Analysis of cardiac ventricular wall motion based on a three-dimensional electromechanical biventricular model

This paper describes a biventricular model, which couples the electrical and mechanical properties of the heart, and computer simulations of ventricular wall motion and deformation by means of a biventricular model. In the constructed electromechanical model, the mechanical analysis was based on composite material theory and the finite-element method; the propagation of electrical excitation was simulated using an electrical heart model, and the resulting active forces were used to calculate ventricular wall motion. Regional deformation and Lagrangian strain tensors were calculated during the systole phase. Displacements, minimum principal strains and torsion angle were used to describe the motion of the two ventricles. The simulations showed that during the period of systole, (1) the right ventricular free wall moves towards the septum, and at the same time, the base and middle of the free wall move towards the apex, which reduces the volume of the right ventricle; the minimum principle strain (E3) is largest at the apex, then at the middle of the free wall and its direction is in the approximate direction of the epicardial muscle fibres; (2) the base and middle of the left ventricular free wall move towards the apex and the apex remains almost static; the torsion angle is largest at the apex; the minimum principle strain E3 is largest at the apex and its direction on the surface of the middle wall of the left ventricle is roughly in the fibre orientation. These results are in good accordance with results obtained from MR tagging images reported in the literature. This study suggests that such an electromechanical biventricular model has the potential to be used to assess the mechanical function of the two ventricles, and also could improve the accuracy ECG simulation when it is used in heart torso model-based body surface potential simulation studies.

Electrodynamic heart model construction and ECG simulation

Objectives: In this paper, we present a unified electrodynamic heart model that permits simulations of the body surface potentials generated by the heart in motion. The inclusion of motion in the heart model significantly improves the accuracy of the simulated body surface potentials and therefore also the 12-lead ECG. Methods: The key step is to construct an electromechanical heart model. The cardiac excitation propagation is simulated by an electrical heart model, and the resulting cardiac active forces are used to calculate the ventricular wall motion based on a mechanical model. The source-field point relative position changes during heart systole and diastole. These can be obtained, and then used to calculate body surface ECG based on the electrical heart-torso model. Results: An electromechanical biventricular heart model is constructed and a standard 12-lead ECG is simulated. Compared with a simulated ECG based on the static electrical heart model, the simulated ECG based on the dynamic heart model is more accordant with a clinically recorded ECG, especially for the ST segment and T wave of a V1-V6 lead ECG. For slight-degree myocardial ischemia ECG simulation, the ST segment and T wave changes can be observed from the simulated ECG based on a dynamic heart model, while the ST segment and T wave of simulated ECG based on a static heart model is almost unchanged when compared with a normal ECG. Conclusions: This study confirms the importance of the mechanical factor in the ECG simulation. The dynamic heart model could provide more accurate ECG simulation, especially for myocardial ischemia or infarction simulation, since the main ECG changes occur at the ST segment and T wave, which correspond with cardiac systole and diastole phases.

GFP-tagged CFTR transgene is functional in the G551D cystic fibrosis mouse colon

Trafficking of the cystic fibrosis transmembrane conductance regulator (CFTR) is central to its function, with the most common mutation, DeltaF508, resulting in abnormal processing and trafficking. Therefore, there is a significant need to develop tools, which enable the trafficking of CFTR to be studied in vitro and in vivo. In previous studies it has been demonstrated that fusion of the green fluorescent protein (GFP) to the N-terminus of CFTR does lead to functional expression of CFTR chloride channels in epithelial cell lines. The aim of the present study was to examine whether it is possible to express GFP-tagged CFTR as a transgene in colonic and airway epithelial cells of cystic fibrosis (CF) mice and to correct the CF defect. Using the epithelial-specific human cytokeratin promoter K18, we generated bitransgenic mice cftr(G551D/G551D) K18-GFP-CFTR+/-, designated GFP mice. Transcripts for GFP-CFTR could be detected in bitransgenic mice by use of RT-PCR techniques. Expression of GFP-CFTR protein was detected specifically in the colonic epithelium by both direct GFP fluorescence and the use of an anti-GFP antibody. Ussing chamber studies showed that the ion transport defect in colon and airways observed in cftr(G551D/G551D) mice was partially corrected in the bitransgenic animals. Thus, K18-GFP-CFTR is functionally expressed in transgenic mice, which will be a valuable tool in studies on CFTR synthesis, processing and ion transport in native epithelial tissues.

