Average FA Research Articles

Abstract T P113: Structural Changes In The Corticospinal Tract After 10 Days Of Combined Physical Therapy And Transcranial Direct Current Stimulation

A few studies have shown that long-term skill acquisition can lead to changes in white matter tracts. Studies examining structural changes in the corticospinal tract in patients recovering from a stroke have yielded mixed results. The current study examines whether 10 days of combined physical therapy (PT) and non-invasive brain-stimulation (using dual transcranial direct current stimulation) can lead to changes in the corticospinal tract (CST) on the affected hemisphere. Seven stroke patients participated in an intense 10-day long treatment of physical therapy (1 hour/day) and tDCS (30 minutes per session) with anodal stimulation applied over the affected motor cortex and cathodal stimulation over the unaffected motor cortex. Each patient also underwent Fugl-Meyer assessments (UE-FM) and diffusion tensor imaging (DTI) before and after the treatment phase. A control group of seven patients were also scanned at two time points and assessed without any intervening therapy. The DTI images were processed using the standard algorithms provided by FSL and normalized to FSL's FA template. We used a section of the CST derived from the JHU atlas, between the internal capsule (below each patient’s lesion) and upper brain stem as our region of interest to extract FA and other diffusivity values before and after therapy. All patients showed an increase in proportional UE-FM scores (+21%; SD 10%) and an increase in average FA (+0.013; SD 0.01) of the descending CST below the lesion after the intervention and no significant change was seen in the patient that were assessed two times but had no treatment. In addition, we found a strong correlation between the change in FA and a proportional improvement in the UE-FM score (r=0.689). These findings support the notion that focal white matter changes can be detected with DTI and that an intense course of an experimental treatment (2x5 days of combined PT+tDCS) induced structural changes in the descending CST that were not seen in patients scanned twice without treatment.

Obesity gene NEGR1 associated with white matter integrity in healthy young adults

Obesity is a crucial public health issue in developed countries, with implications for cardiovascular and brain health as we age. A number of commonly-carried genetic variants are associated with obesity. Here we aim to see whether variants in obesity-associated genes – NEGR1, FTO, MTCH2, MC4R, LRRN6C, MAP2K5, FAIM2, SEC16B, ETV5, BDNF-AS, ATXN2L, ATP2A1, KCTD15, and TNN13K – are associated with white matter microstructural properties, assessed by high angular resolution diffusion imaging (HARDI) in young healthy adults between 20 and 30years of age from the Queensland Twin Imaging study (QTIM). We began with a multi-locus approach testing how a number of common genetic risk factors for obesity at the single nucleotide polymorphism (SNP) level may jointly influence white matter integrity throughout the brain and found a wide spread genetic effect. Risk allele rs2815752 in NEGR1 was most associated with lower white matter integrity across a substantial portion of the brain. Across the area of significance in the bilateral posterior corona radiata, each additional copy of the risk allele was associated with a 2.2% lower average FA. This is the first study to find an association between an obesity risk gene and differences in white matter integrity. As our subjects were young and healthy, our results suggest that NEGR1 has effects on brain structure independent of its effect on obesity.

Fractional anisotropy asymmetry and the side of seizure origin for partial onset-temporal lobe epilepsy

This paper presents a fractional anisotropy asymmetry (FAA) method to detect the asymmetry of white matter (WM) integrity and its correlation with the side of seizure origin for partial onset temporal lobe epilepsy (TLE) using diffusion tensor image (DTI). In this study, FAA analysis is applied to 30 patients of partial TLE (15 left, 15 right) and 14 matched normal controls. Specifically, after registering all the images with the JHU-DTI-MNI template the average FA value of each FA skeleton section is calculated using the tract-based spatial statistics (TBSS) method. Then, FAA is calculated to quantify the WM diffusivity asymmetry of the corresponding region-pairs between the left and right hemispheres. Using FAA the regional asymmetry contributing significantly to the group differences of controls and left/right TLE, as well as the left and right TLE, is identified. As a comparison, the ROI-based average FA values for WM and corresponding FAAs are also calculated. TBSS-based analysis reflects the average of local maximal FA values along the white matter skeleton sections, and ROI-based analysis shows the average of WM FA values within each anatomical region. The FAA statistical results indicated that the FA values of anatomical region-pairs are asymmetric in the ipsilateral hemisphere with seizure origin against the contralateral hemisphere. Particularly, FAA values within the temporal lobe (superior, middle, and inferior temporal WM) are significantly different between the left and right TLE patients, consistently found from both analysis methods. The study suggests that FAA values can be potentially used to identify the seizures of origin of TLE and to help understand the relationship between fiber tracts with the side of seizure origin of TLE.

