fiber structure representation and the minimization problem. It also allows us to adjust the trajectory density by simply changing the vertex-lattice spacing in the graph model, a desirable feature for multiresolution tractography analysis.

Diffusion tensor imaging and histology of developing hearts

Diffusion tensor imaging (DTI) has emerged as a promising method for noninvasive quantification of myocardial microstructure. However, the origin and behavior of DTI measurements during myocardial normal development and remodeling remain poorly understood. In this work, conventional and bicompartmental DTI in addition to three-dimensional histological correlation were performed in a sheep model of myocardial development from third trimester to postnatal 5 months of age. Comparing the earliest time points in the third trimester with the postnatal 5 month group, the scalar transverse diffusivities preferentially increased in both left ventricle (LV) and right ventricle (RV): secondary eigenvalues D2 increased by 54% (LV) and 36% (RV), whereas tertiary eigenvalues D3 increased by 85% (LV) and 67% (RV). The longitudinal diffusivity D1 changes were small, which led to a decrease in fractional anisotropy by 41% (LV) and 33% (RV) in 5 month versus fetal hearts. Histological analysis suggested that myocardial development is associated with hyperplasia in the early stages of the third trimester followed by myocyte growth in the later stages up to 5 months of age (increased average myocyte width by 198%, myocyte length by 128%, and decreased nucleus density by 70% between preterm and postnatal 5 month hearts.) In a few histological samples (N = 6), correlations were observed between DTI longitudinal diffusivity and myocyte length (r = 0.86, P < 0.05), and transverse diffusivity and myocyte width (r = 0.96, P < 0.01). Linear regression analysis showed that transverse diffusivities are more affected by changes in myocyte size and nucleus density changes than longitudinal diffusivities, which is consistent with predictions of classical models of diffusion in porous media. Furthermore, primary and secondary DTI eigenvectors during development changed significantly. Collectively, the findings demonstrate a role for DTI to monitor and quantify myocardial development, and potentially cardiac disease. Copyright © 2016 John Wiley & Sons, Ltd.

Anomalous Diffusion in Cardiac Tissue as an Index of Myocardial Microstructure

Diffusion in biological tissues is known to be hindered by the structural complexity of the underlying medium. In the heart, improved characterisation on how this complexity influences acquired diffusion weighted signals is key to advancing our interpretation of diffusion magnetic resonance imaging, as well as to propose novel biomarkers to further characterise myocardial microstructure. In this work, we propose stretched Mittag-Leffler signal decay models for the quantification of the anomalous decay observed in acquired diffusion weighted signals. Our results, analysed in ex vivo healthy, fixed rat ventricles, indicate that such a representation suffices to capture the anomalous signal decay observed in the myocardial syncytium. The subdiffusive order of signal decay is shown to encode independent information to that encapsulated by standard diffusion tensor metrics, and thus may provide additional information on tissue microstructure. Moreover, subdiffusion gradients are shown to be indicative of the total structural heterogeneity spanning the left ventricular wall, which includes progressive myolaminae branching and spatially varying densities of perimysial collagen, microvasculature and adipose tissue. The proposed approach may therefore have important implications for the characterisation of tissue microstructure, both in cardiac and other tissue types.

Resolving Fine Cardiac Structures in Rats with High-Resolution Diffusion Tensor Imaging

Cardiac architecture is fundamental to cardiac function and can be assessed non-invasively with diffusion tensor imaging (DTI). Here, we aimed to overcome technical challenges in ex vivo DTI in order to extract fine anatomical details and to provide novel insights in the 3D structure of the heart. An integrated set of methods was implemented in ex vivo rat hearts, including dynamic receiver gain adjustment, gradient system scaling calibration, prospective adjustment of diffusion gradients, and interleaving of diffusion-weighted and non-diffusion-weighted scans. Together, these methods enhanced SNR and spatial resolution, minimised orientation bias in diffusion-weighting, and reduced temperature variation, enabling detection of tissue structures such as cell alignment in atria, valves and vessels at an unprecedented level of detail. Improved confidence in eigenvector reproducibility enabled tracking of myolaminar structures as a basis for segmentation of functional groups of cardiomyocytes. Ex vivo DTI facilitates acquisition of high quality structural data that complements readily available in vivo cardiac functional and anatomical MRI. The improvements presented here will facilitate next generation virtual models integrating micro-structural and electro-mechanical properties of the heart.

