Atomic electron affinities and the role of symmetry between electron addition and subtraction in a corrected Koopmans approach

The essential aspects of zero-temperature grand-canonical ensemble density-functional theory are reviewed in the context of spin-density-functional theory and are used to highlight the assumption of symmetry between electron addition and subtraction that underlies the corrected Koopmans approach of Tozer and De Proft (TDP) for computing electron affinities. The issue of symmetry is then investigated in a systematic study of atomic electron affinities, comparing TDP affinities with those from a conventional Koopmans evaluation and electronic energy differences. Although it cannot compete with affinities determined from energy differences, the TDP expression yields results that are a significant improvement over those from the conventional Koopmans expression. Key insight into the results from both expressions is provided by an analysis of plots of the electronic energy as a function of the number of electrons, which highlight the extent of symmetry between addition and subtraction. The accuracy of the TDP affinities is closely related to the nature of the orbitals involved in the electron addition and subtraction, being particularly poor in cases where there is a change in principal quantum number, but relatively accurate within a single manifold of orbitals. The analysis is then extended to a consideration of the ground state Mulliken electronegativity and chemical hardness. The findings further emphasize the key role of symmetry in determining the quality of the results.

Sample sizes for lesion magnetisation transfer ratio outcomes in remyelination trials for multiple sclerosis

BACKGROUND

Enhancing remyelination in MS might improve function and protect axons from future damage. Lesion magnetisation transfer ratio (MTR) is sensitive to myelin content, and may be a useful measure for trials evaluating potential remyelinating agents.

OBJECTIVE

Estimating sample sizes required for a parallel group, placebo-controlled trial in MS using change in mean MTR of all T2lesions as a primary outcome measure.

METHODS

The primary sample size calculation was derived from data from a natural history study of relapsing remitting MS (n=18). The MTR values observed in demyelinated and remyelinated lesions in an ex vivo study were used to estimate the effect of remyelination on lesion MTR. The ex vivo data were also used to independently calculate sample sizes in order to inform the robustness of the in vivo estimates.

RESULTS

Calculations suggest that 30% remyelination of T2 lesions could be detected with 80% power in 38 (95% confidence interval 12-96) patients per arm based on the in vivo data, and in 66 per arm based on the ex vivo data.

CONCLUSION

The sample sizes derived are in a range that makes MTR a feasible outcome measure for proof-of-concept trials of putative therapies achieving remyelination in MS lesions.

Methodology of diffusion-weighted, diffusion tensor and magnetisation transfer imaging

MRI offers a number of opportunities to examine characteristics of tissue well below the spatial resolution of the imaging technique. The best known of these is diffusion imaging, which allows the production of images whose contrast reflects the ability of water molecules to move through the extravascular extracellular space. Less well-known, but increasingly important, is magnetisation transfer imaging, which produces contrast based on the ability of protons to move between the free water pool and local macromolecules. Both of these techniques offer unique information about the microscopic and molecular structure of tumour tissue. This article will briefly review the underlying theory and technical aspects associated with these imaging techniques.

Axonal damage in the making: neurofilament phosphorylation, proton mobility and magnetisation transfer in multiple sclerosis normal appearing white matter

Aims

Multiple sclerosis (MS) leaves a signature on the phosphorylation and thus proton binding capacity of axonal neurofilament (Nf) proteins. The proton binding capacity in a tissue is the major determinant for exchange between bound and free protons and thus the magnetisation transfer ratio (MTR). This study investigated whether the MTR of non-lesional white matter (NLWM) was related to the brain tissue concentration of neurofilament phosphoforms.

Methods

Unfixed post-mortem brain slices of 12 MS patients were analysed using MTR, T1 at 1.5 T. Blocks containing NLWM were processed for embedding in paraffin and inspected microscopically. Adjacent tissue was microdissected, homogenised and specific protein levels were quantified by ELISA for the Nf heavy chain (NfH) phosphoforms, glial fibrillary acidic protein (GFAP), S100B and ferritin.

Results

Averaged hyperphosphorylated NfH (SMI34) but not phosphorylated NfH (SMI35) levels were different between individual patients NLWM. The concentration of hyperphosphorylated NfH-SMI34 correlated with T1 (R = 0.70, p = 0.0114) and — inversely — with MTR (R =−0.73, p = 0.0065). NfH-SMI35 was not correlated to any of the MR indices.

