Unstable dimension variability and heterodimensional cycles in the border-collision normal form.

Chaotic attractors commonly contain periodic solutions with unstable manifolds of different dimensions. This allows for a zoo of dynamical phenomena not possible for hyperbolic attractors. The purpose of this Letter is to emphasize the existence of these phenomena in the border-collision normal form. This is a continuous, piecewise-linear family of maps that is physically relevant as it captures the dynamics created in border-collision bifurcations in diverse applications. Since the maps are piecewise linear, they are relatively amenable to an exact analysis. We explicitly identify parameter values for heterodimensional cycles and argue that the existence of heterodimensional cycles between two given saddles can be dense in parameter space. We numerically identify key bifurcations associated with unstable dimension variability by studying a one-parameter subfamily that transitions continuously from where periodic solutions are all saddles to where they are all repellers. This is facilitated by fast and accurate computations of periodic solutions; indeed the piecewise-linear form should provide a useful testbed for further study.

Pattern Formation in a Spatially Extended Model of Pacemaker Dynamics in Smooth Muscle Cells.

Spatiotemporal patterns are common in biological systems. For electrically coupled cells, previous studies of pattern formation have mainly used applied current as the primary bifurcation parameter. The purpose of this paper is to show that applied current is not needed to generate spatiotemporal patterns for smooth muscle cells. The patterns can be generated solely by external mechanical stimulation (transmural pressure). To do this we study a reaction-diffusion system involving the Morris-Lecar equations and observe a wide range of spatiotemporal patterns for different values of the model parameters. Some aspects of these patterns are explained via a bifurcation analysis of the system without coupling - in particular Type I and Type II excitability both occur. We show the patterns are not due to a Turing instability and that the spatially extended model exhibits spatiotemporal chaos. We also use travelling wave coordinates to analyse travelling waves.

Robust Devaney chaos in the two-dimensional border-collision normal form.

The collection of all non-degenerate, continuous, two-piece, piecewise-linear maps on R2 can be reduced to a four-parameter family known as the two-dimensional border-collision normal form. We prove that throughout an open region of parameter space, this family has an attractor satisfying Devaney's definition of chaos. This strengthens the existing results on the robustness of chaos in piecewise-linear maps. We further show that the stable manifold of a saddle fixed point, despite being a one-dimensional object, densely fills an open region containing the attractor. Finally, we identify a heteroclinic bifurcation, not described previously, at which the attractor undergoes a crisis and may be destroyed.

The presence, morphology and clinical significance of vertebral body malformations in an Australian population of French Bulldogs and Pugs.

OBJECTIVE: To describe the incidence, morphology and clinical significance of congenital vertebral malformations (CVM) in two breeds of brachycephalic dogs presenting to a referral veterinary hospital. DESIGN: Prospective cohort study series. MATERIALS AND METHODS: Forty-nine French Bulldogs and Pugs were prospectively evaluated and placed in one of two groups based on whether or not they presented for neurological signs referable to spinal cord disease. A computed tomography (CT) of their entire spine was obtained and the presence and classification of CVM along with the degree of spinal kyphosis recorded for all dogs. Statistical analysis was performed to identify clinical associations between these factors (P < 0.05). RESULTS: CVM were prevalent across both breeds with the French Bulldog having more malformations than the Pug (Kruskal-Wallis nonparametric analysis of variance, P < 0.0001). Breed associated vertebral malformation subtypes included butterfly subtype in French Bulldogs (Chi-square, P = 0.0002), and transitional subtype in Pugs (odds ratio, 22.7; P = 0.000). A new subtype, dorsal wedge, was observed in 12 cases. The presence, number and subtype of vertebral malformation were not reliable for predicting the development of neurological signs across both breeds (Chi-square, P > 0.05). However, spinal kyphosis >35° calculated via Cobb angle was associated with Pugs that had neurological deficits (Chi-square, P = 0.028). CONCLUSIONS: Congenital vertebral malformations largely appear to be incidental findings in this population of French Bulldogs but are of more significance in the Pug breed when spinal kyphosis is >35°. French Bulldogs that have spinal cord disease and CVM are more likely to have pathology distant to CVM with intervertebral disc herniation most common.

Numerical Bifurcation Analysis of Pacemaker Dynamics in a Model of Smooth Muscle Cells.

