The Association between Cafestol and Cardiovascular Diseases: A Comprehensive Review.

Cafestol, a bioactive compound found in coffee, has attracted considerable attention due to its potential impact on cardiovascular health. This review aims to comprehensively explore the association between cafestol and cardiovascular diseases. We delve into the mechanisms through which cafestol influences lipid metabolism, inflammation, and endothelial function, all of which are pivotal in cardiovascular pathophysiology. Moreover, we meticulously analyze epidemiological studies and clinical trials to elucidate the relationship between cafestol and cardiovascular outcomes. Through a critical examination of existing literature, we aim to provide insights into the potential benefits and risks associated with cafestol concerning cardiovascular health.

The phase 1/2 trial of indomethacin in chronic pancreatitis (The PAIR trial): Protocol for a parallel multi-center randomized controlled trial.

BACKGROUND/OBJECTIVES: Current treatments for chronic pancreatitis focus on symptom management and therapeutics targeting disease reversal are lacking. Given the role of the cyclooxygenase-2 (COX-2) enzyme in producing prostaglandin E2 (PGE2), a key component in the inflammatory pathway of chronic pancreatitis, this study evaluates the physiologic effect of oral indomethacin, a COX-2 inhibitor, on PGE2 levels in pancreatic fluid. METHODS: This pilot two-center randomized controlled trial seeks to examine 32 subjects with chronic pancreatitis who have no contraindications to indomethacin. Subjects will be randomized to either oral indomethacin 50 mg twice a day or placebo twice a day for a total of 28 days. Baseline (pre-treatment) assessment of pain and quality of life will be performed using the Brief Pain Inventory and the PROMIS-10 questionnaires, respectively. Biological specimens including blood, urine, and saliva will be collected at pre-treatment and post-treatment(day 28). Endoscopic pancreatic function testing with concomitant pancreatic fluid collection will also be performed pre- and post-treatment to assess the change in pancreatic fluid PGE2 levels. The relationship between pancreatic fluid PGE2 levels with blood and saliva PGE2 levels will be examined. CONCLUSIONS: This study will elucidate the effect of oral indomethacin on PGE2 levels in the pancreas to assess its role in the inflammatory pathway of chronic pancreatitis. Should indomethacin significantly reduce PGE2 levels, this may represent a potential disease-altering treatment for chronic pancreatitis.

Optimal anti-amyloid-beta therapy for Alzheimer's disease via a personalized mathematical model.

With the recent approval by the FDA of the first disease-modifying drug for Alzheimer's Disease (AD), personalized medicine will be increasingly important for appropriate management and counseling of patients with AD and those at risk. The growing availability of clinical biomarker data and data-driven computational modeling techniques provide an opportunity for new approaches to individualized AD therapeutic planning. In this paper, we develop a new mathematical model, based on AD cognitive, cerebrospinal fluid (CSF) and MRI biomarkers, to provide a personalized optimal treatment plan for individuals. This model is parameterized by biomarker data from the AD Neuroimaging Initiative (ADNI) cohort, a large multi-institutional database monitoring the natural history of subjects with AD and mild cognitive impairment (MCI). Optimal control theory is used to incorporate time-varying treatment controls and side-effects into the model, based on recent clinical trial data, to provide a personalized treatment regimen with anti-amyloid-beta therapy. In-silico treatment studies were conducted on the approved treatment, aducanumab, as well as on another promising anti-amyloid-beta therapy under evaluation, donanemab. Clinical trial simulations were conducted over both short-term (78 weeks) and long-term (10 years) periods with low-dose (6 mg/kg) and high-dose (10 mg/kg) regimens for aducanumab, and a single-dose regimen (1400 mg) for donanemab. Results confirm those of actual clinical trials showing a large and sustained effect of both aducanumab and donanemab on amyloid beta clearance. The effect on slowing cognitive decline was modest for both treatments, but greater for donanemab. This optimal treatment computational modeling framework can be applied to other single and combination treatments for both prediction and optimization, as well as incorporate new clinical trial data as it becomes available.