Conclusions

Post-translational modifications of axonal proteins such as phosphorylation of neurofilaments occur in NLWM and may precede demyelination. The resulting change of proton mobility influences MTR and T1. This permits the in vivo detection of these subtle tissue changes on a proteomic level in patients with MS.

Longitudinal changes in magnetisation transfer ratio in secondary progressive multiple sclerosis: data from a randomised placebo controlled trial of lamotrigine

Sodium blockade with lamotrigine is neuroprotective in animal models of central nervous system demyelination. This study evaluated the effect of lamotrigine on magnetisation transfer ratio (MTR), a putative magnetic resonance imaging measure of intact brain tissue, in a group of subjects with secondary progressive multiple sclerosis (MS). In addition, the utility of MTR measures for detecting change in clinically relevant pathology was evaluated. One hundred seventeen people attending the National Hospital for Neurology and Neurosurgery or the Royal Free Hospital, London, UK, were recruited into a double-blind, parallel-group trial. Subjects were randomly assigned by minimisation to receive lamotrigine (target dose 400 mg/day) or placebo for 2 years. Treating and assessing physicians and patients were masked to treatment allocation. Results of the primary endpoint, central cerebral volume, have been published elsewhere. Significant differences between the verum and placebo arms were seen in only two measures [normal appearing grey matter (NAGM) p = 0.036 and lesion peak height (PH) p = 0.004], and in both cases there was a greater reduction in MTR in the verum arm. Significant correlations were found of change in MS functional composite with all MTR measures except lesion and normal appearing white matter (NAWM) PH. However, the change in MTR measures over 2 years were small, with only NAGM mean (p = 0.001), lesion peak location (p = 0.11) and mean (p < 0.0001) changing significantly from baseline. These data did not show that lamotrigine was neuroprotective. The clinical correlation of MTR measures was consistent, but the responsiveness to change was limited.

Magnetization transfer ratio abnormalities reflect clinically relevant grey matter damage in multiple sclerosis

BACKGROUND

In multiple sclerosis, grey matter (GM) damage appears more clinically relevant than either white matter damage or lesion load.

OBJECTIVE

We investigated if normal-appearing white matter (NAWM) and grey matter tissue changes assessed by magnetization transfer ratio were associated with long-term disability.

METHODS

Sixty-nine people were assessed 20 years after presentation with a clinically isolated syndrome (CIS) [28 still CIS, 31 relapsing-remitting multiple sclerosis, 10 secondary progressive multiple sclerosis], along with 19 healthy subjects. Mean magnetization transfer ratio, peak height (PH) and peak location of the normalized magnetization transfer ratio histograms were determined in NAWM and grey matter, as well as, white matter and GM Fraction (GMF) and T(2)-weighted lesion load.

RESULTS

Median expanded disability status scale for multiple sclerosis patients was 2.5 (range 1-8). GM-PH, and less so, NAWM mean and peak location, were lower in multiple sclerosis patients (P = 0.009) versus controls, relapsing-remitting multiple sclerosis versus CIS (P = 0.008) and secondary progressive multiple sclerosis versus relapsing-remitting multiple sclerosis (P = 0.002). GM-PH (as well as GMF) correlated with expanded disability status scale (r(s) = -0.49; P = 0.001) and multiple sclerosis functional score (r(s) = 0.51; P = 0.001). GM-PH independently predicted disability with similar strength to the associations of GMF with clinical measures.

CONCLUSION

Grey matter damage was related to long-term disability in multiple sclerosis cohort with a relatively low median expanded disability status scale. Markers of intrinsic grey matter damage (magnetization transfer ratio) and tissue loss offer clinically relevant information in multiple sclerosis.

