Narrow Results

The inner structure of compact stars is checked from theoretical as well as observational points of view. In this paper, we determine the possible radii of six compact stars: two binary millisecond pulsars, namely PSR J1614-2230 and PSR J1903+327, studied by [P. B. Demorest, T. Pennucci, S. M. Ransom, M. S. E. Roberts and W. T. Hessels, Nature467, 1081 (2010)] and four X-ray binaries, namely Cen X-3, SMC X-1, Vela X-1 and Her X-1 studied by [M. L. Rawls et al., Astrophys. J.730, 25 (2011)]. Interestingly, we see that density of the star does not vanishes at the boundary though it is maximum at the center which implies that these compact stars may be treated as strange stars rather than neutron stars. We propose a stiff equation of state (EoS) relating to pressure with matter density. We also obtain compactness (u) and surface redshift (Z${}_s$) for the above-mentioned stars and compare it with the recent observational data.

In this paper, we study the inner structure of some neutron stars from theoretical as well as observational points of view. We calculate the probable radii, compactness (u) and surface redshift (Z${}_s$) of five neutron stars (X-ray binaries) namely 4U 1538-52, LMC X-4, 4U 1820-30, 4U 1608-52, EXO 1745-248. Here, we propose a stiff equation of state (EoS) of matter distribution which relates pressure with matter density. Finally, we check the stability of such kind of theoretical structure.

The superficial radial nerve might be compressed or injured at various anatomical sites along its course in the forearm. Most of the superficial radial nerve neuropathy are caused by pathological lesions such as trauma, a mass or tight band at the distal third of the forearm. Wartenberg's syndrome is the most common cause of sensory radial entrapment at the distal forearm. Compression of superficial radial nerve occurring at the proximal third of forearm is unusual. We present a rare case of superficial radial nerve compression due to a parosteal lipoma of proximal radius. Results of complete physical and radiological examinations are also presented. Surgical intervention of the tumour mass was performed for nerve decompression. The patient reported total relief of the neurological symptom post-operatively. This rare case demonstrates the unique characteristics of parosteal lipoma with unusual superficial radial nerve neuropathy at the proximal radius. This report reminds us that there is the possibility of superficial nerve compression caused by tumour mass over the proximal third of forearm.

Loss of median nerve function or a neuropathic pain syndrome may occur in around 20% of distal radius fractures if post-traumatic oedema in the carpal canal generates excessive pressure on the median nerve. No method currently exists to reliably distinguish which patients may benefit from a concomitant carpal tunnel release. This case series details the results of following a prospective plan designed to minimise median nerve related complications associated with distal radius fractures by measuring Semmes-Weinstein monofilament scores in 374 radius fracture patients who underwent surgical stabilisation. One hundred and sixty-nine patients with the clinical symptoms of median nerve compression, a decrement in monofilament score of grade 1 (out of 5) compared to the contralateral side or at least 4.31 g underwent concomitant carpal tunnel release. The remaining 205 patients did not have carpal tunnel release. There were no cases of neuropathic pain or loss of median nerve function.

Non-union at the metaphyseal level is rare following a fracture of the distal radius. When a non-union does occur, it is usually easily treated with cancellous bone graft from the iliac crest. Resistant and multiply operated atrophic non-unions more frequently occur at the diaphyseal level of long bones. A corticoperiosteal free flap based on the articular branch of the descending genicular artery has previously been described to treat such difficult non-union cases in various sites, but not at the distal radius. At the distal radius metaphysis, the close relationship with the extensor tendons raises concern regarding the ability to fit this free flap to the non-union site without significant interference with tendon function. By careful technique of crumbling the cortex of the flap without tearing the periosteal continuity, the flap can be contoured and snugly fit to this particular site while preserving tendon function. A unique case is presented of a multiply operated resistant atrophic non-union of the distal radius metaphysis in a heavy smoker that was rapidly healed using the genicular corticoperiosteal free flap.

We present here two cases wherein we performed radiolunate fusion using vascularized radius graft with the vascular pedicle of the fourth extensor compartment artery (fourth ECA) for the treatment of Bain's grade 2A Kienböck disease with incongruity of the radiolunate joint. The dorsodistal radius graft was levered out and mobilized on the pedicle of the fourth ECA; then the vascularized dorsodistal radius was shifted 1 cm distally and bridges were created between the radius and the lunate. The radiolunate joint was completely fused in both cases at three months after surgery. The capitolunate joint maintained congruity after surgery. The Mayo wrist score was 75 points, and the DASH (JSSH version) score for the two cases was 2.5 and 4.2 points, respectively. Radiolunate fusion using the vascularized radius bridging procedure is one of the satisfactory methods for treating advanced Kienböck disease, especially in Bain's grade 2A cases.

