Giulia Spaletta

Derivation of symmetric composition constants for symmetric integrators

This work focuses on the derivation of composition methods for the numerical integration of ordinary differential equations, which give rise to very challenging optimization problems. Composition is a useful technique for constructing high order approximations, while conserving certain geometric properties. We survey existing composition methods and describe results of an intensive numerical search for new methods. Details of the search procedure are given along with numerical examples, which indicate that the new methods perform better than previously known methods. Some insight into the location of global minima for these problems is obtained as a result.

Precise numerical computation

Abstract Arithmetic systems such as those based on IEEE standards currently make no attempt to track the propagation of errors. A formal error analysis, however, can be complicated and is often confined to the realm of experts in numerical analysis. In recent years, there has been a resurgence of interest in automated methods for accurately monitoring the error propagation. In this article, a floating-point system based on significance arithmetic will be described. Details of the implementation in Mathematica will be given along with examples that illustrate the design goals and differences over conventional fixed-precision floating-point systems.

Ex situ bioengineering of bioartificial endocrine glands: A new frontier in regenerative medicine of soft tissue organs

Ex situ bioengineering is one of the most promising perspectives in the field of regenerative medicine allowing for organ reconstruction outside the living body; i.e. on the laboratory bench. A number of hollow viscera of the cardiovascular, respiratory, genitourinary, and digestive systems have been successfully bioengineered ex situ, exploiting biocompatible scaffolds with a 3D morphology that recapitulates that of the native organ (organomorphic scaffold). In contrast, bioengineering of entire soft tissue organs and, in particular endocrine glands still remains a substantial challenge. Primary reasons are that no organomorphic scaffolding for endocrine viscera have as yet been entirely assembled using biocompatible materials, nor is there a bioreactor performance capable of supporting growth within the thickness range of the regenerating cell mass which has proven to be reliable enough to ensure formation of a complete macroscopic gland ex situ. Current technical options for reconstruction of endocrine viscera include either biocompatible 3D reticular scaffolds lacking any organomorphic geometry, or allogenic/xenogenic acellular 3D matrices derived from a gland similar to that to be bioengineered, eventually recellularized by autologous/heterologous cells. In 2007, our group designed, using biocompatible material, an organomorphic scaffold-bioreactor unit for bioengineering ex situ the human thyroid gland, chosen as a model for its simple anatomical organization (repetitive follicular cavities). This unit reproduces both the 3D native geometry of the human thyroid stromal/vascular scaffold, and the natural thyrocyte/vascular interface. It is now under intense investigation as an experimental tool to test cellular 3D auto-assembly of thyroid tissue and its related vascular system up to the ex situ generation of a 3D macroscopic thyroid gland. We believe that these studies will lay the groundwork for a new concept in regenerative medicine of soft tissue and endocrine organs; i.e. that the organomorphism of a biocompatible scaffold-bioreactor complex is essential to both the 3D organization of seeded stem cells/precursor cells and their phenotypic fate as glandular/parenchymal/vascular elements, eventually leading to a physiologically competent and immuno-tolerant bioconstruct, macroscopically suitable for transplantation and clinical applications.

An image reconstruction algorithm in tomography: a version for the CRAY X-MP vector computer

Abstract The present paper summarizes the main features of an algorithm for image reconstruction from radiographic projections. Starting from an analysis of the “filtered back-projection algorithm,” a new routine is built which performs “filtering” of the projections through a particular filter-function. The results are then tested by means of the simulation of a tomographic problem (C.T.) implemented on the CRAY X-MP/48 vector processor.

A regularizing Lanczos iteration method for underdetermined linear systems

This paper is concerned with the solution of underdetermined linear systems of equations with a very ill-conditioned matrix A, whose dimensions are so large to make solution by direct methods impractical or infeasible. Image reconstruction from projections often gives rise to such systems. In order to facilitate the computation of a meaningful approximate solution, we regularize the linear system, i.e., we replace it by a nearby system that is better conditioned. The amount of regularization is determined by a regularization parameter. Its optimal value is, in most applications, not known a priori. We present a new iterative method based on the Lanczos algorithm for determining a suitable value of the regularization parameter by the discrepancy principle and an approximate solution of the regularized system of equations.

