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Lagrangian numerical methods are particularly suitable to reproduce flows involving large and rapid deformation of the domain, fluid splitting and coalescence, jets and sprays. The absence of the convective terms in the governing equations avoids numerical diffusion. This paper provides a comparative study between two Lagrangian particle models based on the Smoothed Particle Hydrodynamics (SPH) and the Particle Finite Element Method (PFEM). The description of the methods is provided; features and drawbacks of each method are compared and discussed. The introduced models, which represent widely used advanced analysis tools, are compared and validated in the simulation of five test cases: Two solitary waves, two regular wave trains and a non-linear wave-structure impact. Results from each model are similar and quite close to reference data. Therefore, both models have been validated against new test cases never simulated before, showing that these models can be effectively used for the analysis of regular and non-linear wave with structure impact.

Groundwater flow modeling is commonly used to calculate groundwater heads, estimate groundwater flow paths and travel times, and provide insights into solute transport processes within an aquifer. However, the values of input parameters that drive groundwater flow models are often highly uncertain due to subsurface heterogeneity and geologic complexity in combination with lack of measurements/unreliable measurements. This uncertainty affects the accuracy and reliability of model outputs. Therefore, parameters' uncertainty must be quantified before adopting the model as an engineering tool. In this study, we model the uncertain parameters as random variables and use a Bayesian inversion approach to obtain a posterior,data-informed, probability density function (pdf) for them: in particular, the likelihood function we consider takes into account both well measurements and our prior knowledge about the extent of the springs in the domain under study. To keep the modelistic and computational complexities under control, we assume Gaussianity of the posterior pdf of the parameters. To corroborate this assumption, we run an identifiability analysis of the model: we apply the inversion procedure to several sets of synthetic data polluted by increasing levels of noise, and we determine at which levels of noise we can effectively recover the "true value" of the parameters. We then move to real well data (coming from the Ticino River basin, in northern Italy, and spanning a month in summer 2014), and use the posterior pdf of the parameters as a starting point to perform an Uncertainty Quantification analysis on groundwater travel-time distributions., First submission

We propose an adaptive mesh refinement strategy for immersed isogeometric analysis, with application to steady heat conduction and viscous flow problems. The proposed strategy is based on residual-based error estimation, which has been tailored to the immersed setting by the incorporation of appropriately scaled stabilization and boundary terms. Element-wise error indicators are elaborated for the Laplace and Stokes problems, and a THB-spline-based local mesh refinement strategy is proposed. The error estimation .and adaptivity procedure is applied to a series of benchmark problems, demonstrating the suitability of the technique for a range of smooth and non-smooth problems. The adaptivity strategy is also integrated in a scan-based analysis workflow, capable of generating reliable, error-controlled, results from scan data, without the need for extensive user interactions or interventions., Submitted to Journal of Mechanics

The finite element method is classically based on nodal Lagrange basis functions defined on conforming meshes. In this context, total reaction forces are commonly computed from the so-called “nodal forces”, yielding higher accuracy and convergence rates than reactions obtained from the differentiated primal solution (“direct” method). The finite cell method and isogeometric analysis promise to improve the interoperability of computer-aided design and computer-aided engineering, enabling a direct approach to the numerical simulation of trimmed geometries. However, body-unfitted meshes preclude the use of classic nodal reaction algorithms. This work shows that the direct method can perform particularly poorly for immersed methods. Instead, conservative reactions can be obtained from equilibrium expressions given by the weak problem formulation, yielding superior accuracy and convergence rates typical of nodal reactions. This approach is also extended to non-interpolatory basis functions, such as the (truncated) hierarchical B-splines.

We propose a variational principle combining a phase-field functional for structural topology optimization with a mixed (three-field) Hu-Washizu functional, then including directly in the formulation equilibrium, constitutive, and compatibility equations. The resulting mixed variational functional is then specialized to derive a classical topology optimization formulation (where the amount of material to be distributed is an \emph{a priori} assigned quantity acting as a global constraint for the problem) as well as a novel topology optimization formulation (where the amount of material to be distributed is minimized, hence with no pre imposed constraint for the problem). Both formulations are numerically solved by implementing a mixed finite element scheme, with the second approach avoiding the introduction of a global constraint, hence respecting the convenient local nature of the finite element discretization. Furthermore, within the proposed approach it is possible to obtain guidelines for settings proper values of phase-field-related simulation parameters and, thanks to the combined phase-field and Hu-Washizu rationale, a monolithic algorithm solution scheme can be easily adopted. An insightful and extensive numerical investigation results in a detailed convergence study and a discussion on the obtained final designs. The numerical results clearly highlight differences between the two formulations as well as advantages related to the monolithic solution strategy; numerical investigations address both two-dimensional and three-dimensional applications., Comment: 35 pages, 14 figures

