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Tissue engineering is a promising methodology to produce advanced therapy medicinal products (ATMPs). We have developed personalized tissue engineered veins (P-TEV) as an alternative to autologous or synthetic vascular grafts utilized in reconstructive vein surgery. Our hypothesis is that individualization through reconditioning of a decellularized allogenic graft with autologous blood will prime the tissue for efficient recellularization, protect the graft from thrombosis, and decrease the risk of rejection. In this study, P-TEVs were transplanted to vena cava in pig, and the analysis of three veins after six months, six veins after 12 months and one vein after 14 months showed that all P-TEVs were fully patent, and the tissue was well recellularized and revascularized. To confirm that the ATMP product had the expected characteristics one year after transplantation, gene expression profiling of cells from P-TEV and native vena cava were analyzed and compared by qPCR and sequencing. The qPCR and bioinformatics analysis confirmed that the cells from the P-TEV were highly similar to the native cells, and we therefore conclude that P-TEV is functional and safe in large animals and have high potential for use as a clinical transplant graft., CC BY 3.0First published 13 Apr 2023Joakim.hakansson@ri.seThis study was supported by Vinnova project CAMP (contract no. 2017-02130), a common call by VINNOVA and Vetenskapsrådet: Biologcal pharmaseuticals (Dnr 2017-02983), by University of Skövde under grants from the Swedish Knowledge Foundation [#2016-0330, #2020-0014] and Västra Götalandsregionen (consultant check). The company VERIGRAFT AB holds a patent on peripheral whole blood perfusion of decellularized tissues and did also finance the project. We want to acknowledge the staff at the Department of Experimental Biomedicine at Gothenburg University. The swine studies in Spain were conducted by the ICTS ‘NANBIOSIS’, specifically Units 21, 22, and 24 of the CCMIJU. Graphical Abstract image created with BioRender.com.

In this paper we construct a large family of examples of subsets of Euclidean space that support a 1-Poincaré inequality yet have empty interior. These examples are formed from an iterative process that in-volves removing well behaved domains, or more precisely, domains whose complements are uniform in the sense of Martio and Sarvas. While existing arguments rely on explicit constructions of Semmes families of curves, we include a new way of obtaining Poincaré inequalities through the use of relative isoperimetric inequalities, after Korte and Lahti. To do so, we further introduce the notion of of isoperimetric inequalities at given density levels and a way to iterate suc inequalities. These tools are presented and apply to general metric measure measures. Our examples subsume the previous results of Mackay, Tyson, and Wildrick regarding non-self similar Sierpiński carpets, and extend them to many more general shapes as well as higher dimensions.

We study necessary and sufficient conditions for a Muckenhoupt \(\mathscr{A}_p\)-weight \(w \in L^{1}_{\mathrm{loc}}(\mathbb{R}^{d})\) that yield almost sure existence of radial, and vertical, limits at infinity for Sobolev functions \(u \in W^{1,~p}_{\mathrm{loc}}(\mathbb{R}^{d}, w)\) with a \(p\)-integrable gradient \(|\nabla u| \in L^{p}(\mathbb{R}^{d}, w)\) where \(1 \le p \lt \infty\) and \(2 \le d \lt \infty\). The question is shown to subtly depend on the sense in which the limit is taken. First, we fully characterize the existence of radial limits. Second, we give essentially sharp sufficient conditions for the existence of vertical limits. In the specific setting of product and radial weights, we give if and only if statements. These generalize and give new proofs for results of Fefferman and Uspenskiĭ. As applications to partial differential equations, we give results on the limiting behavior of weighted \(q\)-harmonic functions at infinity (\(1 \lt q \lt \infty\) ), which depend on the integrability degree of its gradient.

We study existence, uniqueness, and regularity properties of the Dirichlet problem related to fractional Dirichlet energy minimizers in a complete doubling metric measure space \((X, d_{X}, \mu_{x})\) satisfying a 2-Poincaré inequality. Given a bounded domain \(\Omega \subset X\) with \(\mu_{x}(X \setminus \Omega) > 0\), and a function \(f\) in the Besov class \(B^{\theta}_{2,2}(X) \cap L^{2}(X)\), we study the problem of finding a function \( u \in B^{\theta}_{2,2}(X)\) such that \( u = f\) in \(X \setminus \Omega\) and \(\mathcal{E}_{\theta}(u,u) \leq \mathcal{E}_{\theta}(h,h)\) whenever \( h \in B^{\theta}_{2,2}(X)\) with \(h = f\) in \(X \setminus \Omega\). We show that such a solution always exists and that this solution is unique. We also show that the solution is locally Hölder continuous on \(\Omega\), and satisfies a non-local maximum and strong maximum principle. Part of the results in this paper extends the work of Caffarelli and Silvestre in the Euclidean setting and Franchi and Ferrari in Carnot groups.

In this paper, we study the asymptotic behavior of BV functions in complete metric measure spaces equipped with a doubling measure supporting a 1-Poincaré inequality. We show that at almost every point x outside the Cantor and jump parts of a BV function, the asymptotic limit of the function is a Lipschitz continuous function of least gradient on a tangent space to the metric space based at x. We also show that, at co-dimension 1 Hausdorff measure almost every measure-theoretic boundary point of a set (Ε) of finite perimeter, there is an asymptotic limit set Ε∞ corresponding to the asymptotic expansion of Ε and that every such asymptotic limit (Ε)∞ is a quasiminimal set of finite perimeter. We also show that the perimeter measure of Ε∞ is Ahlfors co-dimension 1 regular.

Here we show existence of many subsets of Euclidean spaces that, despite having empty interior, still support Poincaré inequalities with respect to the restricted Lebesgue measure. Most importantly, despite the explicit constructions in our proofs, our methods do not depend on any rectilinear or self-similar structure of the underlying space. We instead employ the uniform domain condition of Martio and Sarvas. This condition relies on the measure density of such subsets, as well as the regularity and relative separation of their boundary components. In doing so, our results hold true for metric spaces equipped with doubling measures and Poincaré inequalities in general, and for the Heisenberg groups in particular. To our knowledge, these are the first examples of such subsets on any (nonabelian) Carnot group. Such subsets also give new examples of Sobolev extension domains, also in the general setting of doubling metric measure spaces. In the Euclidean case, our construction also includes the non-self-similar Sierpiński carpets of Mackay, Tyson and Wildrick, as well as higher dimensional analogues not treated in the literature. When specialized to the plane, our results lead to new, general sufficient conditions for a planar subset to be 2-Ahlfors regular and to satisfy the Loewner condition. Two of these conditions, uniform separation and regularity of boundary components, are also necessary. The sufficiency is obtained with an additional measure density condition.