A combined additive layer manufacturing / indirect replication method to prototype 3D vascular-like structures of soft tissue and endocrine organs: A combined additive layer manufacturing (ALM)/ indirect replication method to prototype 3D vascular-like structures of soft tissue and endocrine organs is presented in this paper

We describe an innovative methodology combining Additive Layer Manufacturing (ALM) and indirect replication to reconstruct reticular-like, three-dimensional (3D) structures mimicking the vascular network of soft tissue and endocrine organs. Using a fractal-like algorithm capable of modelling the intraparenchymal vascular distribution of these viscera, single intraglandular branches of the human thyroid arteries were prototyped with synthetic resin, based on the algorithmic standard to layer (STL) output and ALM techniques. Satisfactory dimensional accuracy was obtained for these models, which were used as masters to evaluate protocols for their indirect replication, through both single and double procedures. Additional studies were conducted using casts of the human kidney arteries, obtained by injection / corrosion of the isolated organ. Satisfactory 3D reproduction of the external morphology of the kidney vessels was achieved. We conclude that our approach has the potential to develop up to the reconstruction with biomaterials of an entire, intraparenchymal vascular tree of soft tissue and endocrine organs.

A study on the relationship between intraglandular arterial distribution and thyroid lobe shape: Implications for biotechnology of a bioartificial thyroid

We have recently hypothesized that structural and secretory components of the adult human thyroid gland maintain constant reciprocal and geometrical relationships, even if changes occur in the three-dimensional (3D) architecture of any of these elements. This means that thyroid morphology could be studied from the point of view of a 3D topology. As a consequence, we have investigated anatomical aspects that could support this assumption. In the present study, we show that the presence of a constant relationship can be demonstrated between the vascular arrangement of the gland, including the extension of intraglandular arterial fields, arterial anastomoses and arterial calibers, and the shape as well as volume of the thyroid. Specifically, a statistically significant difference has been found between the network amplitudes of the superior and inferior thyroid arteries in relation to either a conic or an ellipsoidal geometry of the thyroid lobe. In addition, a direct relationship has been implicated between the distribution of arterial anastomoses and the behavior of the lobe as a single hemodynamic unit. Finally, a statistically significant correlation has been observed between average arterial caliber of the inferior thyroid artery and thyroid volume. On the basis of these results, we propose a model of architectural assembly between stromal and parenchymal elements of the adult thyroid that might prove useful in designing a bioartificial gland ex situ. Potential clinical applications of this principle in regenerative medicine of other endocrine organs are highlighted.

Symplectic Methods for Separable Hamiltonian Systems

This paper focuses on the solution of separable Hamiltonian systems using explicit symplectic integration methods. Strategies for reducing the effect of cumulative rounding errors are outlined and advantages over a standard formulation are demonstrated. Procedures for automatically choosing appropriate methods are also described.

Increment formulations for rounding error reduction in the numerical solution of structured differential systems

Strategies for reducing the effect of cumulative rounding errors in geometric numerical integration are outlined. The focus is, in particular, on the solution of separable Hamiltonian systems using explicit symplectic integration methods and on solving orthogonal matrix differential systems using projection. Examples are given that demonstrate the advantages of an increment formulation over the standard implementation of conventional integrators. We describe how the aforementioned special purpose integration methods have been set up in a uniform, modular and extensible framework being developed in the problem solving environment Mathematica.

Growth on poly(l-lactic acid) porous scaffold preserves CD73 and CD90 immunophenotype markers of rat bone marrow mesenchymal stromal cells

Few data are available on the effect of biomaterials on surface antigens of mammalian bone marrow-derived, adult mesenchymal stromal cells (MSCs). Since poly(l-lactic acid) or PLLA is largely used in tissue engineering of human bones, and we are developing a reverse engineering program to prototype with biomaterials the vascular architecture of bones for their bioartificial reconstruction, both in humans and animal models, we have studied the effect of porous, flat and smooth PLLA scaffolds on the immunophenotype of in vitro grown, rat MSCs in the absence of any coating, co-polymeric enrichment, and differentiation stimuli. Similar to controls on plastic, we show that our PLLA scaffold does not modify the distribution of some surface markers in rat MSCs. In particular, the maintained expression of CD73 and CD90 on two different subpopulations (small and large cells) is consistent with their adhesion to the PLLA scaffold through specialized appendages, and to their prominent content in actin. In addition, our PLLA scaffold favours retention of the intermediate filament desmin, believed a putative marker of undifferentiated state. Finally, it preserves all rat MSCs morphotypes, and allows for their survival, adhesion to the substrate, and replication. Remarkably, a subpopulation of rat MSCs grown on our PLLA scaffold exhibited formation of membrane protrusions of uncertain significance, although in a size range and morphology compatible with either motility blebs or shedding vesicles. In summary, our PLLA scaffold has no detrimental effect on a number of features of rat MSCs, primarily the expression of CD73 and CD90.