Entanglement Teleportation via One Dissipative Quantum Channel

Entanglement teleportation via one dissipative quantum channel composed by two identical spatially separated atoms in free space is investigated in detail. We mainly study the effects about the channel initial states and the interqubit distance on the entanglement of the output state Cout and the average fidelity Fa. It is shown that the magnitude of teleportated entanglement and the average fidelity is strongly dependent on the above factors. For different channel initial states with increasing input entanglement, the teleportated entanglement is zero initially, but at some finite values the teleportated entanglement emerges, and it then increase linearly as these finite input entanglement values are reached. We also obtain that the interqubit distance enhance the teleportated entanglement and the average fidelity peridicly, so we can find a threshold value of the interqubit distance which is most suitable for entanglement teleportation. Meanwhile, the values of the teleportated entanglement and the average fidelity are always zero when the value of the interqubit distance is zero.

Inter-centre reproducibility of cardiac diffusion tensor measures

the left ventricle were manually drawn, and the average ADC and FA calculated, giving four measures per subject (ADC and FA in systole and diastole). Inspection of the data revealed that they were non-normally distributed, so Friedman’s repeated measures test as implemented in the R agricolae package (R Foundation, Vienna, Austria) was used, with Holm-corrected Fisher’s LSD for post hoc testing. The two centres were deemed the same if p > 0.1. Results Initial results showed statistically significant differences between almost all variables, and the post-hoc analysis indicated that these disparities were driven by differences in the analysis. Therefore the analysis was re-run using only ROIs defined by centre A on all data, the results of which are shown in Table 1. These showed no significant differences between the metrics at the two centres. Example ADC and FA maps for one subject are shown in Figure 1. Conclusions

Coenzyme Q10 oral bioavailability: effect of formulation type

Coenzyme Q10 (Q10) has a poor bioavailability due to its very low aqueous solubility and high molecular weight. The purpose of this review is to discuss the different types of Q10 drug delivery systems (DDS) ranging from the simple oily dispersions to the nanotechnology-oriented systems such as nanocrystals, self-nanoemulsified drug delivery systems, etc. to overcome the solubility issue. The basics of these approaches were discussed in relationship to the effect of Q10 absorption. For that purpose, the percentage of the drug absorbed to the blood stream out of the administered dose was calculated as the fraction absorbed (Fa%). The Fa% for the nanoemulsions discussed in this article did not correlate with droplet size. In human studies most of the delivery systems had a low Fa% being in the range from 1.53 to 12.48 %. The highest Fa% value was found to be for the self-emulsified drug delivery systems (SEDDS). In dogs studies, the Fa% values ranged between 0.28 (cyclodextrin complex) and 4.8 %. In rat studies, some other DDS like emulsions and solubilized formulations showed Fa% of around 0.22 %. The relationship between the average Fa% in rats, dogs and humans was found to be 1:15:20. One recent study applied both oral and intravenous delivery of Q10; the orally tested SEDDS formulation had an absolute bioavailability of 2.2 % corresponding to Fa% = 0.04 %. The studies with Q10 formulations based only on in vitro data were also discussed and assessed regarding the influence of formulation on solubility, release and/or uptake.

Entanglement Teleportation Via Two-Qubit Channel Under the Non-Markovian Environment

Entanglement teleportation via a two-qubit quantum channel under the non-Markovian environment is investigated in detail. We mainly concentrate on the effects about the channel initial states and decoherence environment on the entanglement of the output state C out and the average fidelity F a. It is shown that for different channel initial states with increasing noise environment parameters the teleportated entanglement is initially decreased from the maximum value to a minimum value and then undergoes a increasing tendency finally to be one constant nonzero value. The average fidelity is strongly dependent on the channel initial states and the Non-Markovian environment, tuning these parameters can make the average fidelity larger than the maximum value of classical communication 2/3. Moreover, there is a threshold time t c , when t<t c the average fidelity is always superior to 2/3, tuning the environment parameters and channel initial states not only can make F a superior to 2/3 but also can broaden the region where F a is larger than 2/3. We also obtain the analytic solution values of t c in the limit case of γ→∞ where the non-Markovian environment reduced to the Markovian one.