Geometric distortion in clinical MRI systems - Part II: correction using a 3D phantom

In this paper, we present the correction of the geometric distortion measured in the clinical magnetic resonance imaging (MRI) systems reported in the preceding paper (Part 1) using a 3D method based on the phantom-mapped geometric distortion data. This method allows the correction to be made on phantom images acquired without or with the vendor correction applied. With the vendor's 2D correction applied, the method corrects for both the residual geometric distortion still present in the plane in which the correction method was applied (the axial plane) and the uncorrected geometric distortion along the axis non-nal to the plane. The evaluation of the effectiveness of the correction using this new method was carried out through analyzing the residual geometric distortion in the corrected phantom images. The results show that the new method can restore the distorted images in 3D nearly to perfection. For all the MRI systems investigated, the mean absolute deviations in the positions of the control points (along x-, y- and z-axes) measured on the corrected phantom images were all less than 0.2 mm. The maximum absolute deviations were all below similar to0.8 mm. As expected, the correction of the phantom images acquired with the vendor's correction applied in the axial plane performed equally well. Both the geometric distortion still present in the axial plane after applying the vendor's correction and the uncorrected distortion along the z-axis have all been restored. (C) 2004 Elsevier Inc. All rights reserved.

Geometric distortion in clinical MRI systems - Part I: evaluation using a 3D phantom

Recently, a 3D phantom that can provide a comprehensive and accurate measurement of the geometric distortion in MRI has been developed. Using this phantom, a full assessment of the geometric distortion in a number of clinical MRI systems (GE and Siemens) has been carried out and detailed results are presented in this paper. As expected, the main source of geometric distortion in modern superconducting MRI systems arises from the gradient field nonlinearity. Significantly large distortions with maximum absolute geometric errors ranged between 10 and 25 mm within a volume of 240 x 240 x 240 mm(3) were observed when imaging with the new generation of gradient systems that employs shorter coils. By comparison, the geometric distortion was much less in the older-generation gradient systems. With the vendor's correction method, the geometric distortion measured was significantly reduced but only within the plane in which these 2D correction methods were applied. Distortion along the axis normal to the plane was, as expected, virtually unchanged. Two-dimensional correction methods are a convenient approach and in principle they are the only methods that can be applied to correct geometric distortion in a single slice or in multiple noncontiguous slices. However, these methods only provide an incomplete solution to the problem and their value can be significantly reduced if the distortion along the normal of the correction plane is not small. (C) 2004 Elsevier Inc. All rights reserved.

Electromagnetic fields inside a lossy, multilayered spherical head phantom excited by MRI coils: models and methods

The precise evaluation of electromagnetic field (EMF) distributions inside biological samples is becoming an increasingly important design requirement for high field MRI systems. In evaluating the induced fields caused by magnetic field gradients and RF transmitter coils, a multilayered dielectric spherical head model is proposed to provide a better understanding of electromagnetic interactions when compared to a traditional homogeneous head phantom. This paper presents Debye potential (DP) and Dyadic Green's function (DGF)-based solutions of the EMFs inside a head-sized, stratified sphere with similar radial conductivity and permittivity profiles as a human head. The DP approach is formulated for the symmetric case in which the source is a circular loop carrying a harmonic-formed current over a wide frequency range. The DGF method is developed for generic cases in which the source may be any kind of RF coil whose current distribution can be evaluated using the method of moments. The calculated EMFs can then be used to deduce MRI imaging parameters. The proposed methods, while not representing the full complexity of a head model, offer advantages in rapid prototyping as the computation times are much lower than a full finite difference time domain calculation using a complex head model. Test examples demonstrate the capability of the proposed models/methods. It is anticipated that this model will be of particular value for high field MRI applications, especially the rapid evaluation of RF resonator (surface and volume coils) and high performance gradient set designs.