Acute plastic bowing is an incomplete fracture with a deformation that shows no obvious macroscopic fracture line or cortical discontinuity. Although cases of acute plastic bowing of the ulna with a dislocation of the radial head have been previously reported, we present here a rare case of acute plastic bowing of the radius with a distal radioulnar joint injury in a 16-year-old boy. Internal fixation of the detached fragment to the ulnar styloid and repair of the triangular fibrocartilagenous complex resulted in the disappearance of wrist pain. In cases of distal radioulnar joint injuries in children or adolescents, radiographs of the entire forearm should be taken to evaluate the existence of radial bowing.

Both wrists in 189 patients who had been treated for dorsally displaced distal radius fracture were X-rayed with both right angle and 15° tilted lateral views. Two investigators measured the radial tilt. The mean difference in the angles recorded by the two investigators was 2.5° for the tilted and 3.7° for the right angle projections (p = 4.7 × 10^-8). The precision of the method was 2.6° for the tilted and 3.5° for right angle projection. The mean angle measured on the tilted views was 3° more dorsal than on the right angle views for wrists with a volar tilt between 10° and 15°, and 0° to 2° for wrists with less volar tilt or dorsal displacement.

Lateral projections tilted 15° allow more precise measurements than right angle views. Correction is not necessary when comparing to right angle views, as long as there is displacement in a dorsal direction of the distal fragment.

An intraosseous xanthoma is a very rare condition. It has an aggressive appearance on radiographs mimicking primary or metastatic malignant bone tumors. We report a case of intraosseous xanthoma of the distal radius in a 51-year-old male with no history of hyperlipidaemia. To the best of our knowledge, this condition has not been reported so far in the wrist and forearm region. The lesion was successfully excised and at last follow-up, there were no signs of recurrence and patient has been symptom-free.

Background: Nonunion involving the metaphyseal region of the distal radius is exceedingly rare, usually involving co-morbidity. Patients that have failed multiple prior conventional surgical interventions represent an even more difficult subset to treat; this investigation examined the utility of a specially designed free vascularized medial femoral condyle flap consisting of a central structural block graft with an extended corticoperiosteal sleeve to wrap around the junctions.

Methods: Six patients (5 males, 1 female) with a mean age of 52 years had failed to achieve union involving the distal radius metaphysis after a mean of 3.7 prior surgeries occurring over a mean period of 24 months. Comorbidities included smoking, alcoholism, chronic nutritional deficiency, and prior osteomyelitis. The unique descending genicular artery medial femoral condyle flap designed to address these patients consisted of a central structural block graft in continuity with an extended corticoperiosteal sleeve. The structural block filled the bone defect, and the corticoperiosteal sleeve wrapped around the bone junctions and the neighboring bone margins. The mean flap size was 5.3 (+/- 1.3) cm long by 4.5 (+/- 0.9) cm wide. Pre-operative to post-operative DASH scores were compared using the paired student’ s t-test, with p < 0.05.

Results: All flaps achieved union at a mean of 6.8 (+/- 2.1) weeks following surgery, using the criteria of bridging trabeculae on all 3 radiographs: coronal, sagittal, and oblique. The mean pre-operative DASH score of 63 (+/- 10) was statistically significantly different compared to the mean post-operative DASH score of 18 (+/- 8).

Conclusions: With few alternative solutions able to address this unique and difficult problem, the structural block of vascularized bone with the extended corticoperiosteal sleeve proved able to achieve a union that had failed multiple previous attempts and able to resist reactivation of infection, in a challenging group of patients with comorbidities.

We herein report an unusual case of Brodie’s abscess of the radius in a child. A 13-year-old boy presented with pain on his right distal forearm. A plain radiograph showed an 8 cm translucent lesion in the distal radius. MRI showed a penumbra sign on the T1-weighted image, hyperintensity on T2-weighted images, and ring enhancement on the contrast-enhanced T1 image. ¹⁸F-FDG PET/CT images showed an uptake at the margin of the radius. Curettage and iliac cancellous bone grafting were undertaken for Brodie’s abscess. Bacteriological examinations were found to be negative, however, the pathologic diagnosis showed chronic osteomyelitis. Eight months after surgery, the patient was asymptomatic and there was no sign of recurrence of infection. For Brodie’s abscess in a child, thorough debridement is mandatory in addition to cancellous bone grafting. Brodie’s abscess should be considered in the differential diagnosis of a patient who presents with forearm pain and exhibit the radiolucent osteolytic lesion on simple radiography.