Evidence from experimental studies shows that oscillations due to electro-mechanical coupling can be generated spontaneously in smooth muscle cells. Such cellular dynamics are known as pacemaker dynamics. In this article, we address pacemaker dynamics associated with the interaction of [Formula: see text] and [Formula: see text] fluxes in the cell membrane of a smooth muscle cell. First we reduce a pacemaker model to a two-dimensional system equivalent to the reduced Morris-Lecar model and then perform a detailed numerical bifurcation analysis of the reduced model. Existing bifurcation analyses of the Morris-Lecar model concentrate on external applied current, whereas we focus on parameters that model the response of the cell to changes in transmural pressure. We reveal a transition between Type I and Type II excitabilities with no external current required. We also compute a two-parameter bifurcation diagram and show how the transition is explained by the bifurcation structure.

Retrospective analysis of 736 cases of canine gastric dilatation volvulus.

OBJECTIVE: To identify factors influencing the survival of confirmed gastric dilatation volvulus (GDV) cases presented to a specialist referral and emergency hospital. METHODS: Clinical records of confirmed GDV cases admitted to two specialist referral and emergency centres in Sydney (Animal Referral Hospital (ARH) Homebush and ARH Baulkham Hills) between July 1999 and July 2019 were searched. RESULTS: A total of 736 GDV cases were reviewed, of which 460 dogs were surgically treated and 276 dogs were humanely killed. The survival rates of patients operated on by general surgeons and specialists were 81.7% and 88.7%, respectively. Both incisional gastropexy and belt-loop gastropexy were clinically effective in treating GDV, with no significant difference in survival rates. Intraoperative mortality rates for general surgeons and specialists were 7.0% and 2.9%, respectively. The odds of mortality in dogs operated on by general surgeons were 2.03 times those operated on by specialist surgeons. The odds of mortality in dogs presented between 3:00 and 9:00 am were 3.57 times those of dogs presented between 9:00 am and 9:00 pm. The odds of mortality in dogs where the duration from presentation to completion of surgery was more than 3 h were 2.53 times those of dogs where time lapsed was equal or less than 3 h. CONCLUSION: The results suggested that admission time was statistically significantly related to the survival rate. Dogs operated on by specialist surgeons had a significantly higher survival rate compared to those operated on by general surgeons. Clinicians should aim to stabilise and complete surgical correction of GDV as soon as possible to decrease the mortality.

A general framework for boundary equilibrium bifurcations of Filippov systems.

As parameters are varied, a boundary equilibrium bifurcation (BEB) occurs when an equilibrium collides with a discontinuity surface in a piecewise-smooth system of ordinary differential equations. Under certain genericity conditions, at a BEB, the equilibrium either transitions to a pseudo-equilibrium (on the discontinuity surface) or collides and annihilates with a coexisting pseudo-equilibrium. These two scenarios are distinguished by the sign of a certain inner product. Here, it is shown that this sign can be determined from the number of unstable directions associated with the two equilibria by using techniques developed by Feigin. A normal form is proposed for BEBs in systems of any number of dimensions. The normal form involves a companion matrix, as does the leading order sliding dynamics, and so the connection to the stability of the equilibria is explicit. In two dimensions, the parameters of the normal form distinguish, in a simple way, the eight topologically distinct cases for the generic local dynamics at a BEB. A numerical exploration in three dimensions reveals that BEBs can create multiple attractors and chaotic attractors and that the equilibrium at the BEB can be unstable even if both equilibria are stable. The developments presented here stem from seemingly unutilised similarities between BEBs in discontinuous systems (specifically Filippov systems as studied here) and BEBs in continuous systems for which analogous results are, to date, more advanced.

Long-term control of olfactory neuroblastoma in a dog treated with surgery and radiation therapy.

BACKGROUND: Olfactory neuroblastoma is a rare malignancy of the nasal cavity in dogs that is thought to arise from specialised sensory neuroendocrine olfactory cells derived from the neural crest. CASE REPORT: An 8-year-old dog was presented for reclusiveness and pacing. On CT and MRI, a contract-enhancing mass was disclosed within the rostral fossa, extending caudally from the cribriform plate into the left nasal sinus. Surgical excision was performed and the diagnosis was histological grade III (Hyams grading scheme) olfactory neuroblastoma. Based on human CT criteria this was high stage (modified Kadish stage C). Surgical excision was incomplete and was followed by curative-intent radiation therapy using a linear accelerator to a total dose of 48 Gy. CONCLUSION: The dog survived 20 months after diagnosis. Although olfactory neuroblastoma is a rare tumour in dogs, aggressive local therapy may allow for prolonged survival, even when the tumour is advanced.

