Midpoint Distance Research Articles

The Tibial Tuberosity-Tibial Intercondylar Midpoint Distance: Letter to the Editor.

The Tibial Tuberosity-Tibial Intercondylar Midpoint Distance: Letter to the Editor.

Korean–English Bilingual Children's Productions of Korean and English /l/

Purpose: The aim of this study was to examine acoustic characteristics of Korean–English (KE) bilingual children's productions of Korean and English /l/ sounds. Specifically, individual variability in KE bilingual children's productions of Korean and English /l/ was examined in relation to each child's initial age and duration of exposure to their first and second languages. Method: A total of five KE bilingual children, ranging in age between 5 and 8 years, were included in this study. Each KE child produced word-initial (WI) and -final (WF) English /l/ and WF Korean /l/ embedded in monosyllabic words, using a picture naming task. English /l/ productions of monolingual American English (AE)–speaking children were also included. Productions of AE children were from an existing large data set that includes English WI and WF /l/ productions. The AE group was included as a control group for the productions of English /l/ of the same dialect. First (F1) and second formant frequency (F2) values extracted at the /l/ midpoint and Euclidean distance (ED) between English WI and WF /l/ were analyzed and compared across the productions. Results: KE children produced Korean WF /l/ with significantly higher F2–F1 values than their English counterparts and AE children's WF /l/. Acoustic patterns of KE English WI /l/ were similar to those of AE WI /l/, but variations were seen by the initial age and duration of their exposure to English. Mean ED values between English WI and WF /l/ also differed by KE children's initial age and duration of exposure to English. Conclusions: These results showed that KE children produce Korean and English WF /l/ with acoustic distinctions, but their patterns vary by the initial age and duration of their exposure to English and Korean. These findings suggest that a more detailed language background should be considered when working with bi-/multilingual children to accurately assess and examine their articulation skills.

Multiplatform Radiosurgery for Intracranial Meningiomas and Dose to the Dural Tail.

IntroductionMeningiomas are extra-axial central nervous system tumors. Complete resection is often curative with macroscopically complete removal of the tumor, excision of its dural attachment, and any abnormal bone. Radiosurgery is also an option for high-risk patients or in patients with surgically residual disease. Dural tail is a typical radiological sign on contrast-enhanced MRI; it can contain tumor cells or be a reaction due to vascular congestion and edema. Radiosurgical planning treatment varies regarding the identification and coverage of the dural tail. This study aimed to retrospectively analyze a series of 143 patients with WHO Grade I meningiomas treated with different radiosurgical platforms, and dosing parameters focused on planning and dose delivery to the dural tail.MethodsFrom February 2011 to July 2020, 143 patients with histologically confirmed or radiologically assumed WHO Grade I meningiomas were treated using rotating gamma-ray Infini™ (Gamma [MASEP Medical Science Technology Development Co., Shenzhen, China]), TomoTherapy® (Tomo [Accuray Inc., Sunnyvale, CA]), and CyberKnife® (CK [Accuray Inc.]). All plans were retrospectively reviewed to establish the maximum distance (MaxDis) from the prescription dose to the end of the dural tail and the minimum dose at the dural tail (MinDoseT) at this point. We also established the midpoint distance (MPDis) from the prescription dose to MaxDis and the dose at this point (MPDose). Plans were further distinguished when the physician intended to cover the dural tail versus when not. Patients and tumor response were assessed by imaging and clinical and phone call evaluations.ResultsOf the 143 patients, 81 were treated using Gamma, 34 using Tomo, and 28 using CK. Eighty patients were eligible for follow-up, of whom 58 (72.5%) had an unmistakable dural tail sign. Median follow-up was 1,118 days (range 189-3,496), mean age was 54.5 (range 19-90), and 61 were women, and 19 were men. Overall tumor volume was 6.5 cc (range 0.2-59); mean tumor volumes by different platforms were 2.4, 9.45, and 8 cc; dose prescribed and mean tumor coverage were 14 Gy and 92%, 14.5 Gy and 95%, and 14 Gy and 95.75% with Gamma, Tomo, and CK, respectively. The dural tail was drawn and planned with an attempt to treat in 18 patients (31%); the mean MaxDis, MinDoseT, MPDis, and MPDose were 9.0 mm, 2 Gy, 4.5 mm, and 10.6 Gy, respectively. At last follow-up, tumor control was achieved in 96% of patients for the whole series, and there were no statistical variations regarding tumor volume, dose, conformality, or control when stereotactic radiosurgery was used to cover the dural tail versus when it was not (p=0.105). One patient experienced a Grade 4 Radiation Therapy Oncology Group toxicity as an adverse radiation effect that required surgery, and 11 (7.6%) experienced a Grade 1 toxicity.ConclusionsThis is our preliminary report regarding the efficacy of radiosurgery for meningiomas using diverse platforms at three years of follow-up; the results regarding tumor control are in accordance with the published literature as of this writing. A conscious pursuit of the dural tail with the prescription dose has not proven to provide better tumor control than not doing so - even small areas of the tumor uncovered by the prescription dose did not alter tumor control at current follow-up. The doses delivered to these uncovered areas are quite significant; further follow-up is necessary to validate these findings.

