A mathematical model of aortic aneurysm formation

Data-driven causal model discovery and personalized prediction in Alzheimer's disease

With the explosive growth of biomarker data in Alzheimer's disease (AD) clinical trials, numerous mathematical models have been developed to characterize disease-relevant biomarker trajectories over time. While some of these models are purely empiric, others are causal, built upon various hypotheses of AD pathophysiology, a complex and incompletely understood area of research. One of the most challenging problems in computational causal modeling is using a purely data-driven approach to derive the model's parameters and the mathematical model itself, without any prior hypothesis bias. In this paper, we develop an innovative data-driven modeling approach to build and parameterize a causal model to characterize the trajectories of AD biomarkers. This approach integrates causal model learning, population parameterization, parameter sensitivity analysis, and personalized prediction. By applying this integrated approach to a large multicenter database of AD biomarkers, the Alzheimer's Disease Neuroimaging Initiative, several causal models for different AD stages are revealed. In addition, personalized models for each subject are calibrated and provide accurate predictions of future cognitive status.

Numerical analysis of biothermal-fluids and cardiac thermal pulse of abdominal aortic aneurysm

Abdominal aortic aneurysms are serious and difficult to detect, conditions can be deadly if they rupture. In this study, the heat transfer and flow physics of Abdominal Aortic Aneurysm (AAA) were discussed and associated with cardiac cycle to illustrate the cardiac thermal pulse (CTP) of AAA. A CTP and infrared thermography (IRT) evaluation-based on AAA and abdomen skin surface detection method was proposed, respectively. Infrared thermography (IRT) is a promising imaging technique that may detect AAA quicker and cheaper than other imaging techniques (as biomarker). From CFD rigid-wall and FSI Analysis, the transient bioheat transfer effect resulted in a distinct thermal signature (circular thermal elevation) on the temperature profile of midriff skin surface, at both regular body temperature and supine position, under normal clinical temperature. However, it is important to note that thermography is not a perfect technology, and it does have some limitations, such as lack of clinical trials. There is still work to be done to improve this imaging technique and make it a more viable and accurate method for detecting abdominal aortic aneurysms. However, thermography is currently one of the most convenient technologies in this field, and it has the potential to detect abdominal aortic aneurysms earlier than other techniques. CTP, on the other hand, was used to examine the thermal physics of AAA. In CFD rigid-wall Analysis, AAA had a CTP that only responded to systolic phase at regular body temperature. In contrast, a healthy abdominal aorta displayed a CTP that responded to the full cardiac cycle, including diastolic phase at all simulated cases. Besides, the findings from FSI Analysis suggest the influence of numerical simulation techniques on the prediction of thermal physics behaviours of AAA and abdominal skin surface. Lastly, this study correlated the relationship between natural convective heat transfer coefficient with AAA and provided reference for potential clinical diagnostic using IRT in clinical implications.

Novel Mathematical Modelling of Platelet-Poor Plasma Arising in a Blood Coagulation System with the Fractional Caputo–Fabrizio Derivative

This study develops a fractional model using the Caputo–Fabrizio derivative with order α for platelet-poor plasma arising in a blood coagulation system. The existence of solutions ensures that there are solutions to the considered system of equations. Approximate solutions to the recommended model are presented by selecting different numbers of fractional orders and initial conditions (ICs). For each case, graphs of solutions are supplied through different dimensions.

A PDE Model of Breast Tumor Progression in MMTV-PyMT Mice

The evolution of breast tumors greatly depends on the interaction network among different cell types, including immune cells and cancer cells in the tumor. This study takes advantage of newly collected rich spatio-temporal mouse data to develop a data-driven mathematical model of breast tumors that considers cells' location and key interactions in the tumor. The results show that cancer cells have a minor presence in the area with the most overall immune cells, and the number of activated immune cells in the tumor is depleted over time when there is no influx of immune cells. Interestingly, in the case of the influx of immune cells, the highest concentrations of both T cells and cancer cells are in the boundary of the tumor, as we use the Robin boundary condition to model the influx of immune cells. In other words, the influx of immune cells causes a dominant outward advection for cancer cells. We also investigate the effect of cells' diffusion and immune cells' influx rates in the dynamics of cells in the tumor micro-environment. Sensitivity analyses indicate that cancer cells and adipocytes' diffusion rates are the most sensitive parameters, followed by influx and diffusion rates of cytotoxic T cells, implying that targeting them is a possible treatment strategy for breast cancer.