Prostate cancer can be lethal in advanced stages, for which chemotherapy may become the only viable therapeutic option. While there is no clear clinical management strategy fitting all patients, cytotoxic chemotherapy with docetaxel is currently regarded as the gold standard. However, tumors may regain activity after treatment conclusion and become resistant to docetaxel. This situation calls for new delivery strategies and drug compounds enabling an improved therapeutic outcome. Combination of docetaxel with antiangiogenic therapy has been considered a promising strategy. Bevacizumab is the most common antiangiogenic drug, but clinical studies have not revealed a clear benefit from its combination with docetaxel. Here, we capitalize on our prior work on mathematical modeling of prostate cancer growth subjected to combined cytotoxic and antiangiogenic therapies, and propose an optimal control framework to robustly compute the drug-independent cytotoxic and antiangiogenic effects enabling an optimal therapeutic control of tumor dynamics. We describe the formulation of the optimal control problem, for which we prove the existence of at least a solution and determine the necessary first-order optimality conditions. We then present numerical algorithms based on isogeometric analysis to run a preliminary simulation study over a single cycle of combined therapy. Our results suggest that only cytotoxic chemotherapy is required to optimize therapeutic performance and we show that our framework can produce superior solutions to combined therapy with docetaxel and bevacizumab. We also illustrate how the optimal drug-naïve cytotoxic effects computed in these simulations may be successfully leveraged to guide drug production and delivery strategies by running a nonlinear least-square fit of protocols involving docetaxel and a new design drug. In the future, we believe that our optimal control framework may contribute to accelerate experimental research on chemotherapeutic drugs for advanced prostate cancer and ultimately provide a means to design and monitor its optimal delivery to patients.

Groundwater flow model accuracy is often limited by the uncertainty in model parameters that characterize aquifer properties and aquifer recharge. Aquifer properties such as hydraulic conductivity can have an uncertainty spanning orders of magnitude. Meanwhile, parameters used to configure model boundary conditions can introduce additional uncertainty. In this study, the Morris Method sensitivity analysis is performed on multiple quantities of interest to assess the sensitivity of a steady-state groundwater flow model to uncertain input parameters. The Morris Method determines which of these parameters are less influential on model outputs. Uninfluential parameters can be set constant during subsequent parameter optimization to reduce computational expense. Combining multiple quantities of interest (e.g., RMSE, groundwater fluxes) when performing both the Morris Method and parameter optimization offers a more complete assessment of groundwater models, providing a more reliable and physically consistent estimate of uncertain parameters. The parameter optimization procedure also provides us an estimate of the residual uncertainty in the parameter values, resulting in a more complete estimate of the remaining uncertainty. By employing such techniques, the current study was able to estimate the aquifer hydraulic conductivity and recharge rate due to rice field irrigation in a groundwater basin in Northern Italy, revealing that a significant proportion of surficial aquifer recharge (approximately 81-94%) during the later summer is due to the flood irrigation practices applied to these fields., second submission after minor revisions

Additive manufacturing (AM), and in particular selective laser melting (SLM) technology, allows to produce structural components made of lattice structures. These kinds of structures have received a lot of research attention over recent years due to their capacity to generate easy-to-manufacture and lightweight components with enhanced mechanical properties. Despite a large amount of work available in the literature, the prediction of the mechanical behavior of lattice structures is still an open issue for researchers. Numerical simulations can help to better understand the mechanical behavior of such a kind of structure without undergoing long and expensive experimental campaigns. In this work, we compare numerical and experimental results of a uniaxial tensile test for stainless steel 316L octet-truss lattice specimen. Numerical simulations are based on both the nominal as-designed geometry and the as-build geometry obtained through the analysis of µ-CT images. We find that the use of the as-build geometry is fundamental for an accurate prediction of the mechanical behavior of lattice structures.