Tibial tuberosity-tibial intercondylar midpoint distance measured on computed tomography scanner is not biased during knee rotation and could be clinically more relevant than current measurement systems.

The purpose of this retrospective cross-sectional case-control study was to evaluate an alternative imaging test for lateralization of the tibial tuberosity, unbiased towards knee rotation. On axial CT images of 129 knees, classified as cases (two or more patellar luxations) and controls (no patellar luxations), two raters gauged the standard tibial tuberosity-trochlear groove (TT-TG) distance, tibial tuberosity-femoral intercondylar midpoint (TT-FIM) distance, and new tibial tuberosity-tibial intercondylar midpoint (TT-TIM) distance singly, and knee longitudinal rotation angles (LRAs), and the presence of femoral trochlear dysplasia (FTD) jointly. All imaging tests intercorrelated and discriminated between stability groups. TT-TIM had the lowest values with the highest precision. Though poorly, TT-TG and TT-FIM negatively correlated with age and LRAs regarding femur, but positively with presence of FTD, whereas TT-TIM was unbiased. The accuracy of TT-TG (> 20 mm), TT-FIM (> 20 mm), and TT-TIM (> 13 mm) was good with almost perfect reproducibility. Only TT-TIM was sex-biased (p = 0.009), with > 12 mm cut-off in females and (presumably) > 14 mm in males. TT-TIM is an alternative imaging test for lateralization of the tibial tuberosity, unbiased towards knee rotation.

Midpoint Distance Circle Generation Algorithm based on Midpoint Circle Algorithm and Bresenham Circle Algorithm

In the process of generating a circle, the existing midpoint circle algorithm and Bresenham circle algorithm have the problems of slow drawing speed, high resource consumption, complicated calculation steps and large pixel spacing in some areas, and a combination of midpoint painting is proposed. A new algorithm for the circular algorithm and the Bresenham circular algorithm. The algorithm first calculates the positional relationship between the midpoint and the circumference of two adjacent pixel points, and then calculates the distance difference between two adjacent pixel points and the circle by two approximate distances, and then obtains the decision parameters of the algorithm. A complete circle is obtained by the symmetry of the octant. Experiments show that the proposed algorithm is an effective midpoint distance circle generation algorithm based on the midpoint circle algorithm and the Bresenham algorithm. Compared with similar algorithms, it has higher stability and precision, and has less resource consumption and more flexible calculation methods.

The Safe Distance to the Popliteal Neurovascular Bundle in Pediatric Knee Arthroscopic Surgery: An Age-Based Magnetic Resonance Imaging Anatomic Study.