Neutrophils as Regulators and Biomarkers of Cardiovascular Inflammation in the Context of Abdominal Aortic Aneurysms

Neutrophils represent up to 70% of circulating leukocytes in healthy humans and combat infection mostly by phagocytosis, degranulation and NETosis. It has been reported that neutrophils are centrally involved in abdominal aortic aneurysm (AAA) pathogenesis. The natural course of AAA is growth and rupture, if left undiagnosed or untreated. The rupture of AAA has a very high mortality and is currently among the leading causes of death worldwide. The use of noninvasive cardiovascular imaging techniques for patient screening, surveillance and postoperative follow-up is well established and recommended by the current guidelines. Neutrophil-derived biomarkers may offer clinical value to the monitoring and prognosis of AAA patients, allowing for potential early therapeutic intervention. Numerous promising biomarkers have been studied. In this review, we discuss neutrophils and neutrophil-derived molecules as regulators and biomarkers of AAA, and our aim was to specifically highlight diagnostic and prognostic markers. Neutrophil-derived biomarkers may potentially, in the future, assist in determining AAA presence, predict size, expansion rate, rupture risk, and postoperative outcome once validated in highly warranted future prospective clinical studies.

Predicting the risk of rupture for vertebral aneurysm based on geometric features of blood vessels

A significant proportion of the adult population worldwide suffers from cerebral aneurysms. If left untreated, aneurysms may rupture and lead to fatal massive internal bleeding. On the other hand, treatment of aneurysms also involve significant risks. It is desirable, therefore, to have an objective tool that can be used to predict the risk of rupture and assist in surgical decision for operating on the aneurysms. Currently, such decisions are made mostly based on medical expertise of the healthcare team. In this paper, we investigate the possibility of using machine learning algorithms to predict rupture risk of vertebral artery fusiform aneurysms based on geometric features of the blood vessels surrounding but excluding the aneurysm. For each of the aneurysm images (12 ruptured and 25 unruptured), the vessel is segmented into distal and proximal parts by cross-sectional area and 382 non-aneurysm-related geometric features extracted. The decision tree model using two of the features (standard deviation of eccentricity of proximal vessel, and diameter at the distal endpoint) achieved 83.8% classification accuracy. Additionally, with support vector machine and logistic regression, we also achieved 83.8% accuracy with another set of two features (ratio of mean curvature between distal and proximal parts, and diameter at the distal endpoint). Combining the aforementioned three features with integration of curvature of proximal vessel and also ratio of mean cross-sectional area between distal and proximal parts, these models achieve an impressive 94.6% accuracy. These results strongly suggest the usefulness of geometric features in predicting the risk of rupture.

The Story of Wall Shear Stress in Coronary Artery Atherosclerosis: Biochemical Transport and Mechanotransduction

Coronary artery atherosclerosis is a local, multifactorial, complex disease, and the leading cause of death in the US. Complex interactions between biochemical transport and biomechanical forces influence disease growth. Wall shear stress (WSS) affects coronary artery atherosclerosis by inducing endothelial cell mechanotransduction and by controlling the near-wall transport processes involved in atherosclerosis. Each of these processes is controlled by WSS differently and therefore has complicated the interpretation of WSS in atherosclerosis. In this paper, we present a comprehensive theory for WSS in atherosclerosis. First, a short review of shear stress-mediated mechanotransduction in atherosclerosis was presented. Next, subject-specific computational fluid dynamics (CFD) simulations were performed in ten coronary artery models of diseased and healthy subjects. Biochemical-specific mass transport models were developed to study low-density lipoprotein, nitric oxide, adenosine triphosphate, oxygen, monocyte chemoattractant protein-1, and monocyte transport. The transport results were compared with WSS vectors and WSS Lagrangian coherent structures (WSS LCS). High WSS magnitude protected against atherosclerosis by increasing the production or flux of atheroprotective biochemicals and decreasing the near-wall localization of atherogenic biochemicals. Low WSS magnitude promoted atherosclerosis by increasing atherogenic biochemical localization. Finally, the attracting WSS LCS's role was more complex where it promoted or prevented atherosclerosis based on different biochemicals. We present a summary of the different pathways by which WSS influences coronary artery atherosclerosis and compare different mechanotransduction and biotransport mechanisms.