Active surveillance (AS) is an established clinical strategy for the management of prostate cancer (PCa) exhibiting low to intermediate risk. In AS, treatment is delayed until progression to higher-risk disease is detected during the close monitoring of patients via longitudinal multiparametric magnetic resonance imaging (mpMRI) scans, biopsies, and Prostate Specific Antigen (PSA) tests. Thus, AS has been regarded as a promising strategy to address the current rates of overtreatment and undertreatment in PCa. However, current AS protocols rely on an observational paradigm, which may delay the detection of tumor progression, and the testing frequency is largely fixed according to population studies, which impedes the design of personalized monitoring plans. To address these issues, we propose to advance AS towards a predictive patient-specific paradigm by leveraging computational tumor forecasts obtained with a biomechanistic model informed by the imaging and clinical data collected during standard AS for each individual patient. Here, we present a preliminary study in a cohort of eight PCa patients who enrolled in AS and had three mpMRI scans over a period of 2.6 to 5.6 years. Our model describes PCa growth in terms of the dynamics of tumor cell density as a combination of tumor cell mobility and net proliferation, which are formulated as a diffusion process and logistic growth, respectively. The model is implemented in each patient’s prostate geometry, which is segmented on T2-weighted MRI data. Tumor cell density estimates are derived from Apparent Diffusion Coefficient (ADC) maps obtained from diffusion-weighted MRI data. To facilitate modeling, the longitudinal imaging datasets are non-rigidly co-registered for each patient. We initialize the model with the tumor cell density map obtained from the ADC map of the first mpMRI scan. Then, the model is parameterized by minimizing the model-data mismatch in tumor cell density at the date of a second mpMRI scan. Finally, we perform a tumor forecast up to the date of a third mpMRI scan, which we use to assess the model-data agreement of our predictions of PCa growth. We obtained a concordance correlation coefficient (CCC) for tumor volume and global tumor cell count of 0.87 and 0.95 during model calibration and of 0.91 and 0.87 at forecasting horizon, respectively. For each patient, the spatial fit of tumor cell density yielded a median Dice score and CCC of 0.77 and 0.50 at the second mpMRI date, respectively. Likewise, the tumor cell density predictions at the third scan date resulted in a median Dice coefficient and CCC of 0.74 and 0.51 across the patient cohort, respectively. Thus, while further model development and performance assessment over lager cohorts are required, these results suggest that our forecasting technology is a promising tool to predict PCa progression in AS and, hence, identify patients who require treatment early during the course of AS. Citation Format: Guillermo Lorenzo Gomez, Chengyue Wu, Joshua P. Yung, John F. Ward, Hector Gomez, Alessandro Reali, Thomas E. Yankeelov, Aradhana M. Venkatesan, Thomas J. Hughes. Patient-specific, organ-scale forecasting of prostate cancer growth in active surveillance [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2023; Part 1 (Regular and Invited Abstracts); 2023 Apr 14-19; Orlando, FL. Philadelphia (PA): AACR; Cancer Res 2023;83(7_Suppl):Abstract nr 850.

In this paper, a staggered, nonlinear finite element procedure is developed to solve the large-strain based coupled system of time dependent Ginzburg-Landau (GL) and thermoelasticity equations for ...

We present a displacement-based and a mixed isogeometric collocation (IGA-C) formulation for free-form, three-dimensional, shear-deformable beams with high and rapidly-varying curvature and torsion. When such complex shapes are concerned, the approach used to build the IGA geometric model becomes relevant. Although IGA-C has been so far successfully applied to a wide range of problems, the effects that different parameterization and knot placement techniques may have on the accuracy of collocation-based formulations is still an unexplored field. To fill this gap, primal and mixed formulations are used combining two parameterization methods (chord-length and equally spaced) with two knot placement techniques (uniformly spaced and De Boor). With respect to the space-varying Frenet local frame, we derive the strong form of the governing equations in a compact form through the definition of two matrix operators conveniently used to perform first and second order derivatives of the vector fields involved in the formulations. This approach is very efficient and easy to implement within a collocation-based scheme. Several challenging numerical experiments allow to test the different considered parameterizations and knot placement techniques, revealing in particular that with the primal formulation an equally spaced parameterization is definitively the most recommended choice and it should always be used with an approximation degree of, at least, p = 6 , although some caution must be adopted when very high Jacobians and small curvatures occur. The same holds for the mixed formulation, with the difference that p = 4 is enough to yield accurate results.

The Finite Cell Method (FCM) together with Isogeometric analysis (IGA) has been applied successfully in various problems in solid mechanics, in image-based analysis, fluid-structure interaction and in many other applications. A challenging aspect of the isogeometric finite cell method is the integration of cut cells. In particular in three-dimensional simulations the computational effort associated with integration can be the critical component of a simulation. A myriad of integration strategies has been proposed over the past years to ameliorate the difficulties associated with integration, but a general optimal integration framework that suits a broad class of engineering problems is not yet available. In this contribution we provide a thorough investigation of the accuracy and computational effort of the octree integration scheme. We quantify the contribution of the integration error using the theoretical basis provided by Strang's first lemma. Based on this study we propose an error-estimate-based adaptive integration procedure for immersed isogeometric analysis. Additionally, we present a detailed numerical investigation of the proposed optimal integration algorithm and its application to immersed isogeometric analysis using two- and three-dimensional linear elasticity problems., Comment: To CAMWA

