Atherosclerosis, a chronic inflammatory disorder of the arterial wall, is a complex process whose dynamics are affected by multiple factors. The disease control consists of restraining it by ...administering statins. Slowing down or halting the plaque growth depends on the patient age at which the statin treatment begins and on the thickness of the intima-media (IMT) at that time. In this paper, we propose a mathematical model to estimate the sets of atherosclerosis states, from which the use of statins can restrain the disease. Our model is control-theoretic, and the estimated sets are the viability kernels, in the parlance of viability theory. To our best knowledge, this way of modelling the atherosclerosis progression is original. We compute two viability kernels, each for a different statin-treatment dose. Each kernel is composed of the vector age, IMT from which the disease can be restrained. By extension, the disease can't be restrained from the kernel complements, this being mainly because of the disease and patient-age advancement. The kernels visualise tradeoffs between early and late treatments, which helps the clinician to decide when to start the statin treatment and which statin dose may be sufficient.
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Dostopno za:
DOBA, IZUM, KILJ, NUK, PILJ, PNG, SAZU, SIK, UILJ, UKNU, UL, UM, UPUK
A Control-Theoretic Model of Atherosclerosis Formanowicz, Dorota; Krawczyk, Jacek B; Perek, Bartłomiej ...
International journal of molecular sciences,
02/2019, Letnik:
20, Številka:
3
Journal Article
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We propose a control-theoretic aggregate model of the progression of atherosclerosis plaque, a chronic inflammatory disease of the arterial wall, to study the basic features of this disease. In the ...model, we exploit the role of inflammation in the disease progression, and use statins-drugs commonly recommended in atherosclerosis-to control this progression. We use a logistic function to allow for constrained growth of plaque. In the model, both the patient's age and overall health impact the plaque growth and its sensitivity to statins. The model parameters are estimated using original data, or calibrated using published research as well as our own clinical and laboratory studies. We contend that our model helps to gauge the statins' impact on a patient's plaque thickness, hence the disease's progression and cardiovascular risk, without requiring artery scans.
A qualitative game describes a situation in which antagonistic players strive to keep the evolutions of their state variables in predetermined constraint sets. We argue that a qualitative game model ...is a suitable mathematical representation of the struggle between a domestic central bank of a small open economy and a foreign central bank of a large economy to maintain their respective state variables within an acceptable band regardless of the other player’s choices. The actions of the foreign central bank affect the domestic exchange rate and, hence, domestic inflation, output gap and interest rate. However, these actions do not necessarily aim to destabilise the small open economy, nor do they take into account the state of the latter. The domestic bank’s problem, therefore, is similar to that of a game against nature. We refer to this type of qualitative game as a nuisance-agent game (or NA-game). We use viability theory to derive satisficing rules (in the sense of Simon) of nominal interest-rate adjustments for the domestic central bank of a small open economy in a qualitative NA-game against the foreign central bank.
In patients with leukemia, the portal(s) and reasons for the persistence of an
Escherichia coli
recurrent bacteremia remain unclear. Adult Hematology Clinic (AHC) databases at the State Clinical ...Hospital in Gdańsk were reviewed to evaluate the frequency of
E. coli
bacteremia between 2002 and 2005. Blood and bowel
E. coli
strains were obtained and the genetic relatedness of the strains was analyzed. The rate of
E. coli
bacteremia per 1,000 admissions at the AHC was higher (85.0) than in the other clinics of the hospital (2.9),
p
< 0.001. A higher mortality was observed in patients with a history of
E. coli
versus non-
E. coli
bacteremia 30/95 (31 %) vs. 53/430 (12 %),
p
< 0.001; 72.8 % of patients with leukemia had an unknown source of bacteremia. In 2005, 6 out of 25 (24 %) patients with leukemia had ≥2 episodes of
E. coli
-positive blood cultures. These gastrointestinal
E. coli
isolates were replaced within 3–8 weeks with a new
E. coli
H genotype. A recurrent episode of bacteremia was usually caused by an infection with a transient
E. coli
H genotype identical to that found in the subject’s bowel. Consistent with the definition of bowel/blood translocation, the bowel appeared to be a portal for
E. coli
in these subjects and, hence, a clear source for their recurring bacteremia.
A numerical method based on a relaxation algorithm and the Nikaido-Isoda function is presented for the calculation of Nash-Cournot equilibria in electricity markets. Nash equilibrium is attained ...through a relaxation procedure applied to an objective function, the Nikaido-Isoda function, which is derived from the existing profit maximization functions calculated by the generating companies. We also show how to use the relaxation algorithm to compute, and enforce, a coupled constraint equilibrium, which occurs if regulatory, generation, and distribution (and more) restrictions are placed on the companies and entire markets. Moreover, we use the relaxation algorithm to compute players' payoffs under several player configurations. This is needed for the solution of our game under cooperative game theory concepts, such as the bilateral Shapley value and the kernel. We show that the existence of both depends critically on demand price elasticity. The numerical method converges to a unique solution under rather specific but plausible concavity conditions. A case study from the IEEE 30-bus system, and a three-bus bilateral market example with a dc model of the transmission line constraints are presented and discussed.