Background:The close proximity of the popliteal neurovascular bundle to the posterior horn of the lateral meniscus puts it at risk of compromise during lateral meniscal repair. This is particularly important in smaller pediatric patients, who are commonly treated for lateral meniscal abnormalities in isolation (discoid meniscus) or concomitantly with anterior cruciate ligament reconstruction.Purpose:To quantify the distance between the posterior horn of the lateral meniscus and the popliteal neurovascular bundle along the path of meniscal repair and to investigate for associations with age, sex, height, weight, body mass index (BMI), and skeletal maturity.Study Design:Cross-sectional study; Level of evidence, 3.Methods:A total of 144 magnetic resonance imaging scans were evaluated in a cohort of patients aged 10 to 18 years without meniscal or ligament abnormalities. Measurements were made along a line from the anterolateral portal between the popliteal neurovascular bundle and the free edge, midpoint, and meniscocapsular junctions of the posterior horn of the lateral meniscus. In addition to descriptive statistics of these distances by age and sex, analyses of variance and linear regression analyses were performed to investigate for associations with age, sex, height, weight, BMI, and skeletal maturity.Results:Male participants had a significantly larger mean free edge distance (14.4 ± 2.5 vs 13.1 ± 2.5 mm, respectively; P = .005) and midpoint distance (9.6 ± 2.2 vs 8.9 ± 1.8 mm, respectively; P = .011) than female participants but not a significantly larger meniscocapsular distance (5.2 ± 1.6 vs 4.6 ± 1.4 mm, respectively; P = .096). Linear regression analyses revealed significant associations between these distances and age, height, weight, and BMI (P < .001 for all). There were statistically significant pairwise differences for free edge and midpoint distances to the neurovascular bundle between patients with open and closed physes.Conclusion:The distance between the posterior horn of the lateral meniscus and the popliteal vasculature along a trajectory from the standard anterolateral arthroscopic portal increases linearly throughout development between the ages of 10 and 18 years. There were also significant associations between height, weight, BMI, and skeletal maturity and these anatomic distances. Knowing the safe distance to the popliteal vasculature will increase the safety of arthroscopic lateral meniscal repair in children, especially with all-inside devices that require setting the penetration depth for the advancement of a sharp delivery device beyond the posterior capsule.

Spatial distances between internal jugular vein and carotid artery vary with rotating angles of the neck

Objective To utilize ultrasound as an approach to determine spatial distances between the right internal jugular vein and carotid artery at anterior, middle and posterior puncture sites when the neck turned to the left at various angles. Methods One hundred and twenty patients, classified as ASA Ⅰ or Ⅱ, were enrolled in this study. All subjects lay in supine and with a 5 cm thick pads under the shoulder. Ultrasound was used to determine the diameters of the right internal jugular vein and carotid artery, the proportions of right internal jugular vein spatially overlapping carotid artery, and the distances between the middle of right internal jugular vein and carotid artery(arteriovenous midpoint distance), at anterior, middle and posterior puncture sites when patient's neck turned to the left at angles of 0°, 15°, 30°, 45° and 60°. Results The diameters of the right internal jugular vein and carotid artery, proportions of right internal jugular veins non-overlapping with carotid arteries, and arteriovenous midpoint distance did not vary with puncture sites and turning angles. But at the same turning angles, percentages of right internal jugular veins non-overlapping with carotid arteries at the posterior puncture site were less than those at the anterior and middle puncture sites(P<0.05). At the anterior and middle puncture sites, percentages of right internal jugular vein non-overlapping with carotid arteries, and arteriovenous midpoint distances were similar at the turning angles of 0°, 15°, and 30°. But when the turning angles reached 45° and 60°, the percentages of right internal jugular vein non-overlapping with carotid arteries and arteriovenous midpoint distance were significantly decreased(P<0.05). Conclusions The spatial distances between the right internal jugular vein and carotid arteries reduced when the turning angles of the neck exceeded 45°, and at the posterior puncture site. To avoid the risk of puncturing carotid artery, operators should choose anterior or middle puncture sites and restrain the turning angle of the neck within 45°. Key words: Ultrasound guided; Head rotation; Internal jugular vein

Graft position in arthroscopic anterior cruciate ligament reconstruction: anteromedial versus transtibial technique.