Bilateral sacroiliac luxation fixation using a single transiliosacral pin: surgical technique and clinical outcomes in eight cats.

OBJECTIVES: A very limited safe anatomical window for transiliosacral implant placement exists in cats (<0·5 cm2 ). Lag screw fixation requires multiple bilateral implants thus increasing the risk of iatrogenic trauma and implant interference. We describe a safe and effective method for bilateral sacroiliac fixation in cats using a single implant to minimise inadvertent iatrogenic damage to local structures and restore pelvic canal diameter. MATERIALS AND METHODS: Eight cats underwent surgical fixation for traumatic bilateral sacroiliac luxation using a single smooth intramedullary pin. The pin spanned both ilial wings and sacrum. Implants were applied using a Universal C-guide. Pre- and postsurgery pelvic canal diameter ratios were calculated. Short-term follow-up was performed at 10 to 14 days postoperatively. Long-term follow-up was performed using the Feline Musculoskeletal Pain Index Questionnaire. Long-term radiographic assessment was available in two cases. RESULTS: The technique achieved safe and accurate implant position with precise sacroiliac joint reduction. Pelvic canal diameter ratios were restored to normal in all cases. Rapid return to normal hind leg function and excellent long-term clinical outcomes were achieved. CLINICAL SIGNIFICANCE: This technique offers a simple, safe, repeatable and affordable technique for treating bilateral sacroiliac luxations in the cat without the aid of fluoroscopy. The procedure can be performed using surgical tools and inventory readily available in general small animal practices.

Unfolding homoclinic connections formed by corner intersections in piecewise-smooth maps.

The stable and unstable manifolds of an invariant set of a piecewise-smooth map are themselves piecewise-smooth. Consequently, as parameters of a piecewise-smooth map are varied, an invariant set can develop a homoclinic connection when its stable manifold intersects a non-differentiable point of its unstable manifold (or vice-versa). This is a codimension-one bifurcation analogous to a homoclinic tangency of a smooth map, referred to here as a homoclinic corner. This paper presents an unfolding of generic homoclinic corners for saddle fixed points of planar piecewise-smooth continuous maps. It is shown that a sequence of border-collision bifurcations limits to a homoclinic corner and that all nearby periodic solutions are unstable.

Fast phase randomization via two-folds.

A two-fold is a singular point on the discontinuity surface of a piecewise-smooth vector field, at which the vector field is tangent to the discontinuity surface on both sides. If an orbit passes through an invisible two-fold (also known as a Teixeira singularity) before settling to regular periodic motion, then the phase of that motion cannot be determined from initial conditions, and, in the presence of small noise, the asymptotic phase of a large number of sample solutions is highly random. In this paper, we show how the probability distribution of the asymptotic phase depends on the global nonlinear dynamics. We also show how the phase of a smooth oscillator can be randomized by applying a simple discontinuous control law that generates an invisible two-fold. We propose that such a control law can be used to desynchronize a collection of oscillators, and that this manner of phase randomization is fast compared with existing methods (which use fixed points as phase singularities), because there is no slowing of the dynamics near a two-fold.

Free skin grafts for immediate wound coverage following tumour resection from the canine distal limb.

OBJECTIVE: To evaluate free skin graft as a closure method immediately following extensive oncological resections in the distal limb of dogs. METHOD: Evaluation of medical records of dogs that received a full-thickness, meshed, free skin graft in the distal limb immediately after tumour removal. RESULTS: Oncological resection was performed on the antebrachium of six dogs and the -tarso--metatarsal area of one dog. Tumour types were mast cell tumour (n=4), soft tissue sarcoma (n=2) and -histiocytic sarcoma (n=1). The recipient bed consisted predominately of muscles and tendons. Three grafts survived completely. There was partial, superficial epidermal necrosis in some areas of four grafts. None of the dogs had full thickness necrosis or required further reconstruction. Good to excellent cosmetic results were achieved. Tumour resection was complete in every case. There was no local tumour recurrence at the time of last follow-up (6-49 months). CLINICAL SIGNIFICANCE: Free grafting can be used reliably to reconstruct extensive surgical wounds in the distal limb in dogs after large tumour resection without the need for a delay to allow granulation tissue to form. Immediate grafting is useful as an alternative to other reconstructive surgical techniques or second intention healing.

Load transfer in the proximal tibia following implantation with a unicompartmental knee replacement: a static snapshot.