Screening Older Adult Men for Abdominal Aortic Aneurysm: A Scoping Review

Abdominal aortic aneurysm (AAA) is a potentially fatal condition predominantly affecting older adult men (60 years or over). Based on evidence, preventative health-care guidelines recommend screening older males for AAA using ultrasound. In attempts to reduce AAA mortality among men, screening has been utilized for early detection in some Western countries including the UK and Sweden. The current scoping review includes 19 empirical studies focusing on AAA screening in men. The findings from these studies highlight benefits and potential harms of male AAA screening. The benefits of AAA screening for men include decreased incidence of AAA rupture, decreased AAA mortality, increased effectiveness of elective AAA repair surgery, and cost-effectiveness. The potential harms of AAA screening included lack of AAA mortality reduction, negative impacts on quality of life, and inconsistent screening eligibility criteria being applied by primary care practitioners. The current scoping review findings are discussed to suggest changes to AAA screening guidelines and improve policy and practice.

Surface-directed engineering of tissue anisotropy in microphysiological models of musculoskeletal tissue

Here, we present an approach to model and adapt the mechanical regulation of morphogenesis that uses contractile cells as sculptors of engineered tissue anisotropy in vitro. Our method uses heterobifunctional cross-linkers to create mechanical boundary constraints that guide surface-directed sculpting of cell-laden extracellular matrix hydrogel constructs. Using this approach, we engineered linearly aligned tissues with structural and mechanical anisotropy. A multiscale in silico model of the sculpting process was developed to reveal that cell contractility increases as a function of principal stress polarization in anisotropic tissues. We also show that the anisotropic biophysical microenvironment of linearly aligned tissues potentiates soluble factor-mediated tenogenic and myogenic differentiation of mesenchymal stem cells. The application of our method is demonstrated by (i) skeletal muscle arrays to screen therapeutic modulators of acute oxidative injury and (ii) a 3D microphysiological model of lung cancer cachexia to study inflammatory and oxidative muscle injury induced by tumor-derived signals.

Mathematical model of atherosclerotic aneurysm

Atherosclerosis is a major cause of abdominal aortic aneurysm (AAA) and up to 80% of AAA patients have atherosclerosis. Therefore it is critical to understand the relationship and interactions between atherosclerosis and AAA to treat atherosclerotic aneurysm patients more effectively. In this paper, we develop a mathematical model to mimic the progression of atherosclerotic aneurysms by including both the multi-layer structured arterial wall and the pathophysiology of atherosclerotic aneurysms. The model is given by a system of partial differential equations with free boundaries. Our results reveal a 2D biomarker, the cholesterol ratio and DDR1 level, assessing the risk of atherosclerotic aneurysms. The efficacy of different treatment plans is also explored via our model and suggests that the dosage of anti-cholesterol drugs is significant to slow down the progression of atherosclerotic aneurysms while the additional anti-DDR1 injection can further reduce the risk.

Analysis of a mathematical model of rheumatoid arthritis

Rheumatoid arthritis is an autoimmune disease characterized by inflammation in the synovial fluid within the synovial joint connecting two contiguous bony surfaces. The inflammation diffuses into the cartilage adjacent to each of the bony surfaces, resulting in their gradual destruction. The interface between the cartilage and the synovial fluid is an evolving free boundary. In this paper we consider a two-phase free boundary problem based on a simplified model of rheumatoid arthritis. We prove global existence and uniqueness of a solution, and derive properties of the free boundary. In particular it is proved that the free boundary increases in time, and the cartilage shrinks to zero as [Formula: see text], even under treatment by a drug. It is also shown in the reduced one-phased problem, with cartilage alone, that a larger prescribed inflammation function leads to a faster destruction of the cartilage.

