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This paper presents two observability inequalities for the heat equation over Ω X (0, T) In the first one, the observation is from a subset of positive measure in Ω X (0, T) while in the second, the observation is from a subset of positive surface measure on Ω X (0, T) It also proves the Lebeau-Robbiano spectral inequality when Ω is a bounded Lipschitz and locally star-shaped domain. Some applications for the above-mentioned observability inequalities are provided. [ABSTRACT FROM AUTHOR]

The article presents the use of the strong unique continuation property (SUCP) in resolving the Schrödinger equations. A problem in quantitative unique continuation around the point at infinity is considered to strengthen the hypothesis proposed by Carleman and Müller for nonlinear problems. Mathematical proofs for uncertainty principles of Hardy, Morgan and Ingham types and various theorems are given.

We prove unique continuation properties for solutions of evolutionary Schrödinger's equation with time-dependent potentials. In the case of the free solution, these correspond to uncertainty principles referred to as being of Morgan type. As an application of our method, we also obtain results concerning the possible concentration profiles of solutions of semi-linear Schrödinger equations. [ABSTRACT FROM PUBLISHER]

Objective:  The aim of this study was to report new preoperative and intraoperative techniques performed for canine thoracic or lumbar spine kyphosis stabilization using three-dimensional-printed patient-specific drill guides, polyaxial titanium bone plates and drill stops, and to determine the accuracy of screw placement using these techniques., Study Design:  Retrospective study, five client-owned dogs., Results:  Three-dimensional-printed patient-specific drill guides and drill stops allowed safe drilling and screw placement in all of the cases, with (i) 84% of the screws graded as I (ideal placement) and 16% as IIa, IIIa or IIIb according to the modified Zdichavsky classification (partial penetration of medial pedicle wall, partial penetration of lateral pedicle wall and full penetration of lateral pedicle wall respectively), (ii) mean mediolateral deviation of ± 4.06 degrees (standard deviation: 8.21 degrees) compared to planned trajectories and (iii) variation in screw depth of ± 2.29mm (standard deviation: 3.07mm) compared to planned depth., Conclusion:  We believe that the techniques presented here for thoracic spinal stabilization in dogs show promise; they allowed safe placement of screws along planned trajectories and depth; they also removed the need to use polymethylmethacrylate, while the use of titanium offers the possibility to repeat magnetic resonance imaging in these cases with chronic spinal conditions., Competing Interests: The 3D-PSGs are produced by B.O. of Vet 3D. The rest of the authors report no conflict of interest., (Thieme. All rights reserved.)

Spinal cord injury (SCI) can cause irreversible paralysis, with no regenerative treatment clinically available. Dogs with natural SCI present an established model and can facilitate translation of experimental findings in rodents to people. We conducted a prospective, single arm clinical safety study in companion dogs with chronic SCI to characterize the feasibility of intraspinal transplantation of hydrogel-encapsulated autologous mucosal olfactory ensheathing cell (mOEC) populations expressing chondroitinase ABC (chABC). mOECs and chABC are both promising therapies for SCI, and mOECs expressing chABC drive greater voluntary motor recovery than mOECs alone after SCI in rats. Canine mOECs encapsulated in collagen hydrogel can be matched in stiffness to canine SCI. Four dogs with complete and chronic loss of function caudal to a thoraco-lumbar lesion were recruited. After baseline measures, olfactory mucosal biopsy was performed and autologous mOECs cultured and transduced to express chABC, then hydrogel-encapsulated and percutaneously injected into the spinal cord. Dogs were monitored for 6 months with repeat clinical examinations, spinal MRI, kinematic gait and von Frey assessment. No adverse effects or significant changes on neurological examination were detected. MRI revealed large and variable lesions, with no spinal cord compression or ischemia visible after hydrogel transplantation. Owners reported increased pelvic-limb reflexes with one dog able to take 2-3 unsupported steps, but gait-scoring and kinematic analysis showed no significant improvements. This novel combination approach to regeneration after SCI is therefore feasible and safe in paraplegic dogs in a clinical setting. A randomised-controlled trial in this translational model is proposed to test efficacy., (© 2022 The Authors. Journal of Tissue Engineering and Regenerative Medicine published by John Wiley & Sons Ltd.)

Objective: Hypophysectomy in dogs is a difficult surgery that requires specific learning and training. We aimed to evaluate the accuracy of a 3-dimensional printed patient-specific surgical guide to facilitate choosing the entry point in the basisphenoid bone before approaching the sella turcica during transsphenoidal hypophysectomy in dogs., Methods: Two canine cadavers and 8 dogs undergoing transsphenoidal hypophysectomy for Cushing's disease treatment, involving design and fabrication of a 3-dimensional printed guide. The ideal entry point in the basisphenoid bone outer cortical layer was determined in each dog pre-operatively; its anatomical location was described with a set of measurements then compared to post-operative computed tomography measures describing the location of the outer cortical window created in the basisphenoid bone., Results: Several guide designs were proposed, and a consensus reached based on surgeons' experience performing hypophysectomy. The device chosen could be applied to the size and shape of skulls encountered in this case series. The pre-planned measurements were comparable to post-operative measurement (there was also no statistical difference), with median of differences <0.1 mm, which we judged as clinically acceptable., Clinical Significance: Hypophysectomy in dogs is a challenging procedure that has a learning curve and needs to be performed by specialist neurosurgeons. We propose that a low-profile 3-dimensional printed surgical guide can aid the specialist neurosurgeon to locate the burring site of the outer cortical layer of the basisphenoid bone at a pre-defined location and with good accuracy. It does not alleviate the need to understand the anatomy of the region and to know how to create a slot within the basisphenoid bone, which remains essential to enter the sella turcica . This device could help specialist veterinary neurosurgeons wishing to be trained to perform hypophysectomy., Competing Interests: BO is the manufacturer of the surgical device through the company Vet3D and NG undertakes paid consultancy work for Vet3D in relation to the guide system. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2022 Escauriaza, Fenn, McCue, Roper, Vandenberghe, Nye, Oxley and Granger.)