When treating anterior cruciate ligament (ACL) injuries, the position of the ACL graft plays a key role in regaining postoperative knee function and physiologic kinematics. In this study, we aimed to compare graft angle, graft position in tibial tunnel, and tibial and femoral tunnel positions in patients operated with anteromedial (AM) and transtibial (TT) methods to those of contralateral healthy knees. Forty-eight patients who underwent arthroscopic ACL reconstruction with ipsilateral hamstring tendon autograft were included. Of these, 23 and 25 were treated by AM and TT techniques, respectively. MRI was performed at 18.4 and 19.7months postoperatively in AM and TT groups. Graft angles, graft positions in the tibial tunnel and alignment of tibial and femoral tunnels were noted and compared in these two groups. The sagittal graft insertion tibia midpoint distance (SGON) has been used for evaluation of graft position in tunnel. Sagittal ACL graft angles in operated and healthy knees of AM patients were 57.78° and 46.80° (p<0.01). With respect to TT patients, ACL graft angle was 58.87° and 70.04° on sagittal and frontal planes in operated knees versus 47.38° and 61.82° in healthy knees (p<0.001). ACL graft angle was significantly different between the groups on both sagittal and frontal planes (p<0.001). Sagittal graft insertion tibia midpoint distance ratio was 0.51 and 0.48% in the operated and healthy knees of AM group (p<0.001) and 0.51 and 0.48% in TT group (p<0.001). Sagittal tibial tunnel midpoint distance ratio did not differ from sagittal graft insertion tibia midpoint distance of healthy knees in either group. Femoral tunnel clock position was better in AM [right knee 10:19 o'clock-face position (310°±4°); left knee 1:40 (50°±3°)] compared with TT group [right knee 10:48 (324°±5°); left knee 1:04 (32°±4°)]. With respect to the sagittal plane, the anterior-posterior position of femoral tunnel was better in AM patients. Lysholm scores and range of motion of operated knees in the AM and TT groups showed no significant difference (p>0.05). Precise reconstruction on sagittal plane cannot be obtained with either AM or TT technique. However, AM technique is superior to TT technique in terms of anatomical graft positioning. Posterior-placed grafts in tibial tunnel prevent ACL reconstruction, although tibial tunnel is drilled on sagittal plane.

The Morphometric Study of Degenerative Lateral Canal Stenosis at L4-L5 and L5-S1 Using Magnetic Resonance Imaging (MRI): Feasibility Analysis for Posterior Surgical Decompression.

This study was to evaluate the morphological features of degenerative spinal stenosis and adequacy of lateral canal stenosis decompression via unilateral and bilateral laminectomy. Measurements of facet joint angulation (FJA), mid facet point (MFP), mid facet point distance (MFPD), the narrowest point of the lateral spinal canal (NPLC) and the narrowest point of the lateral spinal canal distance (NPLCD) were performed. At L4L5 of the right and left side, the mean distance between the lateral border of the dura and MFP was 1.0 ± 0.2 cm and 1.0 ± 0.3cm respectively. The mean NPLC was seen at 0.7 ± 0.3 and 0.7 ± 0.3 cm cm from the dura. At L5S1 of the right and left side, the mean distance between the lateral border of the dura and MFP was 1.2± 0.2 and 1.3 ± 0.2 cm respectively. The mean NPLC was seen at 0.8 ± 0.4 and 0.9 ± 0.5 cm from the dura. Unilateral laminectomy may result in incomplete decompression.

Accurate and robust line segment extraction using minimum entropy with Hough transform.

The Hough transform is a popular technique used in the field of image processing and computer vision. With a Hough transform technique, not only the normal angle and distance of a line but also the line-segment's length and midpoint (centroid) can be extracted by analysing the voting distribution around a peak in the Hough space. In this paper, a method based on minimum-entropy analysis is proposed to extract the set of parameters of a line segment. In each column around a peak in Hough space, the voting values specify probabilistic distributions. The corresponding entropies and statistical means are computed. The line-segment's normal angle and length are simultaneously computed by fitting a quadratic polynomial curve to the voting entropies. The line-segment's midpoint and normal distance are computed by fitting and interpolating a linear curve to the voting means. The proposed method is tested on simulated images for detection accuracy by providing comparative results. Experimental results on real-world images verify the method as well. The proposed method for line-segment detection is both accurate and robust in the presence of quantization error, background noise, or pixel disturbances.

Three-dimensional remodelling to determine best fit for hemihamate autograft arthroplasty

