A Novel Parameter Estimation Method for Drug Diffusion, Distribution and Clearance in the Rat Brain Extracellular Space

2014 ◽  
Vol 590 ◽  
pp. 805-813 ◽  
Author(s):  
Kai Li ◽  
Long Zuo ◽  
Dong Qi He ◽  
Hong Bin Han
Keyword(s):  
Drug Delivery ◽  
Rat Brain ◽  
Extracellular Space ◽  
Estimation Method ◽  
Least Square Method ◽  
Least Square ◽  
Drug Diffusion ◽  
Diffusion Pattern ◽  
Magnetic Resonance Imaging Mri ◽  
Brain Extracellular Space

Purposes to estimate parameters for gadolium-diethylenetriaminepentaacetic acid (Gd-DTPA) diffusion and distribution after drug delivery in the rat brain extracellular space (ECS). Methods An isotropic diffusion pattern in the homogeneous media was presumed for Gd-DTPA diffusion in the rat brain ECS, and a mathematical model was established to describe the pharmacokinetics of Gd-DTPA. Results the analytical solution of the diffusion equation was obtained by Laplace transform, and the least square method was utilized to calculate the diffusion coefficient (D) and the clearance rate (k) of drugs in the sphere coordinates. Animal experimental data of Gd-DTPA-related intensity was acquired by magnetic resonance imaging (MRI). D and k were computed as 0.0129 mm2/h and 0.0957 /h, respectively. Conclusions By the proposed method, drug diffusion, distribution, and clearance in the rat brain can be quantitatively analyzed, which will enhance our understanding of drug delivery in the central nervous system.

scholarly journals The Parameter Estimation of Double Exponential Pulse Based on a Least Infinity Norm Fitting Method

2021 ◽  
Vol 2083 (4) ◽  
pp. 042002
Author(s):  
Yuewu Shi ◽  
Wei Wang ◽  
Zhizhen Zhu ◽  
Xin Nie
Keyword(s):  
Estimation Error ◽  
Estimation Method ◽  
Maximum Amplitude ◽  
Least Square Method ◽  
Least Square ◽  
Physical Parameters ◽  
Infinity Norm ◽  
Fitting Method ◽  
Double Exponential ◽  
Exponential Pulse

Abstract This paper presents an estimation method of double exponential pulse (DEP) between the physical parameters rise time (t r), full width at half maximum amplitude (t FWHM) and the mathematical parameters α, β. A newly fitting method based on the least infinity norm criterion is proposed to deal with the estimation problem of DEP. The calculation process and equation of parameters of this method is proposed based on an m-th-order polynomial fitting model. This estimation method is compared with the least square method by the same data and fitting function. The results show that the maximum estimation error of parameters of double exponential pulse obtained by the least infinity norm method is 1.5 %.

scholarly journals A New Distribution for Modeling Lifetime Data with Different Methods of Estimation and Censored Regression Modeling

2020 ◽  
Vol 8 (2) ◽  
pp. 610-630 ◽  
Author(s):  
Mohamed Ibrahim ◽  
Emrah Altun EA ◽  
Haitham M. Yousof
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Method ◽  
Estimation Method ◽  
Least Square Method ◽  
Least Square ◽  
Likelihood Method ◽  
Survival Times ◽  
New Model ◽  
Von Mises ◽  
Bootstrapping Method

In this paper and after introducing a new model along with its properties, we estimate the unknown parameter of the new model using the Maximum likelihood method, Cram er-Von-Mises method, bootstrapping method, least square method and weighted least square method. We assess the performance of all estimation method employing simulations. All methods perform well but bootstrapping method is the best in modeling relief times whereas the maximum likelihood method is the best in modeling survival times. Censored data modeling with covariates is addressed along with the index plot of the modified deviance residuals and its Q-Q plot.

scholarly journals Comparison of M Estimation, S Estimation, with MM Estimation to Get the Best Estimation of Robust Regression in Criminal Cases in Indonesia

2022 ◽  
Vol 18 (2) ◽  
pp. 251-260
Author(s):  
Malecita Nur Atala Singgih ◽  
Achmad Fauzan
Keyword(s):  
Regression Analysis ◽  
Robust Regression ◽  
Estimation Method ◽  
Least Square Method ◽  
Influential Factors ◽  
Least Square ◽  
Method Of Moment ◽  
Best Estimate ◽  
M Estimation ◽  
Mm Estimation

Crime incidents that occurred in Indonesia in 2019 based on Survey Based Data on criminal data sourced from the National Socio-Economic Survey and Village Potential Data Collection produced by the Central Statistics Agency recorded 269,324 cases. The high crime rate is caused by several factors, including poverty and population density. Determination of the most influential factors in criminal acts in Indonesia can be done with Regression Analysis. One method of Regression Analysis that is very commonly used is the Least Square Method. However, Regression Analysis can be used if the assumption test is met. If outliers are found, then the assumption test is not completed. The outlier problem can be overcome by using a robust estimation method. This study aims to determine the best estimation method between Maximum Likelihood Type (M) estimation, Scale (S) estimation, and Method of Moment (MM) estimation on Robust Regression. The best estimate of Robust Regression is the smallest Residual Standard Error (RSE) value and the largest Adjusted R-square. The analysis of case studies of criminal acts in Indonesia in 2019 showed that the best estimate was the S estimate with an RSE value of 4226 and an Adjusted R-square of 0.98  

