Kullback-Leibler Control in Boolean Control Networks.

This article addresses the Kullback-Leibler (KL) control problem in Boolean control networks. In the considered problem, an extended stage cost function depending on the control inputs is introduced; in contrast to a stage cost of the conventional KL control problems in the Markov decision process cannot take into consideration the control inputs. An associated Bellman equation and a matrix-based iteration algorithm are presented. The theoretical analysis shows that the proposed KL control results in an approximated form of conventional dynamic programming (DP). Furthermore, the convergence analysis is presented, with the weight parameter converging to zero and diverging to infinity. In practical application examples, a comparison of the conventional DP and proposed KL control is illustrated.

Maximum-Likelihood State Estimators in Probabilistic Boolean Control Networks.

This study addresses state estimation problems for probabilistic Boolean control networks (PBCNs). Compared with deterministic Boolean networks, PBCNs have the stochastic switching in logical update functions in the state equation. Consequently, statistical analysis is required to estimate unavailable states, which induces an optimization problem called maximum-likelihood estimation. This article mainly focuses on two scenarios: 1) state estimation from partially measured state and 2) state estimation from output data, meaning observer design. The resulting optimization problems are solved using efficient algorithms based on dynamic programming. Concurrently, Dijkstra-type algorithms, which solve equivalent shortest path problems, are also proposed using best-first search. Furthermore, both the proposed algorithms derive novel observer design methods for PBCNs. The proposed algorithms are evaluated with practical estimation problems aiming to the sensor reduction and applied to gene regulatory networks of apoptosis and Lac operon.

Mayer-Type Optimal Control of Probabilistic Boolean Control Network With Uncertain Selection Probabilities.

This article considers a Mayer-type optimal control problem of probabilistic Boolean control networks (PBCNs) with uncertainty on selection probabilities which obey Beta probabilistic distributions. The expectation with respect to both the selection probabilities and the transitions of state variables is set as a cost function, and it deduces an equivalent formulation as a multistage decision problem. Furthermore, the dynamic programming technique is applied to solve the problem and performs a novel optimization algorithm in the fashion of semitensor product. A numerical example of a biological model of apoptosis protein demonstrates the effectiveness and feasibility of the proposed framework and algorithms.

Policy Iteration Approach to the Infinite Horizon Average Optimal Control of Probabilistic Boolean Networks.

This article studies the optimal control of probabilistic Boolean control networks (PBCNs) with the infinite horizon average cost criterion. By resorting to the semitensor product (STP) of matrices, a nested optimality equation for the optimal control problem of PBCNs is proposed. The Laurent series expression technique and the Jordan decomposition method derive a novel policy iteration-type algorithm, where finite iteration steps can provide the optimal state feedback law, which is presented. Finally, the intervention problem of the probabilistic Ara operon in E. coil, as a biological application, is solved to demonstrate the effectiveness and feasibility of the proposed theoretical approach and algorithms.

Machine Learning Classification of Cerebral Aneurysm Rupture Status with Morphologic Variables and Hemodynamic Parameters.

PURPOSE: To construct a classification model of rupture status and to clarify the importance of morphologic variables and hemodynamic parameters on rupture status by applying a machine learning (ML) algorithm to morphologic and hemodynamic data of cerebral aneurysms. MATERIALS AND METHODS: Between 2011 and 2019, 226 (112 ruptured and 114 unruptured) cerebral aneurysms in 188 consecutive patients were retrospectively analyzed with computational fluid dynamics (CFD). A random forest ML algorithm was applied to the results to create three classification models consisting of only morphologic variables (model 1), only hemodynamic parameters (model 2), and both morphologic variables and hemodynamic parameters (model 3). The accuracy of rupture status classification and the importance of each variable or parameter in the models were computed. RESULTS: The accuracy was 77.0% in model 1, 71.2% in model 2, and 78.3% in model 3. The three most important features were projection ratio, size ratio, and aspect ratio in model 1; low shear area ratio, oscillatory shear index, and oscillatory velocity index in model 2; and projection ratio, irregular shape, and size ratio in model 3. CONCLUSION: Classification models of rupture status of cerebral aneurysms were constructed by applying an ML algorithm to morphologic variables and hemodynamic parameters. The model worked with relatively high accuracy, in which projection ratio, irregular shape, and size ratio were important for the discrimination of ruptured aneurysms.Supplemental material is available for this article.© RSNA, 2020.

On Optimal Time-Varying Feedback Controllability for Probabilistic Boolean Control Networks.

This brief studies controllability for probabilistic Boolean control network (PBCN) with time-varying feedback control laws. The concept of feedback controllability with an arbitrary probability for PBCNs is formulated first, and a control problem to maximize the probability of time-varying feedback controllability is investigated afterward. By introducing semitensor product (STP) technique, an equivalent multistage decision problem is deduced, and then a novel optimization algorithm is proposed to obtain the maximum probability of controllability and the corresponding optimal feedback law simultaneously. The advantages of the time-varying optimal controller obtained by the proposed algorithm, compared to the time-invariant one, are illustrated by numerical simulations.

Quantification of hemodynamic irregularity using oscillatory velocity index in the associations with the rupture status of cerebral aneurysms.

BACKGROUND: Complex and unstable flow patterns are reported to be associated with the rupture status of cerebral aneurysms, while their evaluation depends on qualitative analysis of streamlines of bloodflow. Oscillatory velocity index (OVI) is a hemodynamic parameter to quantify flow patterns. The aim of this study is to elucidate the associations between OVI and the rupture status of cerebral aneurysms. METHODS: One hundred and twenty-nine ruptured and unruptured cerebral aneurysms were analyzed with computational fluid dynamics under pulsatile flow conditions. With the use of median value of OVI, all aneurysms were divided into high and low OVI groups. Statistical analysis was performed to compare rupture status, and morphological and hemodynamic parameters between the two groups. RESULTS: The median value of OVI was 0.006. High OVI was more likely observed in ruptured aneurysms (P=0.028) and associated with irregular shape, complex flow patterns, and unstable flow patterns (P<0.001, respectively). In morphological parameters, maximum size, aspect, projection, size, and volume-to-ostium area ratios were significantly higher in the high OVI group (P<0.001, respectively). In hemodynamic parameters, wall shear stress and wall shear stress gradient were significantly lower, and oscillatory shear index and gradient oscillatory number were significantly higher in the high OVI group (P<0.001, respectively). CONCLUSION: High OVI was associated with rupture status, and morphological and hemodynamic characteristics of ruptured aneurysms. These results indicate that OVI may serve as a valuable hemodynamic parameter for diagnosing rupture status and risks of aneurysms.