We present a study on the dependence of the frictional properties of a fault rock on its degree of damage. The purpose is therefore to gain insight into frictional sliding, the governing force that controls earthquake nucleation, propagation and arrest. The focus on this topic is to try to find a reason for the experimental evidence that the friction coefficient seems to be almost independent on lithology. A possible explanation to investigate through the numerical modelling could be that the frictional properties of a realistic fault rock depend mostly on the concentration of micro- to macroscopic cracks and/or of lamellar phyllosilicates in the host rock, rather than on the composition of its bulk materials. The formalism of the Linear Elastic Fracture Mechanics (LEFM) can quantitatively reproduce the stresses and the strains on the interface propagating frictional rupture. The purpose is to use a Finite Element Method (FEM) numerical code in order to simulate the plane strain elastic deformation of a two-dimensional medium crossed by elliptical fractures and weak anisotropic inclusions. The analysis of the distribution and orientation of the stresses resulting from the interaction of a system of randomly oriented elliptical fractures under different loading conditions could provide information on the onset and propagation of frictional ruptures, such as real contact area reduction, slip velocity, number and length of global sliding precursors. The magnitude and orientation of the principal stresses around the tips of elliptical voids are crucial for the understanding of fracture coalescence and frictional reactivation of shear cracks in an elastic rock, which in turn is one of the main factors that govern the seismic cycle of natural faults.

Process-dependent residual stresses are one of the main burdens to a widespread adoption of laser powder bed fusion technology in industry. Residual stresses are directly influenced by process parameters, such as laser path, laser power, and speed. In this work, the influence of various scan speed and laser power control strategies on residual stresses is investigated. A set of nine different laser scan patterns is printed by means of a selective laser melting process on a bare plate of nickel superalloy 625 (IN625). A finite element model is experimentally validated comparing the simulated melt pool areas with high-speed thermal camera in situ measurements. Finite element analysis is then used to evaluate residual stresses for the nine different laser scan control strategies, in order to identify the strategy which minimizes the residual stress magnitude. Numerical results show that a constant power density scan strategy appears the most effective to reduce residual stresses in the considered domain.

Nicola Bellomo acknowledges the support of the University of Granada, Project Modeling in Nature MNat from micro to macro, https://www.modelingnature.org.This paper has been partially supported by the MINECO-Feder (Spain) research Grant Number RTI2018-098850-B-I00, the Junta de Andalucia (Spain) Project PY18-RT-2422, A-FQM-311-UGR18, and B-FQM-580-UGR20. Livio Gibelli, gratefully acknowledges the financial support of the Engineering and Physical Sciences Research Council (EPSRC) Under Grants EP/N016602/1, EP/R007438/1. Annalisa Quaini acknowledges support from the Radcliffe Institute for Advanced Study at Harvard University where she has been a 2021-2022 William and Flora Hewlett Foundation Fellow. Alessandro Reali acknowledges the partial support of the MIUR-PRIN Project XFAST-SIMS (No. 20173C478N)., The first part of our paper presents a general survey on the modeling, analytic problems, and applications of the dynamics of human crowds, where the specific features of living systems are taken into account in the modeling approach. This critical analysis leads to the second part which is devoted to research perspectives on modeling, analytic problems, multiscale topics which are followed by hints towards possible achievements. Perspectives include the modeling of social dynamics, multiscale problems and a detailed study of the link between crowds and swarms modeling., University of Granada, Project Modeling in Nature MNat from micro to macro, Spanish Government RTI2018-098850-B-I00, Junta de Andalucia, European Commission PY18-RT-2422 A-FQM-311-UGR18 B-FQM-580-UGR20, UK Research & Innovation (UKRI), Engineering & Physical Sciences Research Council (EPSRC) EP/N016602/1 EP/R007438/1, Radcliffe Institute for Advanced Study at Harvard University, Ministry of Education, Universities and Research (MIUR) 20173C478N

A theoretical-computational framework is proposed for predicting the failure behavior of two anisotropic brittle materials, namely, single crystal magnesium and boron carbide. Constitutive equations are derived, in both small and large deformations, by using thermodynamics in order to establish a fully coupled and transient twin and crack system. To study the common deformation mechanisms (e.g., twinning and fracture), which can be caused by extreme mechanical loading, a monolithically-solved Ginzburg–Landau-based phase-field theory coupled with the mechanical equilibrium equation is implemented in a finite element simulation framework for the following problems: (i) twin evolution in two-dimensional single crystal magnesium and boron carbide under simple shear deformation; (ii) crack-induced twinning for magnesium under pure mode I and mode II loading; and (iii) study of fracture in homogeneous single crystal boron carbide under biaxial compressive loading. The results are verified by a steady-state phase-field approach and validated by available experimental data in the literature. The success of this computational method relies on using two distinct phase-field (order) parameters related to fracture and twinning. A finite element method-based code is developed within the Python-based open-source platform FEniCS. We make the code publicly available and the developed algorithm may be extended for the study of phase transformations under dynamic loading or thermally-activated mechanisms, where the competition between various deformation mechanisms is accounted for within the current comprehensive modeling approach.

