Using axially loaded MRI to investigate the biomechanics of adolescent idiopathic scoliosis

Introduction. Spinal flexibility measurement is an important aspect of pre-operative clinical assessment in the treatment of Adolescent Idiopathic Scoliosis (AIS). Clinically, curve flexibility is a combined measure for all vertebral levels. We propose that in vivo flexibility for individual spinal joints could provide valuable additional information in planning treatment for scoliosis. Methods. Individual spinal joint flexibility in the coronal plane was measured for a series of AIS patients using axially loaded magnetic resonance imaging. Each patient underwent magnetic resonance imaging in the supine position, with no axial load, and then following application of an axial compressive load equal to half the patient’s bodyweight. Coronal plane disc wedge angles in the unloaded and loaded configurations were measured. Joint moments exerted by the axial compressive load were used to derive estimates of individual joint compliance. Results. Fifteen AIS patients were included in the study (mean clinical Cobb angle 46 degrees, mean age 15.3 years). Mean intra-observer measurement error for endplate inclination was 1.6˚. The mean increase in measured major Cobb angle between unloaded and loaded scans was 7.6˚. For certain spinal levels (+2,+1,-2 relative to the apex) there was a statistically significant relationship between change in wedge angle under load and initial wedge angle, such that initially highly wedged discs demonstrated a smaller change in wedge angle than less wedged discs. Highly wedged discs were observed near the apex of the curve, which corresponded to lower joint compliance in the apical region. Conclusion. Approaches such as this can provide valuable biomechanical data on in vivo spinal biomechanics in AIS. Knowledge of individual joint flexibility may assist surgeons to determine which spinal procedure is most appropriate for a patient, which levels should be included in a spinal fusion and the relative mobility of individual joints in the deformed region of the spine.

The vertebral venous system in healthy and scoliotic adolescent spines - a 3D MRI investigation

Introduction. The venous drainage system within vertebral bodies (VBs) has been well documented previously in cadaveric specimens. Advances in 3D imaging and image processing now allow for in vivo quantification of larger venous vessels, such as the basivertebral vein. Differences between healthy and scoliotic VB veins can therefore be investigated. Methods. 20 healthy adolescent controls and 21 AIS patients were recruited (with ethics approval) to undergo 3D MRI, using a 3 Tesla, T1-weighted 3D gradient echo sequence, resulting in 512 slices across the thoraco-lumbar spine, with a voxel size of 0.5x0.5x0.5mm. Using Amira Filament Editor, five transverse slices through the VB were examined simultaneously and the resulting observable vascular network traced. Each VB was assessed, and a vascular network recorded when observable. A local coordinate system was created in the centre of each VB and the vascular networks aligned to this. The length of the vascular network on the left and right sides (with a small central region) of the VB was calculated, and the spatial patterning of the networks assessed level-by-level within each subject. Results. An average of 6 (range 4-10) vascular networks, consistent with descriptions of the basivertebral vein, were identifiable within each subject, most commonly between T10-L1. Differences were seen in the left/right distribution of vessels in the control and AIS subjects. Healthy controls saw a percentage distribution of 29:18:53 across the left:centre:right regions respectively, whereas the AIS subjects had a slightly shifted distribution of 33:25:42. The control group showed consistent spatial patterning of the vascular networks across most levels, but this was not seen in the AIS group. Conclusion. Observation and quantification of the basivertebral vein in vivo is possible using 3D MRI. The AIS group lacked the spatial pattern repetition seen in the control group and minor differences were seen in the left/right distribution of vessels.

Sequential MRI of growing scoliotic spines reveals individual level deformities that are clinically masked by the cobb angle

INTRODUCTION. Clinically, the Cobb angle method measures the overall scoliotic curve in the coronal plane but does not measure individual vertebra and disc wedging. The contributions of the vertebrae and discs in the growing scoliotic spine were measured to investigate coronal plane deformity progression with growth. METHODS. A 0.49mm isotropic 3D MRI technique was developed to investigate the level-by-level changes that occur in the growing spine of a group of Adolescent Idiopathic Scoliosis (AIS) patients, who received two to four sequential scans (spaced 3-12 months apart). The coronal plane wedge angles of each vertebra and disc in the major curve were measured to capture any changes that occurred during their adolescent growth phase. RESULTS. Seventeen patients had at least two scans. Mean patient age was 12.9 years (SD 1.5 years). Sixteen were classified as right-sided major thoracic Lenke Type 1 (one left sided). Mean standing Cobb angle at initial presentation was 31° (SD 12°). Six received two scans, nine three scans and two four scans, with 65% showing a Cobb angle progression of 5° or more between scans. Overall, there was no clear pattern of deformity progression of individual vertebrae and discs, nor between patients who progressed and those who didn’t. There were measurable changes in the wedging of the vertebrae and discs in all patients. In sequential scans, change in direction of wedging was also seen. In several patients there was reverse wedging in the discs that counteracted increased wedging of the vertebrae such that no change in overall Cobb angle was seen. CONCLUSION. Sequential MRI data showed complex patterns of deformity progression. Changes to the wedging of individual vertebrae and discs may occur in patients who have no increase in Cobb angle measure; the Cobb method alone may be insufficient to capture the complex mechanisms of deformity progression.