Fluctuating Asymmetry as Risk Marker for Stress and Structural Defects in a Toxicologic Experiment

Fluctuating asymmetry (the directionally random asymmetry of bilateral structures, FA) is commonly used as a measure of developmental instability, and may increase with stress. As several studies reported a relation between FA and developmental abnormalities, we investigate whether FA could be an additional perhaps more sensitive marker of developmental toxicity. The aim of this work is analyzing patterns of FA in multiple traits in a large dataset of rabbit fetuses, which were prenatally exposed to a toxic compound and sacrificed just before natural delivery. Gravid females were exposed to three doses of this compound, inducing abnormalities in the fetuses at the high dose only. The average FA, however, was already higher than control in rabbit fetuses of the low-dose group but did not further increase with higher concentrations. Moreover, the increase in FA differed between traits, with the hindlimbs showing the strongest response. In addition, we did not find any association between FA and the presence of fetal abnormalities at the individual level. Although these results suggest that FA may act as "an early warning system," we did not find a dose-response relationship with increasing stress and effects were trait-specific. Further testing is needed before FA may be considered as a sensitive marker in developmental toxicity studies.

Functional Homotopic Changes in Multiple Sclerosis with Resting-State Functional MR Imaging

CC is extensively involved in MS with interhemispheric dysfunction. The purpose of this study was to determine whether interhemispheric correlation is altered in MS by use of a recently developed RS-fMRI homotopy technique and whether these homotopic changes correlate with CC pathology. Twenty-four patients with relapsing-remitting MS and 24 age-matched healthy volunteers were studied with RS-fMRI and DTI acquired at 3T. The Pearson correlation of each pair of symmetric interhemispheric voxels of RS-fMRI time-series data was performed to compute VMHC, and z-transformed for subsequent group-level analysis. In addition, 5 CC segments in the midsagittal area and DTI-derived FA were measured to quantify interhemispheric microstructural changes and correlate with global and regional VMHC in MS. Relative to control participants, patients with MS exhibited an abnormal homotopic pattern with decreased VMHC in the primary visual, somatosensory, and motor cortices and increased VMHC in several regions associated with sensory processing and motor control including the insula, thalamus, pallidum, and cerebellum. The global VMHC correlates moderately with the average FA of the entire CC for all participants in both groups (r = 0.3; P = .03). Our data provide preliminary evidence of the potential usefulness of VMHC analyses for the detection of abnormalities of interhemispheric coordination in MS. We demonstrated that the whole-brain homotopic RS-fMRI pattern was altered in patients with MS, which was partially associated with the underlying structural degenerative changes of CC measured with FA.

202 Diffusion Tensor Imaging Changes with Decompression of Chiari I Malformation

Methods Subjects: We retrospectively reviewed MR studies obtained as part of clinical scans for 112 children who had Chiari I decompression surgery from Jan 2009 till Dec 2011 at Seattle Children Hospital. We excluded 101 patients due following criteria: age less than 24 months (1), missing paired pre or post op DTI images, unacceptable quality of DTI due to protocol, scanner coil difference or imaging artifacts. This resulted in as homogeneous a sample as possible; 11 patients with MR before and after posterior fossa decompression of Chiari I malformations. MR Imaging Data Acquisition and Analysis Imaging was performed on Trio and Allegra magnets (Siemens, Germany) by using phased array coils. Standard clinical imaging included a sagittal T1, axial T2, CINE. DTI used a single-shot echo-planar imaging sequence (b-values: 0, 1000 s/mm2; 10 gradientencoding directions; matrix size of 128 X 128 with 1.8 X 1.8 mm in-plane resolution; slice thickness: 3.5 mm). FSL was used for DTI data processing (2, 3). First, a tensor model fitted to the raw diffusion data created FA images, followed by brain extraction. Nonlinear registration was used to align all subjects' FA data into a common space. Tract Bases Spatial Statistics (TBSS) (2) analysis was used to perform voxel wise statistical analysis. Paired t-tests between pre and post-operative scans were performed to obtain statistical parametric maps for FA and ADC. Multiple comparison correction was performed by using the threshold-free cluster enhancement option. We also applied Region of Interest (ROI) analysis of DTI parameters. Average FA and ADC values of were estimated for Middle, Superior and Inferior Cerebellar Peduncles (MCP, SCP and ICP). FA/ADC statistical parametric maps

Thalamic Damage Predicts the Evolution of Primary-Progressive Multiple Sclerosis at 5 Years