We propose a new family of high-order explicit generalized-$\alpha$ methods for hyperbolic problems with the feature of dissipation control. Our approach delivers $2k,\, \left(k \in \mathbb{N}\right)$ accuracy order in time by solving $k$ matrix systems explicitly and updating the other $2k$ variables at each time-step. The user can control the numerical dissipation in the discrete spectrum's high-frequency regions by adjusting the method's coefficients. We study the method's spectrum behaviour and show that the CFL condition is independent of the accuracy order. The stability region remains invariant while we increase the accuracy order. Next, we exploit efficient preconditioners for the isogeometric matrix to minimize the computational cost. These preconditioners use a diagonal-scaled Kronecker product of univariate parametric mass matrices; they have a robust performance with respect to the spline degree and the mesh size, and their decomposition structure implies that their application is faster than a matrix-vector product involving the fully-assembled mass matrix. Our high-order schemes require simple modifications of the available implementations of the generalized-$\alpha$ method. Finally, we present numerical examples demonstrating the methodology's performance regarding single- and multi-patch IGA discretizations.

Crack initiation and propagation as well as abrupt occurrence of twinning are challenging fracture problems where the transient phase-field approach is proven to be useful. Early-stage twinning growth and interactions are in focus herein for a magnesium single crystal at the nanometer length-scale. We demonstrate a basic methodology in order to determine the mobility parameter that steers the kinetics of phase-field propagation. The concept is to use already existing molecular dynamics simulations and analytical solutions in order to set the mobility parameter correctly. In this way, we exercise the model for gaining new insights into growth of twin morphologies, temporally-evolving spatial distribution of the shear stress field in the vicinity of the nanotwin, multi-twin, and twin-defect interactions. Overall, this research addresses gaps in our fundamental understanding of twin growth, while providing motivation for future discoveries in twin evolution and their effect on next-generation material performance and design.

This paper proposes a multiscale vision to human crowds which provides a consistent description at the three possible modeling scales, namely, microscopic, mesoscopic, and macroscopic. The proposed approach moves from interactions at the microscopic scale and shows how the same modeling principles lead to kinetic and hydrodynamic models. Hence, a unified framework is developed which permits to derive models at each scale using the same principles and similar parameters. This approach can be used to simulate crowd dynamics in complex environments composed of interconnected areas, where the most appropriate scale of description can be selected for each area. This offers a pathway to the development of a multiscale computational model which has the capability to optimize the granularity of the description depending on the pedestrian local flow conditions. An important feature of the modeling at each scale is that the complex interaction between emotional states of walkers and their motion is taken into account.

Numerical simulations of a complete laser powder bed fusion (LPBF) additive manufacturing (AM) process are extremely challenging, or even impossible, to achieve without a radical model reduction of the complex physical phenomena occurring during the process. However, even when we adopt a reduced model with simplified physics, the complex geometries of parts usually produced by the LPBF AM processes make this kind of analysis computationally expensive. In fact, small geometrical features—which might be generated when the part is designed following the principle of the so-called design for AM, for instance, by means of topology optimization procedures—often require complex conformal meshes. Immersed boundary methods offer an alternative to deal with this kind of complexity, without requiring complicated meshing strategies. The two-level method lies within this family of numerical methods and presents a flexible tool to deal with multi-scale problems. In this contribution, we apply a modified version of the recently introduced two-level method to part-scale thermal analysis of LPBF manufactured components. We first validate the proposed part-scale model with respect to experimental measurements from the literature. Then, we apply the presented numerical framework to simulate a complete LPBF process of a topologically optimized structure, showing the capability of the method to easily deal with complex geometrical features.

Dynamic Mode Decomposition (DMD) is an unsupervised machine learning method that has attracted considerable attention in recent years owing to its equation-free structure, ability to easily identify coherent spatio-temporal structures in data, and effectiveness in providing reasonably accurate predictions for certain problems. Despite these successes, the application of DMD to certain problems featuring highly nonlinear transient dynamics remains challenging. In such cases, DMD may not only fail to provide acceptable predictions but may indeed fail to recreate the data in which it was trained, restricting its application to diagnostic purposes. For many problems in the biological and physical sciences, the structure of the system obeys a compartmental framework, in which the transfer of mass within the system moves within states. In these cases, the behavior of the system may not be accurately recreated by applying DMD to a single quantity within the system, as proper knowledge of the system dynamics, even for a single compartment, requires that the behavior of other compartments is taken into account in the DMD process. In this work, we demonstrate, theoretically and numerically, that, when performing DMD on a fully coupled PDE system with compartmental structure, one may recover useful predictive behavior, even when DMD performs poorly when acting compartment-wise. We also establish that important physical quantities, as mass conservation, are maintained in the coupled-DMD extrapolation. The mathematical and numerical analysis suggests that DMD may be a powerful tool when applied to this common class of problems. In particular, we show interesting numerical applications to a continuous delayed-SIRD model for Covid-19, and to a problem from additive manufacturing considering a nonlinear temperature field and the resulting change of material phase from powder, liquid, and solid states.