Sequential MRI reveals individual level deformities in the growing scoliotic spine that are not seen clinically by the cobb angle

Clinically, the Cobb angle method measures the overall scoliotic curve in the coronal plane but does not measure individual vertebra and disc wedging. The contributions of the vertebrae and discs in the growing scoliotic spine were measured to investigate coronal plane deformity progression with growth. Sequential MRI data in this project showed complex patterns of deformity progression. Changes to the wedging of individual vertebrae and discs may occur in patients who have no increase in Cobb angle measure; the Cobb method alone may be insufficient to capture the complex mechanisms of deformity progression.

Fourier spectral methods for fractional-in-space reaction-diffusion equations

Fractional differential equations are becoming increasingly used as a powerful modelling approach for understanding the many aspects of nonlocality and spatial heterogeneity. However, the numerical approximation of these models is demanding and imposes a number of computational constraints. In this paper, we introduce Fourier spectral methods as an attractive and easy-to-code alternative for the integration of fractional-in-space reaction-diffusion equations described by the fractional Laplacian in bounded rectangular domains ofRn. The main advantages of the proposed schemes is that they yield a fully diagonal representation of the fractional operator, with increased accuracy and efficiency when compared to low-order counterparts, and a completely straightforward extension to two and three spatial dimensions. Our approach is illustrated by solving several problems of practical interest, including the fractional Allen–Cahn, FitzHugh–Nagumo and Gray–Scott models, together with an analysis of the properties of these systems in terms of the fractional power of the underlying Laplacian operator.

Fractional diffusion models of cardiac electrical propagation: Role of structural heterogeneity in dispersion of repolarization

Impulse propagation in biological tissues is known to be modulated by structural heterogeneity. In cardiac muscle, improved understanding on how this heterogeneity influences electrical spread is key to advancing our interpretation of dispersion of repolarization. We propose fractional diffusion models as a novel mathematical description of structurally heterogeneous excitable media, as a means of representing the modulation of the total electric field by the secondary electrical sources associated with tissue inhomogeneities. Our results, analysed against in vivo human recordings and experimental data of different animal species, indicate that structural heterogeneity underlies relevant characteristics of cardiac electrical propagation at tissue level. These include conduction effects on action potential (AP) morphology, the shortening of AP duration along the activation pathway and the progressive modulation by premature beats of spatial patterns of dispersion of repolarization. The proposed approach may also have important implications in other research fields involving excitable complex media.

Imaging tumour distribution of a polymeric drug delivery platformin vivoby PET-MRI

Background Over the past decade, molecular imaging has played a key role in the progression of drug delivery platforms from concept to commercialisation. Of the molecular imaging techniques commonly utilised, positron emission tomography (PET) can yield a breadth of information not easily accessible by other methodologies and when combined with other complementary imaging modalities, is a powerful tool for pre- and clinical development of therapeutics. However, very little research has focussed on the information available from complimentary imaging modalities. This paper reports on the data-rich methodologies of contrast enhanced PET/CT and PET/MRI for probing efficacy of polymer drug delivery platforms. Results The information available from an ExiTron nano 6000 contrast enhanced PET/CT and a gadolinium (Gd) enhanced PET/MRI image of a 64Cu labeled HBP in the same mouse was qualitatively compared. Conclusions Gd contrast enhanced PET/MRI offers a powerful methodology for investigating the distribution of polymer drug delivery platforms in vivo and throughout a tumour volume. Furthermore, information about depth of penetration away from primary blood vessels can be gleaned, potentially leading to development of more efficacious delivery vehicles for clinical use.

Determination of diffusion parameters and activation energy of diffusion in V3Si phase with A15 crystal structure

Diffusion such is the integrated diffusion coefficient of the phase, the tracer diffusion coefficient of species at different temperatures and the activation energy for diffusion, are determined in V3Si phase with A15 crystal structure. The tracer diffusion coefficient of Si Was found to be negligible compared to the tracer diffusion coefficient of V. The calculated diffusion parameters will help to validate the theoretical analysis of defect structure of the phase, which plays an important role in the superconductivity.

Molecular theory for the effects of specific solute-solvent interaction on the diffusion of a solute particle in a molecular liquid

An understanding of the effect of specific solute-solvent interactions on the diffusion of a solute probe is a long standing problem of physical chemistry. In this paper a microscopic treatment of this effect is presented. The theory takes into account the modification of the solvent structure around the solute due to this specific interaction between them. It is found that for strong, attractive interaction, there is an enhanced coupling between the solute and the solvent dynamic modes (in particular, the density mode), which leads to a significant increase in the friction on the solute. The diffusion coefficient of the solute is found to depend strongly and nonlinearly on the magnitude of the attractive interaction. An interesting observation is that specific solute-solvent interaction can induce a crossover from a sliplike to a sticklike diffusion. In the limit of strong attractive interaction, we recover a dynamic version of the solvent-berg picture. On the other hand, for repulsive interaction, the diffusion coefficient of the solute increases. These results are in qualitative agreement with recent experimental observations.