Mathematical Modelling for the Role of CD4+T Cells in Tumor-Immune Interactions

Mathematical modelling has been used to study tumor-immune cell interaction. Some models were proposed to examine the effect of circulating lymphocytes, natural killer cells, and CD8+T cells, but they neglected the role of CD4+T cells. Other models were constructed to study the role of CD4+T cells but did not consider the role of other immune cells. In this study, we propose a mathematical model, in the form of a system of nonlinear ordinary differential equations, that predicts the interaction between tumor cells and natural killer cells, CD4+T cells, CD8+T cells, and circulating lymphocytes with or without immunotherapy and/or chemotherapy. This system is stiff, and the Runge-Kutta method failed to solve it. Consequently, the "Adams predictor-corrector" method is used. The results reveal that the patient's immune system can overcome small tumors; however, if the tumor is large, adoptive therapy with CD4+T cells can be an alternative to both CD8+T cell therapy and cytokines in some cases. Moreover, CD4+T cell therapy could replace chemotherapy depending upon tumor size. Even if a combination of chemotherapy and immunotherapy is necessary, using CD4+T cell therapy can better reduce the dose of the associated chemotherapy compared to using combined CD8+T cells and cytokine therapy. Stability analysis is performed for the studied patients. It has been found that all equilibrium points are unstable, and a condition for preventing tumor recurrence after treatment has been deduced. Finally, a bifurcation analysis is performed to study the effect of varying system parameters on the stability, and bifurcation points are specified. New equilibrium points are created or demolished at some bifurcation points, and stability is changed at some others. Hence, for systems turning to be stable, tumors can be eradicated without the possibility of recurrence. The proposed mathematical model provides a valuable tool for designing patients' treatment intervention strategies.

Arterial Hypertension and Unusual Ascending Aortic Dilatation in a Neonate With Acute Kidney Injury: Mechanistic Computer Modeling

Background

Neonatal asphyxia caused kidney injury and severe hypertension in a newborn. An unusually dilatated ascending aorta developed. Dialysis and pharmacological treatment led to partial recovery of the ascending aortic diameters. It was hypothesized that the aortic dilatation may be associated with aortic stiffening, peripheral resistance, and cardiovascular changes. Mathematical modeling was used to better understand the potential causes of the hypertension, and to confirm our clinical treatment within the confines of the model's capabilities.

Methods

The patient's systolic arterial blood pressure showed hypertension. Echocardiographic exams showed ascending aorta dilatation during hypertension, which partially normalized upon antihypertensive treatment. To explore the underlying mechanisms of the aortic dilatation and hypertension, an existing lumped parameter hemodynamics model was deployed. Hypertension was simulated using realistic literature informed parameter values. It was also simulated using large parameter perturbations to demonstrate effects. Simulations were designed to permit examination of causal mechanisms. The hypertension inducing effects of aortic stiffnesses, vascular resistances, and cardiac hypertrophy on blood flow and pressure were simulated. Sensitivity analysis was used to stratify causes.

Results

In agreement with our clinical diagnosis, the model showed that an increase of aortic stiffness followed by augmentation of peripheral resistance are the prime causes of realistic hypertension. Increased left ventricular elastance may also cause hypertension. Ascending aortic pressure and flow increased in the simultaneous presence of left ventricle hypertrophy and augmented small vessel resistance, which indicate a plausible condition for ascending aorta dilatation. In case of realistic hypertension, sensitivity analysis showed that the treatment of both the large vessel stiffness and small vessel resistance are more important in comparison to cardiac hypertrophy.

Conclusion and Discussion

Large vessel stiffness was found to be the prime factor in arterial hypertension, which confirmed the clinical treatment. Treatment of cardiac hypertrophy appears to provide significant benefit but may be secondary to treatment of large vessel stiffness. The quantitative grading of pathophysiological mechanisms provided by the modeling may contribute to treatment recommendations. The model was limited due to a lack of data suitable to permit model identification.

Vertebral artery fusiform aneurysm geometry in predicting rupture risk

Cerebral aneurysms affect a significant portion of the adult population worldwide. Despite significant progress, the development of robust techniques to evaluate the risk of aneurysm rupture remains a critical challenge. We hypothesize that vertebral artery fusiform aneurysm (VAFA) morphology may be predictive of rupture risk and can serve as a deciding factor in clinical management. To investigate the VAFA morphology, we use a combination of image analysis and machine learning techniques to study a geometric feature set computed from a depository of 37 (12 ruptured and 25 un-ruptured) aneurysm images. Of the 571 unique features we compute, we distinguish five features for use by our machine learning classification algorithm by an analysis of statistical significance. These machine learning methods achieve state-of-the-art classification performance (81.43 ± 13.08%) for the VAFA morphology, and identify five features (cross-sectional area change of aneurysm, maximum diameter of nearby distal vessel, solidity of aneurysm, maximum curvature of nearby distal vessel, and ratio of curvature between aneurysm and its nearby proximal vessel) as effective predictors of VAFA rupture risk. These results suggest that the geometric features of VAFA morphology may serve as useful non-invasive indicators for the prediction of aneurysm rupture risk in surgical settings.