Reliable markers to monitor PPMS are still needed. We investigated whether conventional and DTI measures of thalamic damage are predictive of long-term disability accumulation in PPMS. Brain conventional and DTI scans were obtained at baseline and after a mean follow-up of 15 months in 54 patients with PPMS and 8 healthy controls. Patients were reassessed clinically after 5 years. At baseline and follow-up, measures of lesion load, brain atrophy, and NTV were obtained. MD and FA histograms of the NAWM, the whole GM without the thalami, and the thalami were obtained. A multivariate analysis evaluated the predictors of long-term neurologic deterioration. At follow-up, 35 patients showed disability worsening. At baseline, compared with healthy controls, patients with PPMS had lower NTV (P < .001) and thalamic FA (P = .002) and higher thalamic (P = .002) and whole GM without the thalami (P = .005) MD. During follow-up, the change of thalamic FA was higher in PPMS versus healthy controls (P = .01). Baseline NTV and thalamic DTI quantities differed significantly between patients with PPMS with and without thalamic lesions. Baseline thalamic quantities were significantly correlated with the extent of brain T2 lesions and the severity of NAWM damage. The multivariate model included average NAWM MD (OR = 1.46, P = .005) and FA thalamic change (OR = 0.84, P = .02) as independent predictors of EDSS score deterioration (Nagelkerke R(2) = 0.55). Short-term accrual of thalamic damage and the severity of NAWM involvement predict the long-term accumulation of disability in PPMS.

Wheat Production and Economics

Problem statement: The crop in the irrigated scheme has faced by mani fold problems contributed to low level of productivity and high c ost of production of wheat. The crop is commonly produced under pump irrigation from the River Nile. In River Nile State (RNS), wheat is grown under the irrigated sector, the State is considered as a suitable environment for producing this crop. The s tudy was conducted at Elzeidab irrigated scheme of RNS which is regarded as the oldest and biggest scheme belonging to the Ministry of Agriculture of RNS. Approach: Primary data was collected by using structured questionnaire for (70) randomly se lected respondents. More than one technique used to assess economic aspects of the crop. Cobb-Dougla s production function, descriptive statistics and partial budgeting have been employed to analyze the primary data. The study detected that the major socioeconomic characteristics of Elzeidab farmers w ere educated, the scheme tenants have had a cumulative experience in agriculture and average fa rm size is found to be small and the majority 50% of surveyed tenants in Elzeidab scheme were rented. The farming system of Elzeidab scheme is dominated by wheat production which counts to 25% of the farm land. The yield gab with the potential yield obtained by Agricultural Research C orporation (ARC) in the State amounts 66%. The microfinance market in Elzeidab scheme is not well developed. Water charges in the scheme were high. About 53% of the annual running expenses were allocated for fuel that made irrigation costs to be the highest single component of production costs of the crop, while irrigation water cost was considered as the most agricultural constraint, thi s item was found to be as 19% of the total cost of production as the highest percentage overall the va riable cost items. Results: The regression analysis revealed that the most factors affecting w heat productivity under the study were: the average of tenants' age, family labor, distance fro m home to field, hired labor, distance of farm to source of irrigation, number of irrigation, term of irrigation. Furthermore, the weakness of wheat production normally regards as a cost issue and lac k of awareness wheat grower especially about wheat technical package. Conclusion: The study concluded that wheat production contribut e significantly to farm sustainability and contribute to alleviation of malnutrition in the State. The actual production constraints restrict the sustaina bility of this important crop. The cooperation between international organizations and governmental institutions should tackle the hindrances of wheat production and achieve stability of wheat. Th ere is a great potential for improvement the yield of the crop and an intervention of the State is nee ded to ease having the inputs of production especially irrigation water inputs.

Quantitative Fiber Tracking of the Optic Radiation Is Correlated with Visual-Evoked Potential Amplitude in Preterm Infants

Children born preterm are at risk for adverse outcome, including visual impairment. We examined the relationship between neonatal DTI and sVEP in children born preterm to determine whether visual outcomes are related to early measurements of brain microstructure. Subjects were born at <34 weeks gestation and imaged before term-equivalent age. DTI fiber tracking was used to delineate the optic radiations and measure tract-specific average FA, D(av), and parallel and transverse diffusivity. Visual-evoked response amplitudes were measured as a function of spatial frequency, contrast, and vernier offset size with sVEP at 6-20 months after birth. The association between DTI and sVEP was assessed by using the Spearman correlation coefficient and linear regression for repeated measures. Nine children with 15 scans were included. The peak response amplitudes for spatial frequency sweeps were associated with increasing FA and decreasing D(av) and transverse diffusivity (P ≤ .006) but not with parallel diffusivity (P = 1). There was only modest association with the swept contrast condition and no detectable association with the vernier offset sweeps. Microstructure of the optic radiations measured shortly after birth is associated with quantitatively measured responses elicited by moderate-to-high contrast spatiotemporal gratings in infancy. These findings are in keeping with studies showing a relationship between brain microstructure and function. While the clinical impact is not known, quantitative neuroimaging of white matter may ultimately be important for predicting outcome in preterm neonates.