The aim of the study was to investigate whether there are unique pathotypes of
Escherichia coli
capable of transmission from the gastrointestinal tract to the vascular bed. The study included
E. coli
...strains isolated from clinical materials collected from 115 patients suffering from haematologic malignancies diagnosed with bacteraemia. The genotyping techniques established that 89
E. coli
isolates from the blood had the same genotype as the
E. coli
from the patient’s bowel. The presence of 21 genes encoding virulence factors typical of various
E. coli
pathotypes and their relationship with the phylogenetic group was established. One-dimensional analysis showed that the
focG
gene occurred more frequently in the control bowel group, while the ampicillin-resistant
afa
/
dr E. coli
were associated with bacteraemia. Blood isolates with the highest occurrence of virulence factors belonged to pathogenic group B2 and non-pathogenic group A. The co-occurrence of multiple genes encoding
papC
,
sfa
,
usp
and
cnf1
virulence factors probably predisposes
E. coli
to translocation from the gastrointestinal tract to the vascular bed in the group of patients with haematologic malignancies. Based on clustering analysis, dominance of the most virulent strains assigned to the cluster with seven virulence factors encoded by the following genes,
papC
,
sfaD
/
E
,
cnf1
,
usp
,
agn43
,
hlyA
and
iutA
, was found. The obtained results enforce the previously proposed concept of bowel–blood translocation and further expand our hypothesis by defining the unique virulence characteristics of
E. coli
isolates, which predispose them to bowel colonisation or translocation and bacteraemia in this group of patients.
While the use of statins in treating patients with atherosclerosis is an undisputed success, the questions regarding an optimal starting time for treatment and its strength remain open. We proposed ...in our earlier paper published in Int. J. Mol. Sci. (2019, 20) that the growth of intima-media thickness of the carotid artery follows an S-shape (i.e., logistic) curve. In our subsequent paper in PLoS ONE (2020, 15), we incorporated this feature into a logistic control-theoretic model of atherosclerosis progression and showed that some combinations of patient age and intima-media thickness are better suited than others to start treatment. In this study, we perform a new and comprehensive calibration of our logistic model using a recent clinical database. This allows us to propose a procedure for inferring an optimal age to start statin treatment for a particular group of patients. We argue that a decrease in the slope of the IMT logistic growth curve, induced by statin treatment, is most efficient where the curve is at its steepest, whereby the efficiency means lowering the future IMT levels. Using the procedure on an aggregate group of severely sick men, 38 years of age is observed to correlate with the steepest point of the logistic curve, and, thus, it is the preferred time to start statin treatment. We believe that detecting the logistic curve’s steepest fragment and commencing statin administration on that fragment are courses of action that agree with clinician intuition and may support decision-making processes.
The focus of this paper is on how to model and solve an environmental compliance problem using Rosen, J.B., 1965. Existence and uniqueness of equilibrium points for concave n-person games. ...Econometrica 33 (3), 520–534 seminal idea of
coupled constraint equilibrium. First, Rosen's results about the existence and uniqueness of a Nash normalised equilibrium for coupled constraint games are explained. These results are then combined with a numerical approach to game solutions based on the Nikaido–Isoda function. A river basin pollution game, which is a model for a common nonpoint source pollution problem, is solved numerically using this approach. In the game, the agents face a joint constraint on the total pollution, which defines a coupled constraint set in the combined strategy space. This makes the game special in terms of the strategy spaces. Unlike for standard games where they are defined separately for each player, here we have a joint constraint on the combined strategy space of all players. Hence, the game needs coupled constraint equilibrium as the solution concept. Static and (open-loop) dynamic equilibria are computed for the basin problem under the discussed equilibrium concept. All equilibria are instructive for the legislator, in that they contain information on how to choose the “optimal” charges, under which agents obey the constraints.
Our interest is in the relationship between the environment and economic growth. Because various interest groups see this issue differently, the typical optimization approach based on representative ...agent is not suitable. This is mainly because assessing the relative weight between consumption and environment in the utility function in a democracy is a sensitive political process. On the other hand, constraints on capital, consumption, and pollution levels should be agreed considerably easier than the aforementioned weight because the constraints refer to quantifiable measures. We propose that a regulator can look for a feasible strategy for emission control that will maintain capital, consumption, and pollution in a closed set of constraints. Such a strategy is called viable in viability theory. Viability theory is the study of dynamic systems that asks what set of initial conditions will generate evolutions that obey the laws of motion of a system and remain in a certain state constraints set for the duration of the evolution. We apply viability theory to a neoclassical model to identify which current economic states are sustainable under smooth adjustments of abatement-rate in the future. Among many observations, we note that countries that embark on an ambitious abatement program may fail to maintain their economies within the state constraints if their present levels of capital and consumption are low.
For pension-savers, a low payoff is a financial disaster. Such investors will most likely prefer left-skewed payoff distributions over right-skewed payoff distributions. We explore how such ...distributions can be delivered. Cautious-relaxed utility measures are cautious in ensuring that payoffs don't fall much below a reference value, but relaxed about exceeding it. We find that the payoff distribution delivered by a cautious-relaxed utility measure has appealing features which payoff distributions delivered by traditional utility functions don't. In particular, cautious-relaxed distributions can have the mass concentrated on the left, hence be left-skewed. However, cautious-relaxed strategies prescribe frequent portfolio adjustments which may be expensive if transaction costs are charged. In contrast, more traditional strategies can be time-invariant. Thus we investigate the impact of transaction costs on the appeal of cautious-relaxed strategies. We find that relatively high transaction fees are required for the cautious-relaxed strategy to lose its appeal. This paper contributes to the literature which compares utility measures by the payoff distributions they produce and finds that a cautious-relaxed utility measure will deliver payoffs that many investors will prefer.
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