Unicompartmental knee replacement (UKR) is an appealing alternative to total knee replacement when the patient has isolated medial compartment osteoarthritis. A common observation post-operatively is radiolucency between the tibial tray wall and the bone. In addition, some patients complain of persistent pain over the proximal tibia antero-medially; this may be related to elevated bone strains in the tibia. Currently, there is no intentionally made mechanical bond between the vertical wall of an Oxford UKR and the adjacent bone; whether one exists or not will influence the load transmission in the proximal tibia and may affect the elevated tibia strain. The aim of this study was to investigate how introducing a mechanical tie between the tibial tray wall and the adjacent bone might alter the load carried into the tibia for both cemented and cementless UKRs. Strain energy density in the region of bone adjacent to the tray wall was considerably increased when a mechanical tie was introduced; this has the potential of reducing the likelihood of a radiolucency occurring in that region. Moreover, a mechanical tie had the effect of reducing proximal tibia strain, which may decrease the incidence of pain following implantation with a UKR.

Polyethylene wear of mobile-bearing unicompartmental knee replacement at 20 years.

The Oxford unicompartmental knee replacement (UKR) was designed to minimise wear utilising a fully-congruent, mobile, polyethylene bearing. Wear of polyethylene is a significant cause of revision surgery in UKR in the first decade, and the incidence increases in the second decade. Our study used model-based radiostereometric analysis to measure the combined wear of the upper and lower bearing surfaces in 13 medial-compartment Oxford UKRs at a mean of 20.9 years (17.2 to 25.9) post-operatively. The mean linear penetration of the polyethylene bearing was 1.04 mm (0.307 to 2.15), with a mean annual wear rate of 0.045 mm/year (0.016 to 0.099). The annual wear rate of the phase-2 bearings (mean 0.022 mm/year) was significantly less (p = 0.01) than that of phase-1 bearings (mean 0.07 mm/year). The linear wear rate of the Oxford UKR remains very low into the third decade. We believe that phase-2 bearings had lower wear rates than phase-1 implants because of the improved bearing design and surgical technique which decreased the incidence of impingement. We conclude that the design of the Oxford UKR gives low rates of wear in the long term.

A first-principles study of the dielectric properties of TiO2 polymorphs.

We present an analysis of the dielectric properties of the three polymorphs of TiO2 (rutile, anatase and brookite phases), using ab initio time-dependent density functional perturbation theory based on the Vignale-Kohn functional. We implement this functional, which incorporates many-body effects, using the periodic program BAND. The improved result for the density of states spectra for brookite is suggestive of increased titanium ion Jahn-Teller effects for this phase. The imaginary and real components of the frequency-dependent dielectric functions show notable dielectric anisotropies, with implications for excitonic interactions, for all three common phases of TiO2. Comparison of the electron energy-loss spectrum for undoped and doped rutile and anatase reveals the critical role of collective charge excitations in photocatalytic mechanisms. The correlation between plasmon peaks present at lower energies and decreased photocatalytic activity due to substitutional aluminum doping in combination with oxygen vacancies in rutile and anatase is highlighted. Moreover, there is clear correlation between dielectric properties and the microstructure of the TiO2 polymorphs as suggested via the framework of the Born effective charge and Hirshfeld charge distribution schemes.

The migration patterns of two versions of the Furlong cementless femoral stem: a randomised, controlled trial using radiostereometric analysis.

We have evaluated the difference in the migration patterns over two years of two cementless stems in a randomised, controlled trial using radiostereophotogrammetric analysis (RSA). The implants studied were the Furlong HAC stem, which has good long-term results and the Furlong Active stem, which is a modified version of the former designed to minimise stress concentrations between the implant and bone, and thus to improve fixation. A total of 23 Furlong HAC and 20 Furlong Active stems were implanted in 43 patients. RSA examinations were carried out immediately post-operatively and at six, 12 and 24 months post-operatively. The subsidence during the first year in the Furlong HAC stem, was approximately one-third that of the Furlong Active stem, the measured mean subsidence of the femoral head at six months being 0.27 mm (95% confidence interval (CI) 0.03 to 0.51) and 0.99 mm (95% CI 0.38 to 1.60), respectively (p = 0.03). One Active stem continued to subside during the second year. All hips, regardless of the type of stem were clinically successful as judged by the Oxford hip score and a derived pain score without any distinction between the two types of stem. The initial stability of the Furlong Active stem was not as good as the established stem which might compromise osseo-integration to the detriment of long-term success. The changes in the geometry of the stem, to minimise stress have affected the attainment of initial stability.