Objective To determine the best fit of a hamate osteochondral graft to reconstruct a palmar defect of a middle phalanx articular fracture using three-dimensional remodelling. Methods The proximal middle phalanx and distal hamate articular surfaces of 10 cadaveric right hands were scanned using a three-dimensional laser scanner. A defect was marked on the middle phalanx digital image to simulate a 50% palmar lip fracture. A hemihamate autograft surgical procedure was simulated by aligning the middle phalanx and hamate digital articular surfaces. In addition to the second digit measurements, the midpoint distances of the central ridge of proximal articular surface of the middle phalanx digital image for digits 3, 4 and 5 were recorded for reference value, as well as the offset distances for the long and small finger. Results The mean midpoint distance for the index finger was 2.96 mm (95% CI 2.71 mm to 3.21 mm). The mean angle of offset was 20.09° (95% CI 15.54° to 24.64°). The mean graft offset distance was prominent by 1.23 mm (95% CI 0.57 mm to 1.89 mm). The reference values for the third, fourth and fifth middle phalange midpoint distances were 3.26 mm (95% CI 3.09 mm to 3.43 mm), 3.13 mm (95% CI 2.93 mm to 3.33 mm) and 2.48 mm (95% CI 2.33 mm to 2.63 mm), respectively. The offset distances for digits 3 and 5 were 1.24 mm (95% CI 0.48 mm to 2.00 mm) and 1.08 mm (95% CI 0.48 mm to 1.68 mm), respectively. Conclusions The present study provides information about best fit for placing a hamate autograft for the hemihamate arthroplasty procedure. In this model, the hamate graft must be offset to recreate the curvature of the middle phalanx.

Three-dimensional remodelling to determine best fit for hemihamate autograft arthroplasty

To determine the best fit of a hamate osteochondral graft to reconstruct a palmar defect of a middle phalanx articular fracture using three-dimensional remodelling. The proximal middle phalanx and distal hamate articular surfaces of 10 cadaveric right hands were scanned using a three-dimensional laser scanner. A defect was marked on the middle phalanx digital image to simulate a 50% palmar lip fracture. A hemihamate autograft surgical procedure was simulated by aligning the middle phalanx and hamate digital articular surfaces. In addition to the second digit measurements, the midpoint distances of the central ridge of proximal articular surface of the middle phalanx digital image for digits 3, 4 and 5 were recorded for reference value, as well as the offset distances for the long and small finger. The mean midpoint distance for the index finger was 2.96 mm (95% CI 2.71 mm to 3.21 mm). The mean angle of offset was 20.09° (95% CI 15.54° to 24.64°). The mean graft offset distance was prominent by 1.23 mm (95% CI 0.57 mm to 1.89 mm). The reference values for the third, fourth and fifth middle phalange midpoint distances were 3.26 mm (95% CI 3.09 mm to 3.43 mm), 3.13 mm (95% CI 2.93 mm to 3.33 mm) and 2.48 mm (95% CI 2.33 mm to 2.63 mm), respectively. The offset distances for digits 3 and 5 were 1.24 mm (95% CI 0.48 mm to 2.00 mm) and 1.08 mm (95% CI 0.48 mm to 1.68 mm), respectively. The present study provides information about best fit for placing a hamate autograft for the hemihamate arthroplasty procedure. In this model, the hamate graft must be offset to recreate the curvature of the middle phalanx.

Origin of the medial ulnar collateral ligament on the pediatric elbow

Surgical reconstruction of the adult anterior bundle of the medial ulnar collateral elbow ligament (UCL) is a common and established treatment that yields satisfactory results. Children sustain these injuries less frequently, and surgical intervention is complicated by the juxtaposed medial epicondyle apophysis. The purpose of this study was to identify the anatomical origin of the pediatric UCL and determine if this location changes with elbow maturity. A retrospective analysis of children with an elbow MRI between 2009 and 2012 was performed. Ninety children (68 boys, 22 girls), mean age 12.8years (range 6-18), were grouped by age (<11, 11-13, and >13) and gender. Measurements of UCL width and UCL midpoint distance from medial epicondyle apophysis were recorded on coronal T1 images utilizing digital PACS software. Across all groups, boys had a wider UCL than girls (4.05±0.16mm vs 3.72±0.20mm, p=0.03); however, there was no difference in the anatomical origin of the UCL relative to the medial epicondyle apophysis between gender (p=0.52), between gender age-matched groups, or within gender age-matched groups. Yet, the anatomic origin of the UCL always remained medial to the cartilaginous interface of the apophysis with the osseous distal humerus and was centered approximately 3mm medial to the lateral edge of the apophysis. Regardless of age or gender, the humeral origin for the medial ulnar collateral ligament is medial to the interface between the medial epicondyle apophysis and distal humerus, which has surgical implications for anatomic reconstruction in children.