Winding patterns for biplanar MRI shim coils with rectangular and circular target-field regions

A method is presented for calculating the winding patterns required to design independent zonal and tesseral biplanar shim coils for magnetic resonance imaging. Streamline, target-field, Fourier integral and Fourier series methods are utilized. For both Fourier-based methods, the desired target field is specified on the surface of the conducting plates. For the Fourier series method it is possible to specify the target field at additional depths interior to the two conducting plates. The conducting plates are confined symmetrically in the xy plane with dimensions 2a x 2b, and are separated by 2d in the z direction. The specification of the target field is symmetric for the Fourier integral method, but can be over some asymmetric portion pa < x < qa and sb < y < tb of the coil dimensions (-1 < p < q < 1 and -1 < s < t < 1) for the Fourier series method. Arbitrary functions are used in the outer sections to ensure continuity of the magnetic field across the entire coil face. For the Fourier series case, the entire field is periodically extended as double half-range sine or cosine series. The resultant Fourier coefficients are substituted into the Fourier series and integral expressions for the internal and external magnetic fields, and stream functions on both the conducting surfaces. A contour plot of the stream function directly gives the required coil winding patterns. Spherical harmonic analysis of field calculations from a ZX shim coil indicates that example designs and theory are well matched.

An FDTD model for calculation of gradient-induced eddy currents in MRI system

In most magnetic resonance imaging (MRI) systems, pulsed magnetic gradient fields induce eddy currents in the conducting structures of the superconducting magnet. The eddy currents induced in structures within the cryostat are particularly problematic as they are characterized by long time constants by virtue of the low resistivity of the conductors. This paper presents a three-dimensional (3-D) finite-difference time-domain (FDTD) scheme in cylindrical coordinates for eddy-current calculation in conductors. This model is intended to be part of a complete FDTD model of an MRI system including all RF and low-frequency field generating units and electrical models of the patient. The singularity apparent in the governing equations is removed by using a series expansion method and the conductor-air boundary condition is handled using a variant of the surface impedance concept. The numerical difficulty due to the asymmetry of Maxwell equations for low-frequency eddy-current problems is circumvented by taking advantage of the known penetration behavior of the eddy-current fields. A perfectly matched layer absorbing boundary condition in 3-D cylindrical coordinates is also incorporated. The numerical method has been verified against analytical solutions for simple cases. Finally, the algorithm is illustrated by modeling a pulsed field gradient coil system within an MRI magnet system. The results demonstrate that the proposed FDTD scheme can be used to calculate large-scale eddy-current problems in materials with high conductivity at low frequencies.

A diffusion and T2 relaxation MRI study of the ovine lumbar intervertebral disc under compression in vitro

The ovine lumbar intervertebral disc is a useful model for the human lumbar disc. We present preliminary estimates of diffusion coefficients and T-2 relaxation times in a pilot MRI study of the ovine lumbar intervertebral disc during uniaxial compression in vitro, and identify factors that hamper the ability to accurately monitor the temporal evolution of the effective diffusion tensor at high spatial resolution.

An inverse methodology for high-frequency RF coil design for MRI with de-emphasized B-1 fields

An inverse methodology for the design of biologically loaded radio-frequency (RF) coils for magnetic resonance imaging applications is described. Free space time-harmonic electromagnetic Green's functions and de-emphasized B-1 target fields are used to calculate the current density on the coil cylinder. In theory, with the B-1 field de-emphasized in the middle of the RF transverse plane, the calculated current distribution can generate an internal magnetic field that can reduce the central overemphasis effect caused by field/tissue interactions at high frequencies. The current distribution of a head coil operating at 4 T (170 MHz) is calculated using an inverse methodology with de-emphasized B-1. target fields. An in-house finite-difference time-domain routine is employed to evaluate B-1 field and signal intensity inside a homogenous cylindrical phantom and then a complete human head model. A comparison with a conventional RF birdcage coil is carried out and demonstrates that this method can help in decreasing the normal bright region caused by field/tissue interactions in head images at 170 MHz and higher field strengths.