Grey matter magnetization transfer ratio independently correlates with neurological deficit in secondary progressive multiple sclerosis

Although there is substantial brain grey matter pathology in secondary progressive multiple sclerosis (MS), there has been limited investigation of its contribution to disability.This study investigated the correlation of magnetization transfer ratio (MTR) measures taken from brain grey matter, normal appearing white matter (NAWM) and lesions with neurological deficit and disability in 113 people with secondary progressive MS. In order to adjust for the potential effects of focal white matter lesions and global brain atrophy, T2 lesion volume and normalized brain volume (NBV) were also calculated for each subject. Clinical measures included the expanded disability status scale (EDSS) and the multiple sclerosis functional composite (MSFC) scores. Linear regression analysis was used to assess the age- and gender-adjusted correlation of MTR histogram mean, peak height and peak location with the MSFC and individual component measures. Logistic regression analysis was used to determine whether imaging measures could be used to predict if subjects were in the higher disability group (EDSS > or = 6.5).Significant correlations were detected between MSFC composite and mean MTR in (i) normal appearing white matter (NAWM; r = 0.327, p < 0.0001), (ii) grey matter (r = 0.460, p < 0.0001) and (iii) lesions (r = 0.394, p < 0.0001). Although NBV and T2 lesion volume correlated significantly with MSFC, grey matter histogram mean emerged as the best predictor of MSFC score. None of the MRI measures significantly predicted higher EDSS.These results suggest that brain grey matter pathology plays an important role in determining neurological impairment. The apparent paucity of correlation between MRI measures and EDSS is likely to represent the relative insensitivity of the latter measure in this study group.

Magnetization transfer ratio in Alzheimer disease: comparison with volumetric measurements

BACKGROUND AND PURPOSE

Alzheimer disease (AD) is accompanied by macroscopic atrophy on volumetric MR imaging. A few studies have also demonstrated reduction in magnetization transfer ratio (MTR), suggesting microstructural changes in remaining brain tissue. This study assessed the value of measuring MTR in addition to volumetric MR in differentiating patients with AD from control subjects.

MATERIALS AND METHODS

Volumetric T1-weighted images and 3D MTR maps were obtained from 18 patients with AD and 18 age-matched control subjects. Whole-brain (WB) and total hippocampal (Hc) volumes were measured using semiautomated techniques and adjusted for total intracranial volume. Mean MTR was obtained for WB and in the Hc region. Histogram analysis was performed for WB MTR. Among patients, associations between volumetric and MTR parameters and the Mini-Mental State Examination (MMSE) were explored.

RESULTS

Patients with AD had significantly reduced WB volume (P<.0001) and mean WB MTR (P=.002) and Hc volume (P<.0001) and Hc mean MTR (P<.0001) compared with control subjects. Histogram analysis of WB MTR revealed significant reduction in the 25th percentile point in patients with AD (P=.03). Both WB volume and mean MTR were independently associated with case-control status after adjusting for the other using linear regression models. However, measuring Hc mean MTR added no statistically significant discriminatory value over and above Hc volume measurement alone. Of all MR imaging parameters, only WB volume was significantly correlated with MMSE (r=0.47, P=.048).

CONCLUSIONS

This study demonstrates the independent reduction of WB volume and mean MTR in AD. This suggests that the 2 parameters reflect complementary aspects of the AD pathologic lesion at macrostructural and microstructural levels.

Sources of variation in multi-centre brain MTR histogram studies: body-coil transmission eliminates inter-centre differences

OBJECT

1. Identify sources of variation affecting Magnetisation Transfer Ratio (MTR) histogram reproducibility between-centres. 2. Demonstrate complete elimination of inter-centre difference.

MATERIALS AND METHODS

Six principle sources of variation were summarised and analysed. These are: the imager coil used for radiofrequency (RF) transmission, imager stability, the shape and other parameters describing the Magnetisation Transfer (MT) pulse, the MT sequence used (including its parameters), the image segmentation methodology, and the histogram generation technique. Transmit field nonuniformity and B1 errors are often the largest factors. PLUMB (Peak Location Uniformity in MTR histograms of the Brain) plots are a convenient way of visualising differences. Five multi-centres studies were undertaken to investigate and minimise differences.

RESULTS

Transmission using a body coil, with a close-fitting array of surface coils for reception, gave the best uniformity. Differences between two centres, having MR imagers from different manufacturers, were completely eliminated by using body coil excitation, making a small adjustment to the MT pulse flip angle, and carrying out segmentation at a single centre. Histograms and their peak location and height values were indistinguishable.

CONCLUSIONS

Body coil excitation is preferred for multi-centre studies. Analysis (segmentation and histogram generation) should ideally be carried out at a single site.