Analysis of the influence of free ammonia on the accumulation of nitrite in the nitrite nitrification system

Low- and high-concentration nitric wastewater can induce stable nitrite accumulation and realize the nitrification system, with the nitrite accumulation rate between 50% and 90%. In the low-concentration nitrite nitrification system, the average FA concentrations during the period of stable nitrite accumulation remained at 7 to 10 mg/L. In the high-concentration nitrite nitrification system, the nitrogen oxidation activity will not be affected by biomass, the nitrite oxidation activity is related to the system biomass, it is recommended to be measured by FA/MLSS. Keeping the FA sludge load below 0.1 is the precondition of making good nitrite accumulation and nitrogen degradation rate. Nitrite oxidation bacteria cannot be totally eliminated or washed out from the system.

Micromagnetic calculation of dynamic susceptibility in ferromagnetic nanorings

Dynamic magnetic susceptibilities of high-aspect-ratio permalloylike nanorings (outer diameter 20 nm, inner diameter 12 nm, length (L) range 12–500 nm) are studied using three-dimensional micromagnetic simulations. The investigated systems show two major resonance modes associated with volume and shape resonance modes, corresponding to low and high resonance frequencies, respectively. When L is below 40 nm, only the shape resonance mode is seen with a frequency predicted using the Kittel’s equation and demagnetization factor calculated for a ring. At sufficiently large L, the frequency of the volume mode converges to that of the Kittel prediction. For other lengths, however, neither the low resonance frequency nor the high resonance frequency agrees with the Kittel’s equation. A weighted average resonance frequency fa(i) that contains two major modes is introduced and shows the same trend as the results predicted by the Kittel’s equation for all lengths. The frequencies of volume and shape resonance modes have also been investigated by changing the exchange stiffness constant (A) and the saturation magnetization (Ms).

A comparative study of MR diffusion tensor imaging histogram between clinically isolated syndrome and relapsing-remitting multiple sclerosis in normal appearing white matter and grey matter

Objective To investigate whether abnormalities can be detected in normal-appearing white matter(NAWM)and normal-appearing white matter(NAGM)in patients with clinically isolated syndrome(CIS)and comparing them to the abnormalities in relapsing-remitting multiple sclerosis(RRMS)by using diffusion tensor imaging(DTI)histogram.To detect the potential relationship between DTI indices of NAWM,NAGM and patient's clinical condition.Methods Nineteen patients with CIS,19 clinically diagnosed RRMS patients and 19 sex-and age-matched healthy volunteers were included in this study.Conventional MRI and DTI images were obtained using Siemens 1.5 T Magnetom sonata scanner.DTI histograms of NAWM and NAGM were obtained after post-processing.The mean value,peak height,peak location of the histogram were used for analysis.All data was statistically processed with SPSS for Windows.Results NAWM average MD was higher and FA was lower in RRMS[MD(0.83±0.04)×10-3mm2/s,FA 0.36±0.03]when compared to CIS[MD(0.79±0.02)×10-3mm2/s,FA 0.40±0.02]and control[MD(0.78±0.02)×10-3mm2/s,FA 0.41±0.01](P＜0.01).But no statistically significant difference was found between CIS and control.The peak height of NAWM average MD histogram was significantly lower in CIS than control(P＜0.05),while the peak location of average FA histogram shifted to the left(P＜0.01).Patients with CIS[(1.08±0.06)×10-3mm2/s]showed significantly higher NAGM average MD than control[(1.03±0.05)×10-3mm2/s](P＜0.05),but,lower than RRMS[(1.18±0.12)×10-3mm2/s](P＞0.01).There were no correlation between DTI indices and EDSS scores in patients with CIS.Moderate correlation between NAGM average MD(r=0.568,P＜0.05)and EDSS scores were found in patient with RRMS.Conclusion NAWM and NAGM abnormalities do occur in CIS which can be detected by DTI.The underlying pathological changes in NAWM and NAGM in CIS may be milder than RRMS as demonstrated by DTI histogram. Key words: Multiple sclerosis; Diffusion magnetic resonance imaging

The corticospinal tract in Sturge–Weber syndrome: A diffusion tensor tractography study