Computational Modeling of Healthy Myocardium in Diastole

In order to better understand the mechanics of the heart and its disorders, engineers increasingly make use of the finite element method (FEM) to investigate healthy and diseased cardiac tissue. However, FEM is only as good as the underlying constitutive model, which remains a major challenge to the biomechanics community. In this study, a recently developed structurally based constitutive model was implemented to model healthy left ventricular myocardium during passive diastolic filling. This model takes into account the orthotropic response of the heart under loading. In-vivo strains were measured from magnetic resonance images (MRI) of porcine hearts, along with synchronous catheterization pressure data, and used for parameter identification of the passive constitutive model. Optimization was performed by minimizing the difference between MRI measured and FE predicted strains and cavity volumes. A similar approach was followed for the parameter identification of a widely used phenomenological constitutive law, which is based on a transversely isotropic material response. Results indicate that the parameter identification with the structurally based constitutive law is more sensitive to the assigned fiber architecture and the fit between the measured and predicted strains is improved with more realistic sheet angles. In addition, the structurally based model is capable of generating a more physiological end-diastolic pressure-volume relationship in the ventricle.

Maurer-Cartan Forms for Fields on Surfaces: Application to Heart Fiber Geometry

We study the space of first order models of smooth frame fields using the method of moving frames. By exploiting the Maurer-Cartan matrix of connection forms we develop geometrical embeddings for frame fields which lie on spherical, ellipsoidal and generalized helicoid surfaces. We design methods for optimizing connection forms in local neighborhoods and apply these to a statistical analysis of heart fiber geometry, using diffusion magnetic resonance imaging. This application of moving frames corroborates and extends recent characterizations of muscle fiber orientation in the heart wall, but also provides for a rich geometrical interpretation. In particular, we can now obtain direct local measurements of the variation of the helix and transverse angles, of fiber fanning and twisting, and of the curvatures of the heart wall in which these fibers lie.

Cardiac MR imaging: current status and future direction

Coronary artery disease is currently a worldwide epidemic with increasing impact on healthcare systems. Magnetic resonance imaging (MRI) sequences give complementary information on LV function, regional perfusion, angiogenesis, myocardial viability and orientations of myocytes. T2-weighted short-tau inversion recovery (T2-STIR), fat suppression and black blood sequences have been frequently used for detecting edematous area at risk (AAR) of infarction. T2 mapping, however, indicated that the edematous reaction in acute myocardial infarct (AMI) is not stable and warranted the use of edematous area in evaluating therapies. On the other hand, cine MRI demonstrated reproducible data on LV function in healthy volunteers and LV remodeling in patients. Noninvasive first pass perfusion, using exogenous tracer (gadolinium-based contrast media) and arterial spin labeling MRI, using endogenous tracer (water), are sensitive and useful techniques for evaluating myocardial perfusion and angiogenesis. Recently, new strategies have been developed to quantify myocardial viability using T1-mapping and equilibrium contrast enhanced MR techniques because existing delayed contrast enhancement MRI (DE-MRI) sequences are limited in detecting patchy microinfarct and diffuse fibrosis. These new techniques were successfully used for characterizing diffuse myocardial fibrosis associated with myocarditis, amyloidosis, sarcoidosis heart failure, aortic hypertrophic cardiomyopathy, congenital heart disease, restrictive cardiomyopathy, arrhythmogenic right ventricular dysplasia and hypertension). Diffusion MRI provides information regarding microscopic tissue structure, while diffusion tensor imaging (DTI) helps to characterize the myocardium and monitor the process of LV remodeling after AMI. Novel trends in hybrid imaging, such as cardiac positron emission tomography (PET)/MRI and optical imaging/MRI, are recently under intensive investigation. With the promise of higher spatial-temporal resolution and 3D coverage in the near future, cardiac MRI will be an indispensible tool in the diagnosis of cardiac diseases, coronary intervention and myocardial therapeutic delivery.

Finite-Element Extrapolation of Myocardial Structure Alterations Across the Cardiac Cycle in Rats

Myocardial microstructures are responsible for key aspects of cardiac mechanical function. Natural myocardial deformation across the cardiac cycle induces measurable structural alteration, which varies across disease states. Diffusion tensor magnetic resonance imaging (DT-MRI) has become the tool of choice for myocardial structural analysis. Yet, obtaining the comprehensive structural information of the whole organ, in 3D and time, for subject-specific examination is fundamentally limited by scan time. Therefore, subject-specific finite-element (FE) analysis of a group of rat hearts was implemented for extrapolating a set of initial DT-MRI to the rest of the cardiac cycle. The effect of material symmetry (isotropy, transverse isotropy, and orthotropy), structural input, and warping approach was observed by comparing simulated predictions against in vivo MRI displacement measurements and DT-MRI of an isolated heart preparation at relaxed, inflated, and contracture states. Overall, the results indicate that, while ventricular volume and circumferential strain are largely independent of the simulation strategy, structural alteration predictions are generally improved with the sophistication of the material model, which also enhances torsion and radial strain predictions. Moreover, whereas subject-specific transversely isotropic models produced the most accurate descriptions of fiber structural alterations, the orthotropic models best captured changes in sheet structure. These findings underscore the need for subject-specific input data, including structure, to extrapolate DT-MRI measurements across the cardiac cycle.

