Least-squares Minimization Method Research Articles

Model-dependent pharmacokinetic analysis of enalapril administered to healthy adult volunteers using orodispersible minitablets for use in pediatrics.

IntroductionComparative pharmacokinetic (PK) data analysis of drugs administered using developed child-appropriate and market authorized dosage formulation is sparse and is important in pediatric drug development.ObjectivesTo compare and evaluate any differences in PK of enalapril administered using two treatments of child-appropriate orodispersible minitablets (ODMTs) and market authorized reference tablet formulation (Renitec®) using PK compartment model and validated least square minimization method (LSMM) of parameter estimation.MethodsFull profile data sets were obtained from a phase I clinical trial, whereby three treatments of enalapril, ie, reference tablets with 240 mL water (treatment A), child-appropriate ODMTs with 240 mL (treatment B), and ODMTs dispersed in the mouth with 20 mL water (treatment C), were administered to 24 healthy adult volunteers. Virtual validation analysis was conducted using R program to select accurate and precise LSMM of parameter estimation. For the selection of PK model and estimation of parameters, enalapril data were fitted with one-and two-compartment models with first order of absorption and elimination, with and without incorporated lag time parameter (tlag). The log-transformed PK parameters were statistically compared by the two-sided paired t-test with the level of significance of P<0.05.ResultsOne-compartment model with first-order absorption and elimination and incorporated lag time adequately predicted concentrations of enalapril. Reciprocal of predicted concentration using iteratively reweighted LSMM was selected as the most appropriate method of parameter estimation. Comparison of PK parameters including rate constant of absorption and elimination, volume of distribution, and tlag between the three treatments showed significant difference (P=0.018) in tlag between treatments B and A only.ConclusionCompared with reference formulation, enalapril administered from child-appropriate ODMTs administered with 240 mL water appeared 4 minutes earlier in serum. No other differences were observed in absorption, elimination, and relative bioavailability of drug between the three treatment arms.

Complex Permittivity Measurement of Paraffin Phase-Change Material at 26 GHz–1.1 THz Using Time-Domain Spectroscopy

We report complex permittivity measurement of hexatriacontane films at the frequency range of 26 GHz–1.1 THz. Hexatriacontane (C36H74) has a melting point of 75 °C that exhibits a 15% volumetric change which is crucial in developing low-loss RF microactuators with large displacement. In this work, we employ time-domain spectroscopy to measure the transmission coefficient of the paraffin samples in the frequency range of 0.3–1.1 THz. In order to extract the dielectric constant and accurately estimate the small values of loss tangent, we developed a propagation model which measured data are fitted to through a new least-squares minimization method. A Debye relaxation model is used to model the frequency dependence of the permittivity. Described method is rapidly convergent with minimum amount of signal processing. This method can be used to determine the complex permittivity of the materials by devising an appropriate function for the frequency dependence of the complex permittivity. Transmission through 20 samples of paraffin with various thicknesses is measured and the average permittivity is found to be 2.25 with standard deviation of 0.028. The loss tangent is monotonically increasing with frequency and the maximum value is 6.32 × 10− 3 at 1.1 THz. Our study demonstrates that paraffin is a low-loss dielectric which makes it an attractive candidate for development of electro-thermo-mechanical actuators for sub-millimeter- and millimeter wave (mmW) variable capacitors, low-loss reconfigurable antennas, and phase shifters.

Non-invasive assessment of patient-specific aortic haemodynamics from four-dimensional flow MRI data.

We introduce a parameter estimation framework for automatically and robustly personalizing aortic haemodynamic computations from four-dimensional magnetic resonance imaging data. The framework is based on a reduced-order multiscale fluid-structure interaction blood flow model, and on two calibration procedures. First, Windkessel parameters of the outlet boundary conditions are personalized by solving a system of nonlinear equations. Second, the regional mechanical wall properties of the aorta are personalized by employing a nonlinear least-squares minimization method. The two calibration procedures are run sequentially and iteratively until both procedures have converged. The parameter estimation framework was successfully evaluated on 15 datasets from patients with aortic valve disease. On average, only 1.27 ± 0.96 and 7.07 ± 1.44 iterations were required to personalize the outlet boundary conditions and the regional mechanical wall properties, respectively. Overall, the computational model was in close agreement with the clinical measurements used as objectives (pressures, flow rates, cross-sectional areas), with a maximum error of less than 1%. Given its level of automation, robustness and the short execution time (6.2 ± 1.2 min on a standard hardware configuration), the framework is potentially well suited for a clinical setting.