Objective To utilize diffusion tensor tractography and evaluate the integrity of the corticospinal tract in children with unilateral Sturge–Weber syndrome (SWS). Methods: Sixteen children (age: 1.5–12.3 years) with SWS involving one hemisphere and varying degrees of motor deficit, underwent magnetic resonance imaging (MRI) as part of a prospective clinical research study. Diffusion tensor imaging (DTI) was obtained and fiber tracking of the corticospinal tract was performed yielding average FA and ADC values along the pathway. These values were compared between the two hemispheres (affected vs. unaffected) and also correlated with the degree of motor deficits, after correction for age. Results: Corticospinal tract FA values on the side of the affected hemisphere were lower ( p = 0.008) and ADC values were higher ( p = 0.011) compared to the normal side. Furthermore, FA and ADC values on the side of the angioma did not show the normal age-related variations, which the contralateral corticospinal pathway values did demonstrate. Although none of the patients had severe hemiparesis, those with moderate motor deficit had increased ADC values, as compared to those with mild ( p = 0.009) or no motor deficit ( p = 0.045). Conclusion: MRI with DTI shows abnormalities of the corticospinal tract in children with SWS even before severe motor impairment develops. Thus, DTI can be a clinically useful method to evaluate the integrity of the corticospinal tract in young children who are at risk for progressive motor dysfunction.

Entanglement and Teleportation via Thermally Entangled State of Anisotropic Heisenberg XYZ Chain with Inhomogeneous External Magnetic Field

In this paper we study the entanglement in a two-qubit spin in the XYZ model, and teleport a two-qubit entangled state using this spin chain in the condition of the thermal equilibrium as a quantum channel. We investigate the effects of the interaction of z-component JZ, the inhomogeneous magnetic field b, the anisotropy γ, and the temperature T on the entanglement and fidelity. In order to characterize the quality of the teleported state, we research the average fidelity Fa. High average fidelity of the teleportation is obtained when the temperat ure is very low. Under some condition, we also find that when inhomogeneity increases to a certain value, the average fidelity can exhibit a larger revival than that for less values of b.

MRI quantification of gray and white matter damage in patients with early–onset multiple sclerosis

Contrary to what happens in adult-onset multiple sclerosis (MS), in a previous preliminary magnetic resonance imaging (MRI) study we showed only subtle normal-appearing brain tissue changes in patients with earlyonset MS. Our objective was to evaluate the presence and extent of tissue damage in the brain normalappearing white matter (NAWM) and gray matter (GM) from a larger population of patients with earlyonset MS. Using diffusion tensor (DT) and magnetization transfer (MT) MRI, we obtained DT and MT ratio (MTR) maps of the NAWM and GM from 23 patients with early-onset MS and 16 sex- and age-matched healthy volunteers. Compared with healthy volunteers, patients with early-onset MS had significantly increased average MD (p = 0.02) and FA peak height (p = 0.007) and decreased average FA (p <0.0001) of the NAWM. Brain dual-echo lesion load was significantly correlated with average FA (r = -0.48, p = 0.02) and with FA peak height (r = 0.45, p = 0.03) of the NAWM. No MTR and diffusion changes were detected in the GM. This study confirms the paucity of the 'occult' brain tissue damage in patients with earlyonset MS. It also suggests that in these patients GM is spared by the disease process and that NAWM changes are likely to be secondary to Wallerian degeneration of fibers passing through macroscopic lesions.

An efficient coefficient-partitioning algorithm for realizing low-complexity digital filters

Algorithms that minimize the complexity of multiplication in digital filters focus on reducing the number of adders needed to implement the coefficient multipliers. Previous works have not analyzed the complexity of each adder, which is significant in low-complexity implementation. A multiplication algorithm for low-complexity implementation of digital filters with a minimum number of full adders (NFAs) and improved speed is proposed here. The authors exploit the fact that when multiplication is implemented using shifts and adds, the adder width can be minimized by limiting the shifts of the operands to shorter lengths. The coefficient-partitioning (CP) algorithm proposed here minimizes the shifts of the operands of the adders by partitioning each coefficient into two subcomponents. The authors show that by combining three methods, the CP algorithm, an efficient coefficient coding scheme known as pseudo floating-point (PFP) representation, and the well-known common subexpression elimination (CSE), the NFAs required in each adder of the multiplier can be reduced considerably. Design examples show that the method offers an average FA reduction of 30% for finite-impulse response (FIR) filters and 20% for infinite-impulse response (IIR) filters over CSE methods.