Departamento de Ciencia e Ingeniería de los Materiales e Ingeniería Química
http://hdl.handle.net/10016/14126
2016-10-21T18:31:38ZSoliton driven angiogenesis
http://hdl.handle.net/10016/23755
Soliton driven angiogenesis
López Bonilla, Luis Francisco; Carretero Cerrajero, Manuel; Terragni, Filippo; Birnir, Bjorn
Angiogenesis is a multiscale process by which blood vessels grow from existing ones and carry oxygen to distant organs. Angiogenesis is essential for normal organ growth and wounded tissue repair but it may also be induced by tumours to amplify their own growth. Mathematical and computational models contribute to understanding angiogenesis and developing anti-angiogenic drugs, but most work only involves numerical simulations and analysis has lagged. A recent stochastic model of tumour-induced angiogenesis including blood vessel branching, elongation, and anastomosis captures some of its intrinsic multiscale structures, yet allows one to extract a deterministic integropartial differential description of the vessel tip density. Here we find that the latter advances chemotactically towards the tumour driven by a soliton (similar to the famous Korteweg-de Vries soliton) whose shape and velocity change slowly. Analysing these collective coordinates paves the way for controlling angiogenesis through the soliton, the engine that drives this process.
2016-08-09T00:00:00ZDiffuse optical tomography using the one-way radiative transfer equation
http://hdl.handle.net/10016/23561
Diffuse optical tomography using the one-way radiative transfer equation
González Rodríguez, Pedro; Kim, Arnold Dongkyoon
We present a computational study of diffuse optical tomography using the one-way radiative transfer equation. The one-way radiative transfer is a simplification of the radiative transfer equation to approximate the transmission of light through tissues. The major simplification of this approximation is that the intensity satisfies an initial value problem rather than a boundary value problem. Consequently, the inverse problem to reconstruct the absorption and scattering coefficients from transmission measurements of scattered light is simplified. Using the initial value problem for the one-way radiative transfer equation to compute the forward model, we are able to quantitatively reconstruct the absorption and scattering coefficients efficiently and effectively for simple problems and obtain reasonable results for complicated problems.
2015-05-08T00:00:00ZLaurent expansion of the inverse of perturbed, singular matrices
http://hdl.handle.net/10016/23560
Laurent expansion of the inverse of perturbed, singular matrices
González Rodríguez, Pedro; Moscoso Castro, Miguel Ángel; Kindelan Segura, Manuel
In this paper we describe a numerical algorithm to compute the Laurent expansion of the inverse of singularly perturbed matrices. The algorithm is based on the resolvent formalism used in complex analysis to study the spectrum of matrices. The input of the algorithm are the matrix coefficients of the power series expansion of the perturbed matrix. The matrix coefficients of the Laurent expansion of the inverse are computed using recursive analytical formulae. We show that the computational complexity of the proposed algorithm grows algebraically with the size of the matrix, but exponentially with the order of the singularity. We apply this algorithm to several matrices that arise in applications. We make special emphasis to interpolation problems with radial basis functions.
2015-10-15T00:00:00ZIllumination Strategies for Intensity-Only Imaging
http://hdl.handle.net/10016/23559
Illumination Strategies for Intensity-Only Imaging
Novikov, Alexei; Moscoso Castro, Miguel Ángel; Papanicolaou, George
We propose a new strategy for narrow band, active array imaging of weak localized scatterers when only the intensities are recorded and measured at the array. We consider a homogeneous medium so that wave propagation is fully coherent. We show that imaging with intensity-only measurements can be carried out using the time reversal operator of the imaging system, which can be obtained from intensity measurements using an appropriate illumination strategy and the polarization identity. Once the time reversal operator has been obtained, we show that the images can be formed using its singular value decomposition (SVD). We use two SVD-based methods to image the scatterers. The proposed approach is simple and efficient. It does not need prior information about the sought image, and it guarantees exact recovery in the noise-free case. Furthermore, it is robust with respect to additive noise. Detailed numerical simulations illustrate the performance of the proposed imaging strategy when only the intensities are captured.
2015-07-30T00:00:00Z