Bifurcation analysis of a free boundary model of vascular tumor growth with a necrotic core and chemotaxis.

A considerable number of research works has been devoted to the study of tumor models. Several biophysical factors, such as cell proliferation, apoptosis, chemotaxis, angiogenesis and necrosis, have been discovered to have an impact on the complicated biological system of tumors. An indicator of the aggressiveness of tumor development is the instability of the shape of the tumor boundary. Complex patterns of tumor morphology have been explored in Lu et al. (J Comput Phys 459:111153, 2022). In this paper, we continue to carry out a bifurcation analysis on such a vascular tumor model with a controlled necrotic core and chemotaxis. This bifurcation analysis, to the parameter of cell proliferation, is built on the explicit formulas of radially symmetric steady-state solutions. By perturbing the tumor free boundary and establishing rigorous estimates of the free boundary system, we prove the existence of the bifurcation branches with Crandall-Rabinowitz theorem. The parameter of chemotaxis is found to influence the monotonicity of the bifurcation point as the mode l increases both theoretically and numerically.

Discrimination of vascular aging using the arterial pulse spectrum and machine-learning analysis.

Aging contributes to the progression of vascular dysfunction and is a major nonreversible risk factor for cardiovascular disease. The aim of this study was to determine the effectiveness of using arterial pulse-wave measurements, frequency-domain pulse analysis, and machine-learning analysis in distinguishing vascular aging. Radial pulse signals were measured noninvasively for 3 min in 280 subjects aged 40-80 years. The cardio-ankle vascular index (CAVI) was used to evaluate the arterial stiffness of the subjects. Forty frequency-domain pulse indices were used as features, comprising amplitude proportion (Cn), coefficient of variation of Cn, phase angle (Pn), and standard deviation of Pn (n = 1-10). Multilayer perceptron and random forest with supervised learning were used to classify the data. The detected differences were more prominent in the subjects aged 40-50 years. Several indices differed significantly between the non-vascular-aging group (aged 40-50 years; CAVI <9) and the vascular-aging group (aged 70-80 years). Fivefold cross-validation revealed an excellent ability to discriminate the two groups (the accuracy was >80%, and the AUC was >0.8). For subjects aged 50-60 and 60-70 years, the detection accuracies of the two trained algorithms were around 80%, with AUCs of >0.73 for both, which indicated acceptable discrimination. The present method of frequency-domain analysis may improve the index reliability for further machine-learning analyses of the pulse waveform. The present noninvasive and objective methodology may be meaningful for developing a wearable-device system to reduce the threat of vascular dysfunction induced by vascular aging.

A cancer model with nonlocal free boundary dynamics.

Cancer cells at the tumor boundary move in the direction of the oxygen gradient, while cancer cells far within the tumor are in a necrotic state. This paper introduces a simple mathematical model that accounts for these facts. The model consists of cancer cells, cytotoxic T cells, and oxygen satisfying a system of partial differential equations. Some of the model parameters represent the effect of anti-cancer drugs. The tumor boundary is a free boundary whose dynamics is determined by the movement of cancer cells at the boundary. The model is simulated for radially symmetric and axially symmetric tumors, and it is shown that the tumor may increase or decrease in size, depending on the "strength" of the drugs. Existence theorems are proved, global in-time in the radially symmetric case, and local in-time for any shape of tumor. In the radially symmetric case, it is proved, under different conditions, that the tumor may shrink monotonically, or expand monotonically.

Learn bifurcations of nonlinear parametric systems via equation-driven neural networks.

Nonlinear parametric systems have been widely used in modeling nonlinear dynamics in science and engineering. Bifurcation analysis of these nonlinear systems on the parameter space is usually used to study the solution structure, such as the number of solutions and the stability. In this paper, we develop a new machine learning approach to compute the bifurcations via so-called equation-driven neural networks (EDNNs). The EDNNs consist of a two-step optimization: the first step is to approximate the solution function of the parameter by training empirical solution data; the second step is to compute bifurcations using the approximated neural network obtained in the first step. Both theoretical convergence analysis and numerical implementation on several examples have been performed to demonstrate the feasibility of the proposed method.