Generalized minimal principle for rotor filaments

To a reaction-diffusion medium with an inhomogeneous anisotropic diffusion tensor D, we add a fourth spatial dimension such that the determinant of the diffusion tensor is constant in four dimensions. We propose a generalized minimal principle for rotor filaments, stating that the scroll wave filament strives to minimize its surface area in the higher-dimensional space. As a consequence, stationary scroll wave filaments in the original 3D medium are geodesic curves with respect to the metric tensor G=det(D)D(-1). The theory is confirmed by numerical simulations for positive and negative filament tension and a model with a non-stationary spiral core. We conclude that filaments in cardiac tissue with positive tension preferentially reside or anchor in regions where cardiac cells are less interconnected, such as portions of the cardiac wall with a large number of cleavage planes.

Comparison of diffusion tensor imaging by cardiovascular magnetic resonance and gadolinium enhanced 3D image intensity approaches to investigation of structural anisotropy in explanted rat hearts

BACKGROUND

Cardiovascular magnetic resonance (CMR) can through the two methods 3D FLASH and diffusion tensor imaging (DTI) give complementary information on the local orientations of cardiomyocytes and their laminar arrays.

METHODS

Eight explanted rat hearts were perfused with Gd-DTPA contrast agent and fixative and imaged in a 9.4T magnet by two types of acquisition: 3D fast low angle shot (FLASH) imaging, voxels 50 × 50 × 50 μm, and 3D spin echo DTI with monopolar diffusion gradients of 3.6 ms duration at 11.5 ms separation, voxels 200 × 200 × 200 μm. The sensitivity of each approach to imaging parameters was explored.

RESULTS

The FLASH data showed laminar alignments of voxels with high signal, in keeping with the presumed predominance of contrast in the interstices between sheetlets. It was analysed, using structure-tensor (ST) analysis, to determine the most (v1(ST)), intermediate (v2(ST)) and least (v3(ST)) extended orthogonal directions of signal continuity. The DTI data was analysed to determine the most (e1(DTI)), intermediate (e2(DTI)) and least (e3(DTI)) orthogonal eigenvectors of extent of diffusion. The correspondence between the FLASH and DTI methods was measured and appraised. The most extended direction of FLASH signal (v1(ST)) agreed well with that of diffusion (e1(DTI)) throughout the left ventricle (representative discrepancy in the septum of 13.3 ± 6.7°: median ± absolute deviation) and both were in keeping with the expected local orientations of the long-axis of cardiomyocytes. However, the orientation of the least directions of FLASH signal continuity (v3(ST)) and diffusion (e3(ST)) showed greater discrepancies of up to 27.9 ± 17.4°. Both FLASH (v3(ST)) and DTI (e3(DTI)) where compared to directly measured laminar arrays in the FLASH images. For FLASH the discrepancy between the structure-tensor calculated v3(ST) and the directly measured FLASH laminar array normal was of 9 ± 7° for the lateral wall and 7 ± 9° for the septum (median ± inter quartile range), and for DTI the discrepancy between the calculated v3(DTI) and the directly measured FLASH laminar array normal was 22 ± 14° and 61 ± 53.4°. DTI was relatively insensitive to the number of diffusion directions and to time up to 72 hours post fixation, but was moderately affected by b-value (which was scaled by modifying diffusion gradient pulse strength with fixed gradient pulse separation). Optimal DTI parameters were b = 1000 mm/s(2) and 12 diffusion directions. FLASH acquisitions were relatively insensitive to the image processing parameters explored.

CONCLUSIONS

We show that ST analysis of FLASH is a useful and accurate tool in the measurement of cardiac microstructure. While both FLASH and the DTI approaches appear promising for mapping of the alignments of myocytes throughout myocardium, marked discrepancies between the cross myocyte anisotropies deduced from each method call for consideration of their respective limitations.

Images as drivers of progress in cardiac computational modelling

Computational models have become a fundamental tool in cardiac research. Models are evolving to cover multiple scales and physical mechanisms. They are moving towards mechanistic descriptions of personalised structure and function, including effects of natural variability. These developments are underpinned to a large extent by advances in imaging technologies. This article reviews how novel imaging technologies, or the innovative use and extension of established ones, integrate with computational models and drive novel insights into cardiac biophysics. In terms of structural characterization, we discuss how imaging is allowing a wide range of scales to be considered, from cellular levels to whole organs. We analyse how the evolution from structural to functional imaging is opening new avenues for computational models, and in this respect we review methods for measurement of electrical activity, mechanics and flow. Finally, we consider ways in which combined imaging and modelling research is likely to continue advancing cardiac research, and identify some of the main challenges that remain to be solved.