An object-oriented designed finite-difference time-domain simulator for electromagnetic analysis and design in MRI - application to high field analyses

This paper presents a finite-difference time-domain (FDTD) simulator for electromagnetic analysis and design applications in MRI. It is intended to be a complete FDTD model of an MRI system including all RF and low-frequency field generating units and electrical models of the patient. The pro-ram has been constructed in an object-oriented framework. The design procedure is detailed and the numerical solver has been verified against analytical solutions for simple cases and also applied to various field calculation problems. In particular, the simulator is demonstrated for inverse RF coil design, optimized source profile generation, and parallel imaging in high-frequency situations. The examples show new developments enabled by the simulator and demonstrate that the proposed FDTD framework can be used to analyze large-scale computational electromagnetic problems in modern MRI engineering. (C) 2004 Elsevier Inc. All rights reserved.

A theoretical comparison of two optimization methods for radiofrequency drive schemes in high frequency MRI resonators

In this paper, numerical simulations are used in an attempt to find optimal Source profiles for high frequency radiofrequency (RF) volume coils. Biologically loaded, shielded/unshielded circular and elliptical birdcage coils operating at 170 MHz, 300 MHz and 470 MHz are modelled using the FDTD method for both 2D and 3D cases. Taking advantage of the fact that some aspects of the electromagnetic system are linear, two approaches have been proposed for the determination of the drives for individual elements in the RF resonator. The first method is an iterative optimization technique with a kernel for the evaluation of RF fields inside an imaging plane of a human head model using pre-characterized sensitivity profiles of the individual rungs of a resonator; the second method is a regularization-based technique. In the second approach, a sensitivity matrix is explicitly constructed and a regularization procedure is employed to solve the ill-posed problem. Test simulations show that both methods can improve the B-1-field homogeneity in both focused and non-focused scenarios. While the regularization-based method is more efficient, the first optimization method is more flexible as it can take into account other issues such as controlling SAR or reshaping the resonator structures. It is hoped that these schemes and their extensions will be useful for the determination of multi-element RF drives in a variety of applications.

Numerical modeling of 11.1 T MRI of a human head using MoM/FDTD methods

In a recent study, severe distortions in the proton images of an excised, fixed, human brain in an 11.1 Tesla/40 cm MR instrument have been observed, and the effect modeled on phantom images using a finite difference time domain (FDTD) model. in the present study, we extend these simulations to that of a complete human head, employing a hybrid FDTD and method of moments (MoM) approach, which provides a validated method for simulating biological samples in coil structures. The effect of fixative on the image distortions is explored. importantly, temperature distributions within the head are also simulated using a bioheat method based on parameters derived from the electromagnetic simulations. The MoM/FDTD simulations confirm that the transverse magnetic field (B,) from a ReCav resonator exhibits good homogeneity in air but strong inhomogeneity when loaded with the head with or without fixative. The fixative serves to increase the distortions, but they are still significant for the in vivo simulations. The simulated signal intensity (SI) distribution within the sample confirm the distortions in the experimental images are caused by the complex interactions of the incident electromagnetic fields with tissue, which is heterogeneous in terms of conductivity and permittivity. The temperature distribution is likewise heterogeneous, raising concerns regarding hot spot generation in the sample that may exceed acceptable levels in future in vivo studies. As human imaging at 11.1 T is some time away, simulations are important in terms of predicting potential safety issues as well as evaluating practical concerns about the quality of images. Simulation on a whole human head at 11.1 T implies the wave behavior presents significant engineering challenges for ultra-high-field (UHF) MRI. Novel strategies will have to be employed in imaging technique and resonator design for UHF MRI to achieve the theoretical signal-to-noise ratio (SNR) improvements it offers over lower field systems. (C) 2005 Wiley Periodicals, Inc.