Stability preserving data-driven models with latent dynamics.

In this paper, we introduce a data-driven modeling approach for dynamics problems with latent variables. The state-space of the proposed model includes artificial latent variables, in addition to observed variables that can be fitted to a given data set. We present a model framework where the stability of the coupled dynamics can be easily enforced. The model is implemented by recurrent cells and trained using backpropagation through time. Numerical examples using benchmark tests from order reduction problems demonstrate the stability of the model and the efficiency of the recurrent cell implementation. As applications, two fluid-structure interaction problems are considered to illustrate the accuracy and predictive capability of the model.

Spatial pattern formation in reaction-diffusion models: a computational approach.

Reaction-diffusion equations have been widely used to describe biological pattern formation. Nonuniform steady states of reaction-diffusion models correspond to stationary spatial patterns supported by these models. Frequently these steady states are not unique and correspond to various spatial patterns observed in biology. Traditionally, time-marching methods or steady state solvers based on Newton's method were used to compute such solutions. However, the solutions that these methods converge to highly depend on the initial conditions or guesses. In this paper, we present a systematic method to compute multiple nonuniform steady states for reaction-diffusion models and determine their dependence on model parameters. The method is based on homotopy continuation techniques and involves mesh refinement, which significantly reduces computational cost. The method generates one-parameter steady state bifurcation diagrams that may contain multiple unconnected components, as well as two-parameter solution maps that divide the parameter space into different regions according to the number of steady states. We applied the method to two classic reaction-diffusion models and compared our results with available theoretical analysis in the literature. The first is the Schnakenberg model which has been used to describe biological pattern formation due to diffusion-driven instability. The second is the Gray-Scott model which was proposed in the 1980s to describe autocatalytic glycolysis reactions. In each case, the method uncovers many, if not all, nonuniform steady states and their stabilities.

Mathematical model of chronic pancreatitis.

Chronic pancreatitis (CP) is a progressive inflammatory disease of the pancreas, leading to its fibrotic destruction. There are currently no drugs that can stop or slow the progression of the disease. The etiology of the disease is multifactorial, whereas recurrent attacks of acute pancreatitis are thought to precede the development of CP. A better understanding of the pathology of CP is needed to facilitate improved diagnosis and treatment strategies for this disease. The present paper develops a mathematical model of CP based on a dynamic network that includes macrophages, pancreatic stellate cells, and prominent cytokines that are present at high levels in the CP microenvironment. The model is represented by a system of partial differential equations. The model is used to explore in silico potential drugs that could slow the progression of the disease, for example infliximab (anti-TNF-[Formula: see text]) and tocilizumab or siltuximab (anti-IL-6/IL-6R).

Bifurcation analysis of a free boundary model of the atherosclerotic plaque formation associated with the cholesterol ratio.

The low-density lipoprotein (LDL)/high-density lipoprotein (HDL)-cholesterol ratio has been shown to have a high correlation with the cardiovascular risk assessment. Is it possible to quantify the correlation mathematically? In this paper, we develop a bifurcation analysis for a mathematical model of the plaque formation with a free boundary in the early stage of atherosclerosis. This bifurcation analysis, to the ratio of LDL/HDL, is based on explicit formulations of radially symmetric steady-state solutions. By performing the perturbation analysis to these solutions, we establish the existence of bifurcation branches and derive a theoretical condition that a bifurcation occurs for different modes. We also analyze the stability of radially symmetric steady-state solutions and conduct numerical simulations to verify all theoretical results.

The Role of Exosomes in Pancreatic Cancer Microenvironment.

Exosomes are nanovesicles shed by cells as a means of communication with other cells. Exosomes contain mRNAs, microRNAs (miRs) and functional proteins. In the present paper, we develop a mathematical model of tumor-immune interaction by means of exosomes shed by pancreatic cancer cells and dendritic cells. Cancer cells' exosomes contain miRs that promote their proliferation and that inhibit immune response by dendritic cells, and by CD4+ and CD8+ T cells. Dendritic cells release exosomes with proteins that induce apoptosis of cancer cells and that block regulatory T cells. Simulations of the model show how the size of the pancreatic cancer can be determined by measurement of specific miRs (miR-21 and miR-203 in the case of pancreatic cancer), suggesting these miRs as biomarkers for cancer.

