Daniel Millán

Universidad Nacional de Cuyo, Departamento de Ingeniería Mecánica, Facultad de Ciencias Aplicadas a la Industria, Faculty Member

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Research topics mainly related with engineering and applied mathematics. These include point-set manifold processing, nonlinear model order reduction, thin-shell analysis, phase field models of fracture and flexoelectricity, biomechanics of soft biological tissues, collective variables identification in biomolecules, non communicable diseases epidemiology.

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Yongxing Shen

Shanghai Jiao Tong University

Christian Peco Regales

Universitat Politecnica de Catalunya

Timon Rabczuk

Bauhaus-University-Weimar

Max Arroyo

Universidad San Francisco de Quito

Nguyen-Thanh Nhon

Bauhaus-University-Weimar

Ignasi Colominas

Universidade da Coruña

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Millan IJNME

We present a method to process embedded smooth manifolds using sets of points alone. This method ... more We present a method to process embedded smooth manifolds using sets of points alone. This method avoids any global parameterization and hence is applicable to surfaces of any genus. It combines three ingredients: (1) the automatic detection of the local geometric structure of the manifold by statistical learning methods, (2) the local parameterization of the surface using smooth meshfree (here maximum-entropy) approximants, and (3) patching together the local representations by means of a partition of unity. Mesh-based methods can deal with surfaces of complex topology, since they rely on the element-level parameterizations, but cannot handle high-dimensional manifolds, while previous meshfree methods for thin shells consider a global parametric domain, which seriously limits the kinds of surfaces that can be treated. We present the implementation of the method in the context of Kirchhoff-Love shells, but it is applicable to other calculations on manifolds in any dimension. With the smooth approximants, this fourth-order partial differential equation is treated directly. We show the good performance of the method on the basis of the classical obstacle course. Additional calculations exemplify the flexibility of the proposed approach in treating surfaces of complex topology and geometry.

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On the optimum support size in meshfree methods: A variational adaptivity approach with maximum-entropy approximants

We present a method for the automatic adaption of the support size of meshfree basis functions in... more We present a method for the automatic adaption of the support size of meshfree basis functions in the context of the numerical approximation of boundary value problems stemming from a minimum principle. The method is based on a variational approach, and the central idea is that the variational principle selects both the discretized physical fields and the discretization parameters, here those defining the support size of each basis function. We consider local maximum-entropy approximation schemes, which exhibit smooth basis functions with respect to both space and the discretization parameters (the node location and the locality parameters). We illustrate by the Poisson, linear and non-linear elasticity problems the effectivity of the method, which produces very accurate solutions with very coarse discretizations and finds unexpected patterns of the support size of the shape functions.

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Morphological Characterization of Intracranial Aneurysms by Using 3D Moment Invariants

Rupture of intracranial saccular aneurysms is the most common cause of spontaneous subarachnoid h... more Rupture of intracranial saccular aneurysms is the most common cause of spontaneous subarachnoid hemorrhage, which has significant morbidity and mortality. Although there is still controversy regarding the decision on which unruptured aneurysms should be treated, this is based primarily on their size. Nonetheless, many large lesions do not rupture whereas some small ones do. It is commonly accepted that hemodynamical factors are important to better understand the natural history of cerebral aneurysms. However, it might not always be practical to carry out a detailed computational analysis of such factors if a prompt assessment is required. Since shape is likely to be dependent on the balance between hemodynamic forces and the aneurysmal surrounding environment, an appropriate morphological 3D characterization is likely to provide a practical surrogate to quickly evaluate the risk of rupture. In this paper, an efficient and novel methodology for 3D shape characterization of cerebral aneurysms is described. The aneurysms are isolated by taking into account a portion of their adjacent vessels. Two methods to characterize the morphology of the aneurysms models using moment invariants have been used considered: Geometrical Moment Invariants (GMI) and Zernike Moment Invariants (ZMI). The results have been validated in a database containing 53 patients with a total of 31 ruptured aneurysms and 24 unruptured aneurysms. It has been found that ZMI indices are more robust than GMI, and seem to provide a reliable way to discriminate between ruptured and unruptured aneurysms. Correct rupture prediction rates of 80% were achieved in contrast to 66% that is found when the aspect ratio index is considered.