Neoadjuvant chemotherapy in breast cancer: early response prediction with quantitative MR imaging and spectroscopy

A prospective study was undertaken in women undergoing neoadjuvant chemotherapy for locally advanced breast cancer in order to determine the ability of quantitative magnetic resonance imaging (MRI) and proton spectroscopy (MRS) to predict ultimate tumour response (percentage decrease in volume) or to detect early response. Magnetic resonance imaging and MRS were carried out before treatment and after the second of six treatment cycles. Pharmacokinetic parameters were derived from T₁-weighted dynamic contrast-enhanced MRI, water apparent diffusion coefficient (ADC) was measured, and tissue water : fat peak area ratios and water T₂ were measured using unsuppressed one-dimensional proton spectroscopic imaging (30 and 135 ms echo times). Pharmacokinetic parameters and ADC did not detect early response; however, early changes in water : fat ratios and water T₂ (after cycle two) demonstrated substantial prognostic efficacy. Larger decreases in water T₂ accurately predicted final volume response in 69% of cases (11/16) while maintaining 100% specificity and positive predictive value. Small/absent decreases in water : fat ratios accurately predicted final volume non-response in 50% of cases (3/6) while maintaining 100% sensitivity and negative predictive value. This level of accuracy might permit clinical application where early, accurate prediction of non-response would permit an early change to second-line treatment, thus sparing patients unnecessary toxicity, psychological morbidity and delay of initiation of effective treatment.

Magnetization transfer histograms in clinically isolated syndromes suggestive of multiple sclerosis

In established multiple sclerosis, magnetization transfer ratio (MTR) histograms reveal abnormalities of normal-appearing white matter (NAWM) and grey matter (NAGM). The aim of this study was to investigate for such abnormalities in a large cohort of patients presenting with clinically isolated syndromes suggestive of multiple sclerosis. Magnetization transfer imaging was performed on 100 patients (67 women, 33 men, median age 32 years) a mean of 19 weeks (SD 3.8, range 12-33 weeks) after symptom onset with a clinically isolated syndrome and in 50 healthy controls (34 women, 16 men, median age 32.5 years). SPM99 software was used to generate segmented NAWM and NAGM MTR maps. The volumes of T2 lesions, white matter and grey matter were calculated. Eighty-one patients were followed up clinically and with conventional MRI after 3 years (n = 61) or until they developed multiple sclerosis if this occurred sooner (n = 20). Multiple regression analysis was used to investigate differences between patients and controls with age, gender and volume measures as covariates to control for potential confounding effects. The MTR histograms for both NAWM and NAGM showed a reduction in the mean (NAWM, 38.14 versus 38.33, P = 0.001; NAGM 32.29 versus 32.50, P = 0.009; units in pu) and peak location, with a left shift in the histogram. Mean NAWM and NAGM MTR were also reduced in the patients who developed clinically definite multiple sclerosis and multiple sclerosis according to the McDonald criteria but not in the 24 patients with normal T2-weighted brain magnetic resonance imaging (MRI). MTR abnormalities occur in the NAWM and NAGM at the earliest clinical stages of multiple sclerosis.

Estimation of the macromolecular proton fraction and bound pool T2 in multiple sclerosis

This study used a model for magnetization transfer (MT) to estimate two underlying parameters: the macromolecular proton fraction (f) and the bound pool T2 (T2b) in patients with multiple sclerosis (MS). Sixty patients with clinically definite MS and 27 healthy controls were imaged using: (1) a dual echo fast spin echo sequence, (2) a MT sequence (with ten MT power and offset frequency combinations) and (3) proton density and T1 weighted sequences (for T1 relaxation time estimation). Fourteen normal-appearing white matter (NAWM) regions of interest (ROI) and six normal-appearing gray matter (NAGM) ROIs were outlined in all subjects. Lesions were also contoured in subjects affected by MS. The model was fitted to the data leading to estimates of T2b and f. Results showed that T2b was increased in lesions whereas f was reduced. In NAWM, f was decreased while T2b was only increased in secondary progressive MS. NAWM f correlated modestly with disability. Further studies are needed to investigate the pathological basis of the abnormalities observed.