Diffusion of Epidermal Growth Factor in Rat Brain Extracellular Space Measured by Integrative Optical Imaging

2004 ◽  
Vol 92 (6) ◽  
pp. 3471-3481 ◽  
Author(s):  
Robert G. Thorne ◽  
Sabina Hrabětová ◽  
Charles Nicholson
Keyword(s):  
Diffusion Coefficient ◽  
Growth Factors ◽  
Growth Factor ◽  
Epidermal Growth Factor ◽  
Optical Imaging ◽  
Rat Brain ◽  
Extracellular Space ◽  
Target Cells ◽  
Epidermal Growth ◽  
Brain Extracellular Space

Epidermal growth factor (EGF) stimulates proliferation, process outgrowth, and survival in the CNS. Understanding the actions of EGF necessitates characterizing its distribution in brain tissue following drug delivery or release from cellular sources. We used the integrative optical imaging (IOI) method to measure diffusion of fluorescently labeled EGF (6,600 Mr; 4 μg/ml) in the presence of excess unlabeled EGF (90 μg/ml) to compete off specific receptor binding and reveal the “true” EGF diffusion coefficient following injection in rat brain slices (400 μm). The effective diffusion coefficient was 5.18 ± 0.16 × 10−7 (SE) cm2/s ( n = 22) in rat somatosensory cortex and the free diffusion coefficient, determined in dilute agarose gel, was 16.6 ± 0.12 × 10−7 cm2/s ( n = 27). Tortuosity (λ), a parameter representing the hindrance imposed on EGF by the convoluted brain extracellular space (ECS), was 1.8, the lowest yet measured by IOI for a protein in brain. Control experiments with fluorescent dextran of similar molecular weight and tetramethylammonium confirmed EGF did not affect local ECS structure. We conclude that transport of smaller growth factors such as EGF through brain ECS is less hindered than that of larger proteins (>10,000 Mr, e.g., nerve growth factor) where typically λ > 2.1. Modeling was used to predict that low λ will allow EGF sources in the brain to be further from target cells and still elicit a biological response. High λ values for larger growth factors imply more constrained local biological effects than with smaller proteins such as EGF.

Polyamines in rat brain extracellular space after ischemia

1993 ◽  
Vol 18 (1-2) ◽  
pp. 27-33 ◽  
Author(s):  
Gad M. Gilad ◽  
Robert A. Casero ◽  
Raul Busto ◽  
Mordecai Y. -T. Globus
Keyword(s):  
Rat Brain ◽  
Extracellular Space ◽  
Brain Extracellular Space

scholarly journals Path generation for flying robots in mountainous regions

2016 ◽  
Vol 9 (1) ◽  
pp. 44-60 ◽  
Author(s):  
Amirreza Kosari ◽  
Hossein Maghsoudi ◽  
Abolfazl Lavaei
Keyword(s):  
Numerical Technique ◽  
Estimation Method ◽  
Least Square Method ◽  
Least Square ◽  
Performance Criteria ◽  
Mission Design ◽  
Vertical Acceleration ◽  
Mountainous Regions ◽  
Terrain Following ◽  
Flying Robots

In this paper, a new path planning method is proposed to resolve the problem of two-dimensional terrain following flight of flying robots in mountainous regions. The performance criteria considered for this mission design could include either the minimum vertical acceleration or the minimum flying time. To impose the terrain following/terrain avoidance constraints, various approaches such as least square method, Fourier series method, Gaussian estimation method, and Chebyshev orthogonal polynomial are explored. The resulting optimal control problem is discretized by employing a numerical technique namely direct collocation and then transformed into a nonlinear programming problem. The efficacy of the proposed method is demonstrated by extensive simulations, and particularly, it has been verified that this method is able to produce a solution that satisfies all hard constraints of the underlying problem.

scholarly journals Terrain Feature Estimation Method for a Lower Limb Exoskeleton Using Kinematic Analysis and Center of Pressure

Sensors ◽  
2019 ◽  
Vol 19 (20) ◽  
pp. 4418 ◽  
Author(s):  
Myounghoon Shim ◽  
Jong In Han ◽  
Ho Seon Choi ◽  
Seong Min Ha ◽  
Jung-Hoon Kim ◽  
...  
Keyword(s):  
Lower Limb ◽  
Kinematic Analysis ◽  
Center Of Pressure ◽  
Contact Point ◽  
Estimation Method ◽  
Least Square Method ◽  
Least Square ◽  
Estimation Accuracy ◽  
Lower Limb Exoskeleton ◽  
Contact Points

While controlling a lower limb exoskeleton providing walking assistance to wearers, the walking terrain is an important factor that should be considered for meeting performance and safety requirements. Therefore, we developed a method to estimate the slope and elevation using the contact points between the limb exoskeleton and ground. We used the center of pressure as a contact point on the ground and calculated the location of the contact points on the walking terrain based on kinematic analysis of the exoskeleton. Then, a set of contact points collected from each step during walking was modeled as the plane that represents the surface of the walking terrain through the least-square method. Finally, by comparing the normal vectors of the modeled planes for each step, features of the walking terrain were estimated. We analyzed the estimation accuracy of the proposed method through experiments on level ground, stairs, and a ramp. Classification using the estimated features showed recognition accuracy higher than 95% for all experimental motions. The proposed method approximately analyzed the movement of the exoskeleton on various terrains even though no prior information on the walking terrain was provided. The method can enable exoskeleton systems to actively assist walking in various environments.

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