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Characterization of Cerebral Aneurysms Using 3D Moment Invariants

The rupture mechanism of intracranial aneurysms is still not fully understood. Although the size ... more The rupture mechanism of intracranial aneurysms is still not fully understood. Although the size of the aneurysm is the shape index most commonly used to predict rupture, some controversy still exists about its adequateness as an aneurysm rupture predictor. In this work, an automatic method to geometrically characterize the shape of cerebral saccular aneurysms using 3D moment invariants is proposed. Geometric moments are efficiently computed via application of the Divergence Theorem over the aneurysm surface using a non-structured mesh. 3D models of the aneurysm and its connected parent vessels have been reconstructed from segmentations of both 3DRA and CTA images. Two alternative approaches have been used for segmentation, the first one based on isosurface deformable models, and the second one based on the level set method. Several experiments were also conducted to both assess the influence of pre-processing steps in the stability of the aneurysm shape descriptors, and to know the robustness of the proposed method. Moment invariants have proved to be a robust technique while providing a reliable way to discriminate between ruptured and unruptured aneurysms (Sensitivity=0.83, Specificity=0.74) on a data set containing 55 aneurysms. Further investigation over larger databases is necessary to establish their adequateness as reliable predictors of rupture risk.

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Efficient Pipeline for Image-Based Patient-Specific Analysis of Cerebral Aneurysm Hemodynamics: Technique and Sensitivity

Hemodynamic factors are thought to be implicated in the progression and rupture of intracranial a... more Hemodynamic factors are thought to be implicated in the progression and rupture of intracranial aneurysms. Current efforts aim to study the possible associations of hemodynamic characteristics such as complexity and stability of intra-aneurysmal flow patterns, size and location of the region of flow impingement with the clinical history of aneurysmal rupture. However, there are no reliable methods for measuring blood flow patterns in vivo. In this paper, an efficient methodology for patient-specific modeling and characterization of the hemodynamics in cerebral aneurysms from medical images is described. A sensitivity analysis of the hemodynamic characteristics with respect to variations of several variables over the expected physiologic range of conditions is also presented. This sensitivity analysis shows that although changes in the velocity fields can be observed, the characterization of the intra-aneurysmal flow patterns is not altered when the mean input flow, the flow division, the viscosity model, or mesh resolution are changed. It was also found that the variable that has the greater impact on the computed flow fields is the geometry of the vascular structures. We conclude that with the proposed modeling pipeline clinical studies involving large numbers cerebral aneurysms are feasible.

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Cebral SPIE

by Marcelo Castro and Daniel Millán

Although the natural history of cerebral aneurysms remains unknown, hemodynamics is thought to pl... more Although the natural history of cerebral aneurysms remains unknown, hemodynamics is thought to play an important role in their initiation, growth and rupture. This paper describes a pilot clinical study of the association between intraaneurysmal hemodynamic characteristics and the rupture of cerebral aneurysms. A total of 62 patientspecific models of cerebral aneurysms were constructed from 3D angiography images. Computational fluid dynamics simulations were performed under pulsatile flow conditions. The aneurysms were classified into different categories depending on the complexity and stability of the flow pattern, the location and size of the flow impingement region, and the size of the inflow jet. These features were analyzed for associations with history of rupture. A large variety of flow patterns was observed. It was found that 72% of ruptured aneurysms had complex or unstable flow patterns, 80% had small impingement regions and 76% had small jet sizes. Conversely, unruptured aneurysms accounted for 73%, 82% and 75% of aneurysms with simple stable flow patterns, large impingement regions and large jet sizes, respectively.

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Millan IJNME

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On the optimum support size in meshfree methods: A variational adaptivity approach with maximum-entropy approximants

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Morphological Characterization of Intracranial Aneurysms by Using 3D Moment Invariants

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Characterization of Cerebral Aneurysms Using 3D Moment Invariants

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Efficient Pipeline for Image-Based Patient-Specific Analysis of Cerebral Aneurysm Hemodynamics: Technique and Sensitivity

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Cebral SPIE

by Marcelo Castro and Daniel Millán

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Daniel Millán

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