The outbreak of COVID-19, beginning in 2019 and continuing through the time of writing, has led to renewed interest in the mathematical modeling of infectious disease. Recent works have focused on partial differential equation (PDE) models, particularly reaction-diffusion models, able to describe the progression of an epidemic in both space and time. These studies have shown generally promising results in describing and predicting COVID-19 progression. However, people often travel long distances in short periods of time, leading to nonlocal transmission of the disease. Such contagion dynamics are not well-represented by diffusion alone. In contrast, ordinary differential equation (ODE) models may easily account for this behavior by considering disparate regions as nodes in a network, with the edges defining nonlocal transmission. In this work, we attempt to combine these modeling paradigms via the introduction of a network structure within a reaction-diffusion PDE system. This is achieved through the definition of a population-transfer operator, which couples disjoint and potentially distant geographic regions, facilitating nonlocal population movement between them. We provide analytical results demonstrating that this operator does not disrupt the physical consistency or mathematical well-posedness of the system, and verify these results through numerical experiments. We then use this technique to simulate the COVID-19 epidemic in the Brazilian region of Rio de Janeiro, showcasing its ability to capture important nonlocal behaviors, while maintaining the advantages of a reaction-diffusion model for describing local dynamics.

Isogeometric Kirchhoff–Love elements have received an increasing attention in geometrically nonlinear analysis of elastic shells. Nevertheless, some difficulties still remain. Among the others, the highly nonlinear expression of the strain measure, which leads to a complicated and costly computation of the discrete operators, and the existence of locking, which prevents the use of coarse meshes for slender shells and low order NURBS, are key issues that need to be addressed. In this work, exploiting the hypothesis of small membrane strains, we propose a simplified strain measure with a third order polynomial dependence on the displacement variables which allows an efficient evaluation of the discrete quantities. Numerical results show practically no difference to the original model, even for very large displacements and composite structures. Patch-wise reduced integrations are then investigated to deal with membrane locking in large deformation problems. An optimal integration scheme for third order C 2 NURBS, in terms of accuracy and efficiency, is identified. Finally, the recently proposed Newton method with mixed integration points is used for the solution of the discrete nonlinear equations with a great reduction of the iterative burden with respect to the standard Newton scheme.

We present a systematic study on higher-order penalty techniques for isogeometric mortar methods. In addition to the weak-continuity enforced by a mortar method, normal derivatives across the interface are penalized. The considered applications are fourth order problems as well as eigenvalue problems for second and fourth order equations. The hybrid coupling, which combines mortar and penalty methods, enables the discretization of fourth order problems in a multi-patch setting as well as a convenient implementation of natural boundary conditions. For second order eigenvalue problems, the pollution of the discrete spectrum – typically referred to as “outliers” – can be avoided. Numerical results illustrate the good behaviour of the proposed method in simple systematic studies as well as more complex multi-patch mapped geometries for linear elasticity and Kirchhoff plates.

In this contribution, we validate a physical model based on a transient temperature equation (including latent heat), w.r.t. the experimental set AMB2018-02 provided within the additive manufacturing benchmark series, established at the National Institute of Standards and Technology, USA. We aim at predicting the following quantities of interest, width, depth, and length of the melt pool by numerical simulation, and report also on the obtainable numerical results of the cooling rate. We first assume the laser to possess a double-ellipsoidal shape and demonstrate that a well-calibrated, purely thermal model based on isotropic thermal conductivity is able to predict all the quantities of interest, up to a deviation of maximum 7.3% from the experimentally measured values. However, it is interesting to observe that if we directly introduce, whenever available, the measured laser profile in the model (instead of the double-ellipsoidal shape), the investigated model returns a deviation of 19.3% from the experimental values. This motivates a model update by introducing anisotropic conductivity, which is intended to be a simplistic model for heat material convection inside the melt pool. Such an anisotropic model enables the prediction of all quantities of interest mentioned above with a maximum deviation from the experimental values of 6.5%. We note that, although more predictive, the anisotropic model induces only a marginal increase in computational complexity.