Lipopolysaccharide pretreatment increases protease-activated receptor-2 expression and monocyte chemoattractant protein-1 secretion in vascular endothelial cells.

BACKGROUND: This study investigated whether lipopolysaccharide (LPS) increase protease-activated receptor-2 (PAR-2) expression and enhance the association between PAR-2 expression and chemokine production in human vascular endothelial cells (ECs). METHODS: The morphology of ECs was observed through microphotography in cultured human umbilical vein ECs (EA. hy926 cells) treated with various LPS concentrations (0, 0.25, 0.5, 1, and 2 µg/mL) for 24 h, and cell viability was assessed using the MTT assay. Intracellular calcium imaging was performed to assess agonist (trypsin)-induced PAR-2 activity. Western blotting was used to explore the LPS-mediated signal transduction pathway and the expression of PAR-2 and adhesion molecule monocyte chemoattractant protein-1 (MCP-1) in ECs. RESULTS: Trypsin stimulation increased intracellular calcium release in ECs. The calcium influx was augmented in cells pretreated with a high LPS concentration (1 µg/mL). After 24 h treatment of LPS, no changes in ECs viability or morphology were observed. Western blotting revealed that LPS increased PAR-2 expression and enhanced trypsin-induced extracellular signal-regulated kinase (ERK)/p38 phosphorylation and MCP-1 secretion. However, pretreatment with selective ERK (PD98059), p38 mitogen-activated protein kinase (MAPK) (SB203580) inhibitors, and the selective PAR-2 antagonist (FSLLRY-NH2) blocked the effects of LPS-activated PAR-2 on MCP-1 secretion. CONCLUSIONS: Our findings provide the first evidence that the bacterial endotoxin LPS potentiates calcium mobilization and ERK/p38 MAPK pathway activation and leads to the secretion of the pro-inflammatory chemokine MCP-1 by inducing PAR-2 expression and its associated activity in vascular ECs. Therefore, PAR-2 exerts vascular inflammatory effects and plays an important role in bacterial infection-induced pathological responses.

Dimorphism by Singularity Theory in a Model for River Ecology.

Geritz, Gyllenberg, Jacobs, and Parvinen show that two similar species can coexist only if their strategies are in a sector of parameter space near a nondegenerate evolutionarily singular strategy. We show that the dimorphism region can be more general by using the unfolding theory of Wang and Golubitsky near a degenerate evolutionarily singular strategy. Specifically, we use a PDE model of river species as an example of this approach. Our finding shows that the dimorphism region can exhibit various different forms that are strikingly different from previously known results in adaptive dynamics.

Mathematical model of sarcoidosis.

Sarcoidosis is a disease involving abnormal collection of inflammatory cells forming nodules, called granulomas. Such granulomas occur in the lung and the mediastinal lymph nodes, in the heart, and in other vital and nonvital organs. The origin of the disease is unknown, and there are only limited clinical data on lung tissue of patients. No current model of sarcoidosis exists. In this paper we develop a mathematical model on the dynamics of the disease in the lung and use patients' lung tissue data to validate the model. The model is used to explore potential treatments.

Mathematical model of renal interstitial fibrosis.

Lupus nephritis (LN) is an autoimmune disease that occurs when autoantibodies complex with self-antigen and form immune complexes that accumulate in the glomeruli. These immune complexes initiate an inflammatory response resulting in glomerular injury. LN often concomitantly affects the tubulointerstitial compartment of the kidney, leading first to interstitial inflammation and subsequently to interstitial fibrosis and atrophy of the renal tubules if not appropriately treated. Presently the only way to assess interstitial inflammation and fibrosis is through kidney biopsy, which is invasive and cannot be repeated frequently. Hence, monitoring of disease progression and response to therapy is suboptimal. In this paper we describe a mathematical model of the progress from tubulointerstitial inflammation to fibrosis. We demonstrate how the model can be used to monitor treatments for interstitial fibrosis in LN with drugs currently being developed or used for nonrenal fibrosis.

