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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Discontinuity induced bifurcations in a model of Saccharomyces cerevisiae.

We perform a bifurcation analysis of the mathematical model of Jones and Kompala [K.D. Jones, D.S. Kompala, Cybernetic model of the growth dynamics of Saccharomyces cerevisiae in batch and continuous cultures, J. Biotechnol. 71 (1999) 105-131]. Stable oscillations arise via Andronov-Hopf bifurcations and exist for intermediate values of the dilution rate as has been noted from experiments previously. A variety of discontinuity induced bifurcations arise from a lack of global differentiability. We identify and classify discontinuous bifurcations including several codimension-two scenarios. Bifurcation diagrams are explained by a general unfolding of these singularities.

Simultaneous border-collision and period-doubling bifurcations.

We unfold the codimension-two simultaneous occurrence of a border-collision bifurcation and a period-doubling bifurcation for a general piecewise-smooth, continuous map. We find that with sufficient nondegeneracy conditions, a locus of period-doubling bifurcations emanates nontangentially from a locus of border-collision bifurcations. The corresponding period-doubled solution undergoes a border-collision bifurcation along a curve emanating from the codimension-two point and tangent to the period-doubling locus here. In the case that the map is one-dimensional local dynamics is completely classified; in particular, we give conditions that ensure chaos.

Unfolding a codimension-two, discontinuous, Andronov-Hopf bifurcation.

We present an unfolding of the codimension-two scenario of the simultaneous occurrence of a discontinuous bifurcation and an Andronov-Hopf bifurcation in a piecewise-smooth, continuous system of autonomous ordinary differential equations in the plane. We find that the Hopf cycle undergoes a grazing bifurcation that may be very shortly followed by a saddle-node bifurcation of the orbit. We derive scaling laws for the bifurcation curves that emanate from the codimension-two bifurcation.

The effect of bearing congruency, thickness and alignment on the stresses in unicompartmental knee replacements.

BACKGROUND: Unicompartmental knee replacement offers an effective treatment for patients with single compartment knee disease and is becoming an increasingly popular alternative to total knee replacement. An important cause of failure in a unicompartmental knee replacement implant is polyethylene wear. Significant contributory factors to the amount of polyethylene wear are contact stress, bearing alignment, congruency and thickness. METHODS: Four different unicompartmental knee replacement implant designs (Fully-Congruent; Partially-Congruent; Non-Congruent-metal-backed; Non-Congruent-all-polyethylene) were inserted into a validated finite element model of a proximal tibia. The effect that bearing congruency, alignment and thickness had on the polyethylene stresses during a simulated step-up activity for each design was investigated. Additionally, contact pressures were compared to those calculated from Hertz elastic theory. FINDINGS: Only the Fully-Congruent bearing experienced peak von Mises and contact stresses below the lower fatigue limit for polyethylene during the step-up activity. The highest polyethylene contact stresses were observed for the Partially-Congruent and Non-Congruent-metal-backed designs, which experienced approximately three times the polyethylene lower fatigue limit. Increasing the bearing thickness from 3.5mm to 8.5mm of the Non-Congruent design decreased the contact stresses in the bearing; however they did not fall below the lower fatigue limit for polyethylene. Good agreement between finite element and Hertz contact pressures was found. INTERPRETATION: Fully congruent unicompartmental knee replacement bearings can be markedly thinner without approaching the material failure limit, have a greater potential to preserve bone stock and are less likely to fail mechanically.

Finite element analysis of intramedullary devices: the effect of the gap between the implant and the bone.

This paper examines the interaction interface between the implant and the bone for an intramedullary femoral nailing system using a finite element (FE) model and specifically considers the hypothesis that the local geometry at the interface is significant to the resulting localized contact stress between the medial and lateral aspect of nail and endosteum. Contact mechanics algorithms are used in the FE modelling technique that can be developed to deal with any form of intramedullary device for which contact at the bone-implant interface is important. Global stiffness data from the FE model are compared with available data from an experiment carried out on a construct of the bone and the device that uses intramedullary femoral nails. Acceptable agreement is obtained. The results demonstrate that the mechanical interface between the implant and the bone is significantly affected by the gap geometry and magnitude. In particular, larger gaps lead to greater concentrations of stress on the medial side, while the distribution of stress is more uniform at the lateral contacts. Furthermore, the results show that the gap can have a marked effect on the stresses that occur on the fracture plane.

Surgical management of a recurrent spinal meningioma in a cat.

A 13-year-old male neutered Persian crossbred cat was evaluated for hindlimb paresis, ataxia and urinary incontinence that had been progressing over the previous 3 months. Neurologically, the cat had thoracolumbar spinal cord deficits and a myelogram detected the presence of a mass compressing the thoracic spinal cord. A hemilaminectomy was performed to excise the soft tissue mass, subsequently identified histologically as a psammomatous meningioma. The cat regained ambulatory function and continence following surgery until a recurrence of paresis and ataxia 36 months later. A second myelogram suggested local recurrence of the tumour, which was confirmed by histological examination of the tumour after its removal at a second laminectomy. The cat again regained normal neurological function, until a further recurrence 16 months after the second surgery. The meningioma was surgically debulked a third time and the cat regained ambulation and continence postoperatively. This case demonstrates the successful use of repeated surgical resection in the management of a recurrent spinal meningioma in a cat. The cat was ambulatory and continent at a follow-up examination 63 months after the initial presentation.

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.

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.