The Wiener number $W(G)$ of a graph $G$ was introduced by Harold Wiener in connection with the modeling of various physic-chemical, biological and pharmacological properties of organic molecules in chemistry. Milan Randić introduced a modification of the Wiener index for trees (acyclic graphs), and it is known as the hyper-Wiener index. Then Klein et al. generalized Randić’s definition for all connected (cyclic) graphs, as a generalization of the Wiener index, denoted by $WW(G)$ and defined as $WW(G)=\frac{1}{2}{\sum }_{u\in V}[d(u|G)+d^2(u|G)]$. In this paper, we establish some upper and lower bounds for $WW(G)$, in terms of other graph-theoretic parameters. Moreover, we compute hyper-Wiener number of some classes of graphs.

The aim is to provide a necessary and sufficient condition under which both a graph and its complement have (a) identical radius, (b) identical diameter, (c) identical center, and (d) identical periphery.

For a connected graph $G(V,E)$, we use the notation $d(a_1,a_2)$ to represent the distance between two node points $a_1$ and $a_2$ and it is the minimum of the lengths of all paths between them. The eccentricity $e(a)$ of a node point $a\in V$ is considered as the maximum length of all shortest paths starts from $a$ to the remaining nodes, i.e., $e(a)=max\{d(a,u_1):u_1\in V\}$. The diameter of a graph $G$, we denote it by $d(G)$ and it is the length of the longest shortest path in $G$, i.e., $d(G)=max\{e(a):a\in V\}$. Also, the radius of a graph $G$, we denote it by the symbol $r(G)$ and it is the least eccentricity of all node points in $V$, i.e., $r(G)=min\{e(a):a\in V\}$. The central vertex/node point $x$ of a graph $G$ is a node whose eccentricity is same as $G$’s radius, i.e., $e(x)=r(G)$. The collection of all central nodes of a graph $G$ is considered as the center of $G$ and it is symbolized by $c(G)$, i.e., $c(G)=\{x\in V:e(x)=r(G)\}$. A graph may have one or more central vertices. This paper develops an optimal algorithm to compute the diameter, radius and central node (s) of the permutation graph having $n$ node points in $O(n)$ time. We have also established a tight relation between radius and diameter of permutation graphs.

The rings considered in this paper are commutative with identity which are not integral domains. Let $R$ be a ring. An ideal $I$ of $R$ is said to be an annihilating ideal if there exists $r\in R\backslash \{0\}$ such that $Ir=(0)$. Let $𝔸(R)$ denote the set of all annihilating ideals of $R$ and we denote $𝔸(R)\backslash \{(0)\}$ by $𝔸{(R)}^{\ast }$. With $R$, in this paper, we associate an undirected graph denoted by $S\mathrm{\Omega }(R)$ whose vertex set is $𝔸{(R)}^{\ast }$ and two distinct vertices $I,J$ are adjacent in this graph if and only if either $IJ=(0)$ or $I+J\in 𝔸(R)$. The aim of this paper is to study the interplay between some graph properties of $S\mathrm{\Omega }(R)$ and the algebraic properties of $R$ and to compare some graph properties of $S\mathrm{\Omega }(R)$ with the corresponding graph properties of the annihilating ideal graph of $R$ and the sum annihilating ideal graph of $R$.

Background: Metaphyseal core decompression of the distal radius (MCD) is clinically effective in early lunate necrosis without changing individual wrist mechanics. Its concept is based on the induction of physiologic mechanisms known as physiologic fracture healing response. However, this biological concept does not yet have its place in the historically developed mechanical concepts about Kienböck’s disease and requires more detailed clarifications to understand when a change of individual wrist mechanics might be unnecessary.

Methods: Thirteen consecutive cases, Lichtman stage I (n = 1) or II (n = 12), confirmed by conventional MRI, were treated by MCD. Time off work, changes in magnetic resonance imaging of the lunate, as well as clinical outcome using modified Mayo wrist score were evaluated at final follow-up.

Results: Return to work was at six (1–10) weeks after surgery. MRI controls at short-term generally demonstrated stop of progression and signs of bone healing. Independently from ulna variance complete signal normalization was observed in six and a distinct, yet incomplete decrease of lunate bone marrow edema and zones of fat necrosis was confirmed in further six cases after a mean of 21 (13–51) weeks. One patient had radiographic controls only, stating normal healing at 56 months. After a mean follow-up of 37 (12–70) months the clinical outcomes were excellent in eleven and good in two cases (mean 95% in modified Mayo wrist score).