Prostate cancer and benign prostatic hyperplasia are common genitourinary diseases in aging men. Both pathologies may coexist and share numerous similarities, which have suggested several connections or some interplay between them. However, solid evidence confirming their existence is lacking. Recent studies on extensive series of prostatectomy specimens have shown that tumors originating in larger prostates present favorable pathological features. Hence, large prostates may exert a protective effect against prostate cancer. In this work, we propose a mechanical explanation for this phenomenon. The mechanical stress fields that originate as tumors enlarge have been shown to slow down their dynamics. Benign prostatic hyperplasia contributes to these mechanical stress fields, hence further restraining prostate cancer growth. We derived a tissue-scale, patient-specific mechanically coupled mathematical model to qualitatively investigate the mechanical interaction of prostate cancer and benign prostatic hyperplasia. This model was calibrated by studying the deformation caused by each disease independently. Our simulations show that a history of benign prostatic hyperplasia creates mechanical stress fields in the prostate that impede prostatic tumor growth and limit its invasiveness. The technology presented herein may assist physicians in the clinical management of benign prostate hyperplasia and prostate cancer by predicting pathological outcomes on a tissue-scale, patient-specific basis.

Although Thoracic EndoVascular Aortic Repair (TEVAR) is a consolidated procedure to treat thoracic aortic diseases, it still has relevant complications mainly related to suboptimal wall apposition of the stent-graft, impairing the post-operative hemodynamics and the clinical outcomes. Accurate stent-graft sizing and patient selection are the key aspects to minimize drawbacks. Unfortunately, current TEVAR planning is only based on geometrical measurements performed on static images, completely neglecting the biomechanical interplay between the stent-graft and the aorta. Despite an extensive literature dealing with bioengineering simulation of endovascular implants, studies on the prediction of the post-TEVAR hemodynamics based on both pre-operative patient-specific aortic anatomy and stent-graft mechanical features are still missing. The present study aims at providing a realistic and robust computational framework to support TEVAR planning in the clinical practice by predicting the post-operative hemodynamics given a selected stent-graft model and pre-operative medical images of the aorta to be treated. A novel approach based on a distance image aimed at transforming the result of the structural analysis of stent-graft deployment in a volume mesh suitable for a computational study of the post-TEVAR hemodynamics is presented. The study discusses two clinical cases as illustrative examples of the framework application and, for one of the two cases, a comparison of the predicted hemodynamics with a simulation based on real post-operative images is shown. Such a comparison proves that the proposed computational framework is able to capture the main hemodynamic aspects related to the stent-graft implant. In particular, the use of simulations has confirmed the unsuitability for the endovascular repair of one of the two patients due to the short proximal landing zone, leading to a high risk of the so-called bird-beak. The proposed computational framework is shown to be a useful tool to support planning of elective TEVAR, especially in those borderline cases when the sole geometrical analysis of static images is not exhaustive.

Active surveillance (AS) is a suitable management option for many newly-diagnosed prostate cancer (PCa) cases, which usually exhibit low to intermediate clinical risk. In AS, patients are closely monitored via multiparametric magnetic resonance imaging (mpMRI), prostate-specific antigen tests, and biopsies until these reveal an increase in PCa risk that warrants treatment. Thus, AS can contribute to reduce the current overtreatment of PCa and avoid treatment side-effects that may adversely impact patients’ lives without necessarily improving their longevity. However, current AS protocols rely on assessing PCa according to population-based studies, which complicates the design of personalized monitoring plans and the early detection of tumor progression. To address these issues, we propose to predict PCa growth using patient-specific forecasts based on an mpMRI-informed mechanistic model. Here, we present a preliminary study in a cohort of seven PCa patients who enrolled in AS and had three mpMRI scans over a period of 1.4 to 4.9 years. Our mechanistic model describes PCa growth in terms of tumor cell density dynamics, consisting of mobility and proliferation modeled via a diffusion process and a logistic law, respectively. We segment each patient’s prostate geometry on T2-weighted images and estimate tumor cell density from standard apparent diffusion coefficient (ADC) maps. To facilitate PCa modeling, we co-register each patient’s mpMRI datasets with a biomechanical elastic method that aligns the prostate segmentations across the imaging datasets. The model is initialized with the data from the first mpMRI scan. Model calibration relies on a nonlinear least-squares algorithm that minimizes the mismatch between ADC-measured and model-predicted tumor cell density at the second mpMRI date. For validation, we initialize the patient-specific calibrated model with the second mpMRI dataset and forecast PCa growth at the third mpMRI date, which we compare to the corresponding ADC-estimated tumor cell density. Model calibration resulted in a concordance correlation coefficient (CCC) > 0.99 for both tumor volume and global tumor cell count across the cohort. For each patient, the spatial fit of tumor cell density at the second scan date rendered a median Dice score and CCC of 0.79 and 0.52, respectively. Model validation resulted in CCCs of 0.88 and 0.81 for tumor volume and global tumor cell count across the cohort. Comparing the patient-specific ADC-estimated and model forecasts of tumor cell density at the third scan date, we obtained a median Dice score and CCC of 0.65 and 0.46, respectively. Thus, while improvement and further testing in larger cohorts are still needed, these results do suggest that our computational forecasting approach is a promising technology to predict the spatiotemporal growth of PCa during AS on a patient-specific basis. Citation Format: Guillermo Lorenzo, Jon S. Heiselman, Michael A. Liss, Michael I. Miga, Hector Gomez, Thomas E. Yankeelov, Thomas J. Hughes, Alessandro Reali. Patient-specific forecasting of prostate cancer growth during active surveillance using an imaging-informed mechanistic model [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2022; 2022 Apr 8-13. Philadelphia (PA): AACR; Cancer Res 2022;82(12_Suppl):Abstract nr 5064.