Origin of the Medial Ulnar Collateral Ligament on the Pediatric Elbow

Objectives:Surgical reconstruction of the torn anterior bundle of the medial ulnar collateral elbow ligament (UCL) is an established treatment that yields satisfactory results in adults. Children sustain these injuries less frequently and surgical intervention is complicated by the juxtaposed medial epicondyle apophysis. The purpose of this study was to identify the anatomical origin of the pediatric UCL and determine if this location changes with elbow maturity.Methods:A retrospective analysis of children with elbow MRI between 2009 and 2012 was performed. Grouped by age (<11, 11-13, and >13) and gender, the exclusion criteria included: poor imaging quality due to motion artifact, elbow flexion beyond 45 degrees, and prior elbow injury obscuring anatomic structures. Measurements of UCL width and UCL midpoint distance from medial epicondyle apophysis were recorded on coronal T1 images utilizing digital PACS software.Results:Ninety children (68 boys, 22 girls), mean age 12.8 years (range 6-18), met criteria. Across all groups, boys had a wider UCL than girls (4.05 ± 0.16 mm vs 3.72 ± 0.20 mm, p = 0.03); however, there was no difference in the anatomical origin of the UCL relative to the medial epicondyle apophysis between gender (p = 0.52), between gender age-matched groups, or within gender age-matched groups (Table 1). However, the anatomic origin of the UCL always remained medial to the distal periphery of the apophysis. There was, however, a statistical trend in girls between the <11 and >13 groups for the UCL origin to move closer to the medial epicondyle apophysis with maturity (p=0.053).Conclusion:Although surgical reconstruction of the UCL in children is infrequent, it may be the best treatment for a given skeletally immature patient with elbow instability. The procedure requires a choice regarding ligament placement on the humerus versus preservation of the medial epicondyle apophysis. This study elucidates the anatomical origin of the UCL across gender and age for the at risk pediatric group and demonstrates no differences in the UCL center of attachment based on skeletal maturity or gender. Therefore, surgical intervention of the pediatric torn elbow UCL does not require specific consideration of age and gender regarding placement of the reconstructed ligament; however, an anatomic reconstruction of the UCL does place the medial epicondyle apophysis at risk for injury.

Dual-hop amplify-and-forward relaying in the presence of co-channel interference: performance study and system optimisation

In this study, the authors investigate the effect of co-channel interference on the performance of dual-hop communications with amplify-and-forward relaying. First, the exact equivalent signal-to-interference-plus-noise ratio (SINR) at the destination is formulated and upper bounded. Then, the cumulative distribution function, probability density function (PDF) and moment generating function of the upper bounded SINR are determined. Further, expressions for the error and the outage probabilities are obtained. Moreover, an approximate PDF of the dual-hop link&apos;s instantaneous SINR is derived. In particular, simple expressions for the error and outage probabilities are presented and discussed. Numerical and simulation results are provided and confirm the tightness of the presented asymptotic expressions. Besides, optimisation of the power allocation and relay positioning are addressed. Specifically, the authors study adaptive power allocation with fixed relay location, optimal relay location with fixed power allocation, and joint optimisation of the power allocation and relay location under total transmit power constraint, in order to minimise the asymptotic average error probability and outage probability. Results show that optimum power allocation, optimum relay location and joint optimisation significantly improve the system performance in terms of error and outage probabilities compared to uniform power allocation and mid-point distance location of the relay node.

Interaction of Radical Pairs Through-Bond and Through-Space: Scope and Limitations of the Point−Dipole Approximation in Electron Paramagnetic Resonance Spectroscopy