Conclusions: In stage I and II lunate necrosis MCD stops disease progression, it improves clinical symptoms and induces normalization of lunate bone signal alterations in MRI. Findings suggest that stage I and II lunate necrosis can be effectively treated without alterations of individual wrist mechanics. Future studies are necessary to readjust common concepts regarding Kienböck’s disease, especially focusing on conservative therapy.

Background: There are many options to treat post osteomyelitic gaps in forearm bones. We report a pediatric series with postosteomyelitic forearm segmental defects reconstructed with fibular only graft: the non vascular fibular intramedullary bridging bone and additional grafting (FIBBAG) and the results thereof.

Methods: Outcomes in 8 patients treated with fibular strut and overlay matchstick grafts were retrospectively assessed. The clinical results were expressed as forearm shortening, range of motion at elbow and wrist joint. The radiological evaluation included time to union, presence of fractures and recurrence of infection, if any.

Results: The average patient age was 6 years (range, 3–12 years). The radius was involved in 6 and ulna in 2. Union occurred in all patients. The average intraoperative gap to be spanned was 5.86 cm (range, 3–14 cm). The average time for union was 6.63 months (range, 2–14 months). Two patients required additional bone grafting procedures. No graft fatigues/fractures were noted in available follow up. There was no recurrence of infection in any case. A positive ulnar variance was seen in 3 patients at follow up. Forearm shortening was a major cosmetic limitation following the procedure.

Conclusions: Fibular strut and additional bone grafting (FIBBAG) is one of the viable options for reconstruction of post osteomyelitic forearm defects in children with low procedural complication rate.

Background: Numerous studies have indicated the presence of mesenchymal stem cells (MSCs) in the bone marrow aspirated from the vertebral body, distal femur, proximal tibia, humeral head, sternum, and iliac crest. However, their presence has not been reported in the radius thus far. In this study, we aimed to compare the number of MSCs in bone marrow aspirated from radius and iliac crest in patients with Kienböck’s disease. Furthermore, we examined the association between the number of MSCs in the bone marrow and patient age.

Methods: A total of 17 patients were recruited. Owing to difficulties in obtaining samples for 5 cases, only 12 cases were included. Hematological analyses and fibroblastic colony-forming unit (CFU-F) assay were performed using bone marrow samples aspirated from the radius (group R), the first sample aspirated from the iliac crest (group I-1), and the second sample aspirated from the iliac crest (group I-2). The CFU-F numbers among the three groups were compared using Mann–Whitney U-test. Pearson’s correlation coefficient was calculated to evaluate the association between the CFU-F numbers and patient age.

Results: The average numbers of CFU-Fs/ml in the bone marrow samples from the R, I-1, and I-2 groups were 3.4, 57.3, and 13.7, respectively. The CFU-F number in Group I-1 was significantly higher than that in the other two groups; the CFU-F number was lower in group R than in group I-2. The correlation coefficients were -0.168, 0.166, and 0.036 for samples from groups R, I-1, and I-2, respectively. No significant association between the CFU-F numbers and patient age was observed.

Conclusions: The presence of MSCs in the radius was indicated by CFU-Fs in patients with Kienböck’s disease. The number of CFU-Fs was lower in the radius than in the iliac crest; the CFU-F number was not associated with patient age.

A double-barreled fibular graft was used to reconstruct both forearm bones and the humeroradial joint after tumor resection. The patient had a tumor of radius that invaded the ulna and extensor groups. After a wide tumor resection, vascularized fibular autograft and soft tissue reconstruction was performed. A fibular graft were placed as a double barrel in the proximal ulnar and radial defects including the radial head and fixed using two locking plates. Simultaneously, reconstruction of the humeroradial joint and wrist dorsiflexion was performed. Two years postoperatively, the patient is satisfied with his elbow function while performing activities of daily living. Although amputation was one of the options considered during the preoperative planning in this case, the affected limb could be preserved by grafting a double-barreled fibula and tendon transfer, which could maintain the function of his upper left limb.

We report a 94-year-old patient with a fractured radius that was being managed conservatively. At 2 months, an abscess was observed overlying the fracture site. An MRI scan was done and samples obtained for microbiological and pathological analyses. The patient was diagnosed with tuberculous osteomyelitis. Surgical debridement of the fracture site was performed, and the bone defect was filled with bone cement impregnated with gentamicin and rifampicin. Anti-tuberculosis therapy was administered for 9 months and the patient made an uneventful recovery. Early diagnosis and correct medical treatment depend on sound evidence of tuberculous osteomyelitis. Surgical debridement is essential if abscesses are present in the bone.

Level of Evidence: Level V (Therapeutic)