Correlation of apparent myelin measures obtained in multiple sclerosis patients and controls from magnetization transfer and multicompartmentalT2 analysis

Two relatively new techniques purport to give measures of the myelin content of brain tissue. These measures are the myelin water fraction from multicompartmental T(2) analysis, and the semisolid proton fraction from analysis of magnetization transfer (MT). The myelin water fraction is the fraction of signal with a T(2) of less than 50 ms measured from a 32-echo sequence. It is believed to originate from water trapped between the myelin bilayers. The semisolid proton fraction is thought to include protons within phospholipid bilayers and macromolecular protons, and may also be a measure of myelin content. Multicompartmental T(2) and MT imaging were carried out on controls and patients with multiple sclerosis (MS), and estimates of the semisolid proton and myelin water fractions were obtained from white matter (WM), gray matter (GM), and MS lesions. These were then correlated for each tissue and subject group. Positive correlations were seen for MS lesions (r approximately 0.2) and in WM in patients (r = 0.6). A negative correlation (r approximately -0.3) was seen for GM. These results indicate that the two techniques measure, to some extent, the same thing (most likely myelin content), but that other factors, such as inflammation, mean they may provide complementary information.

Preliminary magnetic resonance study of the macromolecular proton fraction in white matter: a potential marker of myelin?

We report on a new quantitative magnetization transfer (MT) technique that allows for the in vivo estimation of the macromolecular proton fraction (f) and the bound pool T2 relaxation time (T2b), whilst permitting whole brain coverage. In this pilot study, five subjects with multiple sclerosis (MS) and five healthy controls were studied. Both f and T2b were significantly different between MS lesions and normal control white matter (WM). Relationships between f and T1 relaxation time [Spearmans rank correlation coefficient (r(s)) = -0.97, P < 0.001] and f and the magnetization transfer ratio (MTR; r(s) = 0.80, P < 0.001) were observed. Compared with MTR, f and T2b have the potential advantage of relative independence from MT acquisition protocol while offering more pathologically specific information. In particular, f may provide a more direct indication of myelin content in WM.

Comparison of quantitative T2 mapping and diffusion-weighted imaging in the normal and pathologic prostate

In this study, diffusion-weighted images of the human prostate were successfully obtained, enabling quantification of apparent diffusion coefficients (ADCs) in normal and pathologic regions. A dual acquisition fast spin-echo sequence was used for accurate T2 calculation. T2 values were significantly higher in the peripheral zone than the central gland (P = 0.015). No significant correlations were found in either normal or pathologic tissue between ADC values and relaxation rates for all three gradient directions and the orientationally averaged water diffusion coefficient. Evidence suggesting that diffusional anisotropy is present in normal prostatic tissue is also detailed, with significant differences noted between the z-component and both the x- and y-components of the ADC for peripheral zone (P < 0.040) and central gland (P < 0.001).

Experimental assessment of lanthanide ion donor preference: spectroscopic and theoretical dissection of static charge and dynamic polarisation contributions to axial ligation in a C4-symmetric chiral europium complex

Measurements of the equilibrium constants for ligand exchange (MeCN, 295 K) involving the axial donor in a C4-symmetric, mono-capped, square antiprismatic cationic Eu complex, supported by calculations based on an electrostatic perturbation model, have been interpreted in terms of a predominant ligand polarisation interaction defined by observation of the hypersensitive delta J = 2 normalised emission intensity, in association with measurements correlating delta J = 1 band splitting and 1H NMR dipolar shifts that vindicate Bleaney's theory of magnetic anisotropy.

Bilateral open breast coil and compatible intervention device

Dynamic contrast-enhanced breast MRI is an extremely sensitive method for breast lesion detection. For MR-only detected lesions it is essential that needle biopsy or localization prior to surgery is carried out under MR guidance. This work describes a bilateral open breast coil and prototype intervention device, which may be used in these situations. Results demonstrate that the open coil provides images superior to those obtained with a conventional closed breast coil. Initial phantom tests with the intervention device indicate a potential for this system to be used in the MR-guided localization of breast lesions. J. Magn. Reson. Imaging 2000;12:984-990.

A simple and realistic tissue-equivalent breast phantom for MRI

A simple and inexpensive breast phantom is described for use in magnetic resonance imaging. The work demonstrates the similarity of the phantom materials to in vivo breast tissue in terms of T(1) relaxation times. The phantom is also qualitatively compared with images acquired from a patient with a primary breast lesion.J. Magn. Reson. Imaging 10:968-971, 1999.