Quantitative study of the effect of tissue microstructure on contraction in a computational model of rat left ventricle

Tissue microstructure, in particular the alignment of myocytes (fibre direction) and their lateral organisation into sheets, is fundamental to cardiac function. We studied the effect of microstructure on contraction in a computational model of rat left ventricular electromechanics. Different fibre models, globally rule-based or locally optimised to DT-MRI data, were compared, in order to understand whether a subject-specific fibre model would enhance the predictive power of our model with respect to the global ones. We also studied the impact of sheets on ventricular deformation by comparing: (a) a transversely isotropic versus an orthotropic material law and (b) a linear model with a bimodal model of sheet transmural variation. We estimated ejection fraction, wall thickening and base-to-apex shortening and compared them with measures from cine-MRI. We also evaluated Lagrangian strains as local metrics of cardiac deformation. Our results show that the subject-specific fibre model provides little improvement in the metric predictions with respect to global fibre models while material orthotropy allows closer agreement with measures than transverse isotropy. Nonetheless, the impact of sheets in our model is smaller than that of fibres. We conclude that further investigation of the modelling of sheet dynamics is necessary to fully understand the impact of tissue structure on cardiac deformation.

Effects of activation pattern and active stress development on myocardial shear in a model with adaptive myofiber reorientation

It has been hypothesized that myofiber orientation adapts to achieve a preferred mechanical loading state in the myocardial tissue. Earlier studies tested this hypothesis in a combined model of left ventricular (LV) mechanics and remodeling of myofiber orientation in response to fiber cross-fiber shear, assuming synchronous timing of activation and uniaxial active stress development. Differences between computed and measured patterns of circumferential-radial shear strain Ecr were assumed to be caused by limitations in either the LV mechanics model or the myofiber reorientation model. Therefore, we extended the LV mechanics model with a physiological transmural and longitudinal gradient in activation pattern and with triaxial active stress development. We investigated the effects on myofiber reorientation, LV function, and deformation. The effect on the developed pattern of the transverse fiber angle αt,0 and the effect on global pump function were minor. Triaxial active stress development decreased amplitudes of Ecr towards values within the experimental range and resulted in a similar base-to-apex gradient during ejection in model computed and measured Ecr. The physiological pattern of mechanical activation resulted in better agreement between computed and measured strain in myofiber direction, especially during isovolumic contraction phase and first half of ejection. In addition, remodeling was favorable for LV pump and myofiber function. In conclusion, the outcome of the combined model of LV mechanics and remodeling of myofiber orientation is found to become more physiologic by extending the mechanics model with triaxial active stress development and physiological activation pattern.

Computational modeling of electromechanical propagation in the helical ventricular anatomy of the heart

The classical interpretation of myocardial activation assumes that the myocardium is homogeneous and that the electrical propagation is radial. However, anatomical studies have described a layered anatomical structure resulting from a continuous anatomical helical disposition of the myocardial fibers. To further investigate the sequence of electromechanical propagation based on the helical architecture of the heart, a simplified computational model was designed. This model was then used to test four activation patterns, which were generated by propagating the action potential along the myocardial band from different activation sites.

DT-MRI measurement of myolaminar structure: accuracy and sensitivity to time post-fixation, b-value and number of directions

DT-MRI has been widely used to quantify myocardial fiber and laminar orientations. These structural orientations influence both the spread of excitation and the reorganization of the myocardium during contraction and are altered in disease states. Studies have sought to validate DT-MRI but questions remain about the accuracy of the method and its sensitivity to the time post-fixation and imaging parameters, including b-value, number of diffusion directions and image voxel size. The advent of high-spatial resolution ex vivo MRI and structure tensor (ST) analysis provides a means of direct validation of DT-MRI and assessment of sensitivity to the b-value, the number of diffusion directions and the image voxel size. We find that, with the fixation method we used, structure does not change with time (up to 72 hours). We show that DT-MRI and ST/HR-MRI are markedly similar measures of fiber orientation but DT-MRI and ST are much less similar measures of laminar orientation. DT-MRI performance is not sensitive to the number of directions, with similar structural orientations measured with 6 or 12 directions. Likewise, DT-MRI performance is generally insensitive to b-value, but laminar measurement is moderately more accurate at b = 500 than for higher b-values.