Stability of a Random Diffusion with Linear Drift

We consider a Linear system with Markovian switching which is perturbed by Gaussian type noise, If the linear system is mean square stable then we show that under certain conditions the perturbed system is also stable, We also shaw that under certain conditions the linear system with Markovian switching can be stabilized by such noisy perturbation.

Interdiffusion and Growth of the Superconductor Nb3Sn in Nb/Cu(Sn) Diffusion Couples

The confusion over the growth rate of the Nb3Sn superconductor compound following the bronze technique is addressed. Furthermore, a possible explanation for the corrugated structure of the product phase in the multifilamentary structure is discussed. Kirkendall marker experiments are conducted to study the relative mobilities of the species, which also explains the reason for finding pores in the product phase layer. The movement of the markers after interdiffusion reflects that Sn is the faster diffusing species. Furthermore, different concentrations of Sn in the bronze alloy are considered to study the effect of Sn content on the growth rate. Based on the parabolic growth constant at different temperatures, the activation energy for the growth is determined.

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.

A follow up MRI-based geometry and computational fluid dynamics study of carotid bifurcation

Cardiovascular disease is the leading causes of death in the developed world. Wall shear stress (WSS) is associated with the initiation and progression of atherogenesis. This study combined the recent advances in MR imaging and computational fluid dynamics (CFD) and evaluated the patient-specific carotid bifurcation. The patient was followed up for 3 years. The geometry changes (tortuosity, curvature, ICA/CCA area ratios, central to the cross-sectional curvature, maximum stenosis) and the CFD factors (Velocity distribute, Wall Shear Stress (WSS) and Oscillatory Shear Index (OSI)) were compared at different time points.The carotid stenosis was a slight increase in the central to the cross-sectional curvature, and it was minor and variable curvature changes for carotid centerline. The OSI distribution presents ahigh-values in the same region where carotid stenosis and normal border, indicating complex flow and recirculation.The significant geometric changes observed during the follow-up may also cause significant changes in bifurcation hemodynamics.

A new method for the in vivo identification of mechanical properties in arteries from cine MRI images: Theoretical framework and validation

Quantifying the stiffness properties of soft tissues is essential for the diagnosis of many cardiovascular diseases such as atherosclerosis. In these pathologies it is widely agreed that the arterial wall stiffness is an indicator of vulnerability. The present paper focuses on the carotid artery and proposes a new inversion methodology for deriving the stiffness properties of the wall from cine-MRI (magnetic resonance imaging) data. We address this problem by setting-up a cost function defined as the distance between the modeled pixel signals and the measured ones. Minimizing this cost function yields the unknown stiffness properties of both the arterial wall and the surrounding tissues. The sensitivity of the identified properties to various sources of uncertainty is studied. Validation of the method is performed on a rubber phantom. The elastic modulus identified using the developed methodology lies within a mean error of 9.6%. It is then applied to two young healthy subjects as a proof of practical feasibility, with identified values of 625 kPa and 587 kPa for one of the carotid of each subject.

MRI-based fatigue analysis predicts plaque vulnerability: A study comparing symptomatic and asymptomatic individuals

BACKGROUND: Rupture of atheromatous plaque in the carotid artery often leads to thrombosis and subsequent stroke. The mechanism of plaque rupture is not entirely clear but is thought to be a multi-factorial process involving thinning and weakening of the fibrous cap and biomechanical stress as the trigger leading to plaque rupture. As the cardiovascular system is a classic fatigue environment, the weakening of plaque leading to rupture may be a fatigue process, which is a symptomatically quiescent but potentially progressive failure process. In this study, we used a fatigue analysis based on in vivo magnetic resonance imaging (MRI) to investigate the rupture initiation location, crack propagation path and fatigue life within plaques of asymptomatic and symptomatic individuals. METHODS: Forty non-consecutive subjects (20 symptomatic and 20 asymptomatic) underwent high-resolution multi-sequence in vivo MRI of the carotid bifurcation. Fatigue analysis was performed based on the plaque geometry derived from in vivo MRI of the carotid artery at the point of maximum stenosis. Paris’ Law in fracture mechanics is adopted to determine the fatigue crack growth rate. Incremental crack propagation was dynamically simulated based on stress distributions. Plaque initiation location, crack propagation path and fatigue cycle of symptomatic and asymptomatic individuals were compared. RESULTS: Cracks were often found to begin at the lumen wall at areas of stress concentration. The preferred rupture direction was radial from the lumen center. The crack initially advanced slowly but accelerated as it developed, depending on plaque morphology. The fatigue cycles of symptomatic plaques were significantly less than those in the asymptomatic group (2.3 ± 0.9 vs 3.1 ± 0.7 (x106); p = 0.003). CONCLUSIONS: The number of cycles to rupture in symptomatic patients was higher than those predicted in asymptomatic patients by fatigue analysis, suggesting the possibility that plaques with a less fatigue life may be more prone to be symptomatic and rupture. If further validated by large-scale longitudinal studies, fatigue analysis based on high resolution in vivo MRI could potentially act as a useful tool for risk assessment of carotid atheroma.