Tibial tuberosity advancement in 92 canine stifles: initial results, clinical outcome and owner evaluation.

OBJECTIVE: To investigate the clinical outcomes, complications and owners' evaluation of the tibial tuberosity advancement (TTA) procedure in canine stifles. METHODS: A retrospective study of hospital records was performed to identify dogs diagnosed with partial or complete cranial cruciate ligament (CCL) rupture that had undergone TTA repair. Information obtained included signalment, period of lameness, surgical report, evidence of meniscal injury, postoperative recovery and peri-operative complications. Owners were asked to assess the long-term outcome. RESULTS: In a total of 72 dogs (median age, 6 years; median body weight, 34.8 kg), TTA was performed in 92 stifles. Twenty breeds were represented, with Labrador Retrievers and Rottweilers the most common. The period of lameness ranged from 3 days to 24 months. The median pre-operative lameness score was 3/4 and meniscal injury was present in 51 stifles. Minor complications occurred in 29% of cases. Major complications occurred in 6.5% of cases and consisted of meniscal injury and two tibial tuberosity fractures. All were successfully managed, with good limb function when subsequently assessed. In the owner evaluation, 96% reported moderate to great improvement postoperatively, with no lameness at rest and mild to no lameness after vigorous exercise. CONCLUSION: Clinical outcome and owner evaluations in this case series indicate favourable results can be expected when CCL-deficient stifles are treated with TTA.

Lip commissure to eyelid transposition for repair of feline eyelid agenesis.

Repair of eyelid agenesis in nine eyes of five cats using a lip commissure to eyelid transposition is described. The procedure is a modification of the technique described by Pavletic for reconstruction of the canine inferior eyelid and provides skin, mucosa, a mucocutaneous junction, and muscle to reconstruct the superior and inferior eyelid and lateral canthus. The technique was successful in all eyes and resulted in improvement in corneal protection, cosmesis and in several cats a return of the palpebral reflex.

Analysis of wear of retrieved metal-on-metal hip resurfacing implants revised due to pseudotumours.

The presence of pseudotumours, which are soft-tissue masses relating to the hip, after metal-on-metal hip resurfacing arthroplasty has been associated with elevated levels of metal ions in serum, suggesting that pseudotumours occur when there is increased wear. We aimed to quantify the wear in vivo of implants revised for pseudotumours (eight) and of a control group of implants (22) revised for other reasons of failure. We found that the implant group with pseudotumours had a significantly higher rate of median linear wear of the femoral component at 8.1 microm/year (2.75 to 25.4) than the 1.79 microm/year (0.82 to 4.15; p = 0.002) of the non-pseudotumour group. For the acetabular component a significantly higher rate of median linear wear of 7.36 microm/year (1.61 to 24.9) was observed in the pseudotumour group compared with 1.28 microm/year (0.81 to 3.33, p = 0.001) in the other group. Wear of the acetabular component in the pseudotumour group always involved the edge of the implant, indicating that edge-loading had occurred. Our findings are the first direct evidence that pseudotumour is associated with increased wear at the metal-on-metal articulation. Furthermore, edge-loading with the loss of fluid-film lubrication may be an important mechanism of generation of wear in patients with a pseudotumour.

Development of a model-based Roentgen stereophotogrammetric analysis system to measure polyethylene wear in unicompartmental arthroplasty.

One of the most important causes of failure in unicompartmental knee replacement (UKR) is polyethylene wear. The aim of this study was to develop and assess a novel Roentgen stereophotogrammetric analysis (RSA)-based method for the measurement of linear wear suitable for UKR. Model-based RSA was used to estimate the linear wear of polyethylene bearings in UKR. A phantom was used to validate the method using in vitro measured bearing thicknesses and the linear wear of ten control bearings was estimated in vivo. Computer aided design (CAD) models for the UKRs were used in the model-based RSA system. There was no statistically significant difference between the estimated and measured bearing thicknesses using the CAD models (p = 0.386). The precision of the linear wear measurement, expressed as the standard deviation of the difference between the estimated and measured bearing thickness was 0.163 mm. The bias (mean difference) was 0.030 mm. The use of RSA to measure in vivo wear in a UKR has been shown to be accurate in a phantom, and has been verified with in vivo measured controls. The technique does not require surgical implantation of marker balls and can be used retrospectively.