Dynamic mode decomposition (DMD) is a powerful data-driven method used to extract spatio-temporal coherent structures that dictate a given dynamical system. The method consists of stacking collected temporal snapshots into a matrix and mapping the nonlinear dynamics using a linear operator. The classical procedure considers that snapshots possess the same dimensionality for all the observable data. However, this often does not occur in numerical simulations with adaptive mesh refinement/coarsening schemes (AMR/C). This paper proposes a strategy to enable DMD to extract features from observations with different mesh topologies and dimensions, such as those found in AMR/C simulations. For this purpose, the adaptive snapshots are projected onto the same reference function space, enabling the use of snapshot-based methods such as DMD. The present strategy is applied to challenging AMR/C simulations: a continuous diffusion–reaction epidemiological model for COVID-19, a density-driven gravity current simulation, and a bubble rising problem. We also evaluate the DMD efficiency to reconstruct the dynamics and some relevant quantities of interest. In particular, for the SEIRD model and the bubble rising problem, we evaluate DMD’s ability to extrapolate in time (short-time future estimates).

The outbreak of COVID-19 in 2020 has led to a surge in interest in the mathematical modeling of infectious diseases. Such models are usually defined as compartmental models, in which the population under study is divided into compartments based on qualitative characteristics, with different assumptions about the nature and rate of transfer across compartments. Though most commonly formulated as ordinary differential equation (ODE) models, in which the compartments depend only on time, recent works have also focused on partial differential equation (PDE) models, incorporating the variation of an epidemic in space. Such research on PDE models within a Susceptible, Infected, Exposed, Recovered, and Deceased (SEIRD) framework has led to promising results in reproducing COVID-19 contagion dynamics. In this paper, we assess the robustness of this modeling framework by considering different geometries over more extended periods than in other similar studies. We first validate our code by reproducing previously shown results for Lombardy, Italy. We then focus on the U.S. state of Georgia and on the Brazilian state of Rio de Janeiro, one of the most impacted areas in the world. Our results show good agreement with real-world epidemiological data in both time and space for all regions across major areas and across three different continents, suggesting that the modeling approach is both valid and robust., Comment: 23 pages, 19 figures

Isogeometric Kirchhoff-Love elements have received an increasing attention in geometrically nonlinear analysis of thin walled structures. They make it possible to meet the C1requirement in the interior of surface patches, to avoid the use of finite rotations and to reduce the number of unknowns compared to shear flexible models. Locking elimination, patch coupling and iterative solution are crucial points for a robust and efficient nonlinear analysis and represent the main focus of this work. Patch-wise reduced integrations are investigated to deal with locking in large deformation problems discretized via a standard displacement-based formulation. An optimal integration scheme for third order C2NURBS, in terms of accuracy and efficiency, is identified, allowing to avoid locking without resorting to a mixed formulation. The Newton method with mixed integration points (MIP) is used for the solution of the discrete nonlinear equations with a great reduction of the iterative burden and a superior robustness with respect to the standard Newton scheme. A simple penalty approach for coupling adjacent patches, applicable to either smooth or non-smooth interfaces, is proposed. An accurate coupling, also for a nonmatching discretization, is obtained using an interface-wise reduced integration while the MIP iterative scheme allows for a robust and efficient solution also with very high values of the penalty parameter.

We investigate primal and mixed u−p isogeometric collocation methods for application to nearly-incompressible isotropic elasticity. The primal method employs Navier’s equations in terms of the displacement unknowns, and the mixed method employs both displacement and pressure unknowns. As benchmarks for what might be considered acceptable accuracy, we employ constant-pressure Abaqus finite elements that are widely used in engineering applications. As a basis of comparisons, we present results for compressible elasticity. All the methods were completely satisfactory for the compressible case. However, results for low-degree primal methods exhibited displacement locking and in general deteriorated in the nearly-incompressible case. The results for the mixed methods behaved very well for two of the problems we studied, achieving levels of accuracy very similar to those for the compressible case. The third problem, which we consider a “torture test” presented a more complex story for the mixed methods in the nearly-incompressible case., CMES: Computer Modeling in Engineering & Sciences, 129 (3), ISSN:1526-1492, ISSN:1526-1506