The validity of the popular point-dipole approximation for interpretation of the zero-field splitting (ZFS) parameter (D-value) in EPR spectroscopy is studied. This approximation is of central importance for the determination of distances by analysis of EPR data. In this work, a detailed experimental (EPR spectroscopy and X-ray crystallography) and theoretical study for a model system (2,2',5,5'-tetra(tert-butyl)-4,4'-bis(ethoxy-carbonyl)-3,3'-bipyrrolyl-1,1'-dioxyl) was performed to understand the scope and limitations of the point-dipole model in EPR spectroscopy. For this diradical, the radical-radical distance derived with the point-dipole approximation deviates significantly (by approximately 40%) from the results derived from the X-ray analysis. Explicit quantum chemical calculation of the D-value on the basis of B3LYP density functional calculations leads to excellent quantitative agreement with the measured D-value. The quantitative accuracy of the employed methodology was confirmed for two additional systems that have previously been experimentally characterized. We therefore analyzed the contributions to the D-value of the target system in detail. This analysis leads to insight into the reasons for the failure of the point-dipole approximation. The analysis was then extended to an in silico study of five classes of model systems. Linkers of varying length and bond saturation were introduced between the radical-carrying groups. This allows for the analysis of the distance dependence of the D-parameter as well as the through-bond and through-space spin-spin interaction. From these results we established the limitations of the point-dipole approximation. The results of this analysis demonstrate that even very modest amounts of spin delocalization can cause significant deviations from pure point-dipole behavior and consequently cause the EPR derived distances to deviate from the N-O midpoint distance by up to several angstroms. If unsaturated linkers are used, the distance dependence of D does not follow the inverse cubic behavior predicted by the point-dipole model. However, for commonly used nonaromatic nitroxide rings connected by a saturated linker, the point-dipole approximation works well. Among the various point-dipole variants tested in this work for delocalized spins, the most successful one is based on distributed point-dipoles with spin populations derived from quantum chemical calculations. The distance dependence of the isotropic Heisenberg exchange parameter J has also been studied theoretically. The decay was found to be monoexponential with a decay constant of approximately 1 A(-1). Thus at linker lengths between 6-8 carbon atoms between a nitroxide radical pair, a switch from the strong to the weak exchange limit is predicted.

Combination of an electrochemical tunneling microscope (ECSTM) and a scanning electrochemical microscope (SECM): application for tip-induced modification of self-assembled monolayers

A combined instrument for electrochemical scanning tunneling microscopy (ECSTM) and scanning electrochemical microscopy (SECM) was constructed. It brings a combined ECSTM–SECM probe into tunneling contact with a sample and retracts it by defined distances to perform electrochemical experiments outside the tunneling distance but within a separation of 5–30 nm from the sample. The capabilities have been illustrated by the investigation of self-assembled monolayers (SAM) of dodecanethiolate on flame-annealed gold. By establishing a tunneling contact between the tip and the SAM-covered gold surface the structure of the SAM is disturbed. This is evident from current–distance curves in the SECM feedback mode. Depending on the time allowed for relaxation, the signal changes from positive feedback to negative feedback as it would be expected above undisturbed SAM. Spatially correlated images of topography and reactivity could be recorded by acquiring an ECSTM line scan first and than using the topographic information to guide the probe parallel to the surface in a much larger distance after changing the probe potential to cause the diffusion-controlled oxidation of a mediator. This mode was used to image rough gold electrodes where an almost complete suppression of the topographic information in the SECM data could be achieved. A sample with an inhomogeneous distribution of electrochemical reactivity was created by tip-induced removal of two 100×100 nm 2 large regions of a dodecanethiolate SAM on a rough gold surface. The two areas with a midpoint–midpoint distance of 850 nm could clearly be resolved by SECM imaging in the feedback mode.

Superconvergence results on mildly structured triangulations

Many results on superconvergence for recovered gradients of piecewise linear Galerkin approximations on triangular mesh partitions to the weak solutions of elliptic boundary value problems in two dimensions have been proved in recent years. These were obtained first for ∞-regular (fully-structured) partitions in which the mid-points of the diagonals of all quadrilaterals formed by pairs of adjacent elements are coincident. This condition was then relaxed to allow for strongly-regular meshes, in which the distance between the above mid-points is O( h 2), h being the mesh size parameter. In this paper these conditions are weakend still further to the case of globally mildly structured meshes, where the mid-point distance is O( h 1+ α ), 0< α<1, and to meshes of this type where locally α=0. After a review of recovery and gradient superconvergence, a unified approach is presented in terms of a generic gradient recovery operator which possesses specific properties on rectangular domains. Then the well-known classic theorem of Oganesyan and Rukhovets is extended to the case of mildly structured triangulations of polygonal approximations of C 3( d) domains. A class of gradient recovery operators is described on these mildly structured meshes and, using the extended Oganesyan–Rukhovets theorem, superconvergence is proved. We also obtain global superconvergence results for the recovered gradients over plane polygonal domains patchwise partitioned by fully-structured meshes. A feature of our results is that they allow local refinements of such meshes without loss of superconvergence. For the sake of completeness we have referenced the works of others in order to demonstrate the place of our work in the field.