A mathematical model of pre-diagnostic glioma growth.

Due to their location, the malignant gliomas of the brain in humans are very difficult to treat in advanced stages. Blood-based biomarkers for glioma are needed for more accurate evaluation of treatment response as well as early diagnosis. However, biomarker research in primary brain tumors is challenging given their relative rarity and genetic diversity. It is further complicated by variations in the permeability of the blood brain barrier that affects the amount of marker released into the bloodstream. Inspired by recent temporal data indicating a possible decrease in serum glucose levels in patients with gliomas yet to be diagnosed, we present an ordinary differential equation model to capture early stage glioma growth. The model contains glioma-glucose-immune interactions and poses a potential mechanism by which this glucose drop can be explained. We present numerical simulations, parameter sensitivity analysis, linear stability analysis and a numerical experiment whereby we show how a dormant glioma can become malignant.

A mathematical model of atherosclerosis with reverse cholesterol transport and associated risk factors.

Atherosclerosis, the leading cause of death in the US, is a disease in which a plaque builds up inside the arteries. The low density lipoprotein (LDL) and high density lipoprotein (HDL) concentrations in the blood are commonly used to predict the risk factor for plaque growth. In a recent paper (Hao and Friedman in Plos One e90497, 2014), we have developed a mathematical model of plaque growth which includes the (LDL, HDL) concentrations. In the present paper, we have refined that model by including the effect of reverse cholesterol transport. By exploration-by-examples of regression of a plaque in mice, our model simulations suggest that such drugs as used for mice may also slow plaque growth in humans. We next proceeded to explore the effects of oxidative stress or antioxidant deficiency, high blood pressure and cigarette smoking as risk factors. We suggest for an individual in one of these three risk categories and with specified (LDL, HDL) concentration, how to reduce or eliminate the risk of atherosclerosis.

Emergence of non-trivial solutions from trivial solutions in reaction-diffusion equations for pattern formation.

Reaction-diffusion equations serve as fundamental tools in describing pattern formation in biology. In these models, nonuniform steady states often represent stationary spatial patterns. Notably, these steady states are not unique, and unveiling them mathematically presents challenges. In this paper, we introduce a framework based on bifurcation theory to address pattern formation problems, specifically examining whether nonuniform steady states can bifurcate from trivial ones. Furthermore, we employ linear stability analysis to investigate the stability of the trivial steady-state solutions. We apply the method to two classic reaction-diffusion models: the Schnakenberg model and the Gray-Scott model. For both models, our approach effectively reveals many nonuniform steady states and assesses the stability of the trivial solution. Numerical computations are also presented to validate the solution structures for these models.

HomPINNs: homotopy physics-informed neural networks for solving the inverse problems of nonlinear differential equations with multiple solutions.

Due to the complex behavior arising from non-uniqueness, symmetry, and bifurcations in the solution space, solving inverse problems of nonlinear differential equations (DEs) with multiple solutions is a challenging task. To address this, we propose homotopy physics-informed neural networks (HomPINNs), a novel framework that leverages homotopy continuation and neural networks (NNs) to solve inverse problems. The proposed framework begins with the use of NNs to simultaneously approximate unlabeled observations across diverse solutions while adhering to DE constraints. Through homotopy continuation, the proposed method solves the inverse problem by tracing the observations and identifying multiple solutions. The experiments involve testing the performance of the proposed method on one-dimensional DEs and applying it to solve a two-dimensional Gray-Scott simulation. Our findings demonstrate that the proposed method is scalable and adaptable, providing an effective solution for solving DEs with multiple solutions and unknown parameters. Moreover, it has significant potential for various applications in scientific computing, such as modeling complex systems and solving inverse problems in physics, chemistry, biology, etc.