Finite element model focused on stress distribution in the levator ani muscle during vaginal delivery

Introduction and hypothesisDuring vaginal delivery, the levator ani muscle (LAM) undergoes severe deformation. This stress can lead to stretch-related LAM injuries. The objective of this study was to develop a sophisticated MRI-based model to simulate changes in the LAM during vaginal delivery.MethodsA 3D finite element model of the female pelvic floor and fetal head was developed. The model geometry was based on MRI data from a nulliparous woman and 1-day-old neonate. Material parameters were estimated using uniaxial test data from the literature and by least-square minimization method. The boundary conditions reflected all anatomical constraints and supports. A simulation of vaginal delivery with regard to the cardinal movements of labor was then performed.ResultsThe mean stress values in the iliococcygeus portion of the LAM during fetal head extension were 4.91–7.93 MPa. The highest stress values were induced in the pubovisceral and puborectal LAM portions (mean 27.46 MPa) at the outset of fetal head extension. The last LAM subdivision engaged in the changes in stress was the posteromedial section of the puborectal muscle. The mean stress values were 16.89 MPa at the end of fetal head extension. The LAM was elongated by nearly 2.5 times from its initial resting position.ConclusionsThe cardinal movements of labor significantly affect the subsequent heterogeneous stress distribution in the LAM. The absolute stress values were highest in portions of the muscle that arise from the pubic bone. These areas are at the highest risk for muscle injuries with long-term complications.

The effect of roughness in simultaneously retrieval of land surface parameters

Using remotely-sensed data, various soil moisture estimation models have been developed for bare soil areas. Previous studies have shown that the brightness temperature (BT) measured by passive microwave sensors were affected by characteristics of the land surface parameters including soil moisture, vegetation cover and soil roughness. Therefore knowledge of vegetation cover and soil roughness is important for obtaining frequent and global estimations of land surface parameters especially soil moisture.In this study, a model called Simultaneous Land Parameters Retrieval Model (SLPRM) that is an iterative least-squares minimization method is proposed. The algorithm estimates surface soil moisture, land surface temperature and canopy temperature simultaneously in vegetated areas using AMSR-E (Advance Microwave Scanning Radiometer-EOS) brightness temperature data. The simultaneous estimations of the three parameters are based on a multi-parameter inversion algorithm which includes model construction, calibration and validation using observations carried out for the SMEX03 (Soil Moisture Experiment, 2003) region in the South and North of Oklahoma.Roughness parameter has also been included in the algorithm to increase the soil parameters retrieval accuracy. Unlike other methods, the SLPRM method works efficiently in all land covers types.The study focuses on soil parameters estimation by comparing three different scenarios with the inclusion of roughness data and selects the most appropriate one. The difference between the resulted accuracies of scenarios is due to the roughness calculation approach.The analysis on the retrieval model shows a meaningful and acceptable accuracy on soil moisture estimation according to the three scenarios.The SLPRM method has shown better performance when the SAR (Synthetic Aperture RADAR) data are used for roughness calculation.

Solutions to the Inverse LQR Problem with Application to Biological Systems Analysis.

In this paper, we present a set of techniques for finding a cost function to the time-invariant Linear Quadratic Regulator (LQR) problem in both continuous- and discrete-time cases. Our methodology is based on the solution to the inverse LQR problem, which can be stated as: does a given controller K describe the solution to a time-invariant LQR problem, and if so, what weights Q and R produce K as the optimal solution? Our motivation for investigating this problem is the analysis of motion goals in biological systems. We first describe an efficient Linear Matrix Inequality (LMI) method for determining a solution to the general case of this inverse LQR problem when both the weighting matrices Q and R are unknown. Our first LMI-based formulation provides a unique solution when it is feasible. Additionally, we propose a gradient-based, least-squares minimization method that can be applied to approximate a solution in cases when the LMIs are infeasible. This new method is very useful in practice since the estimated gain matrix K from the noisy experimental data could be perturbed by the estimation error, which may result in the infeasibility of the LMIs. We also provide an LMI minimization problem to find a good initial point for the minimization using the proposed gradient descent algorithm. We then provide a set of examples to illustrate how to apply our approaches to several different types of problems. An important result is the application of the technique to human subject posture control when seated on a moving robot. Results show that we can recover a cost function which may provide a useful insight on the human motor control goal.

Soft Tissue Artifact compensation using Triangular Cosserat Point Elements (TCPEs)

Existing methods which compensate for the Soft Tissue Artifact (STA) in optoelectronic motion measurements estimate the rigid motion of a nearly rigid underlying body segment based on analysis of the motion of all fiducial markers. The objective of the proposed Triangular Cosserat Point Elements (TCPE) method is to estimate the motion of the underlying body segment even when the STA in the entire cluster of markers can be large. This is accomplished by characterizing the cluster of markers with TCPEs defined by triangles based on all combinations of three markers. Then, scalar deformation measures characterizing the magnitudes of strain and relative rotation of pairs of TCPEs are defined for each TCPE. These deformation measures are used to define a filtered group of TCPEs which best represents the motion of the underlying body segment. The method was tested using an experimental setup that consists of a rigid pendulum with a deformable 300ml silicone breast implant attached to it as a simulation of the soft tissue around a bony segment. The rotation angles extracted from markers on the deformable implant were compared with simultaneous measurements of the rigid pendulum using an optoelectronic system. Analysis of the experimental data shows that this filtering process substantially reduces the error due to the STA even though the data set includes large deformations. In particular, the analysis shows that the error reduction using the TCPE approach is larger than the reductions obtained using standard least-squares minimization methods.

Quantitative MUC5AC and MUC6 mucin estimations in gastric mucus by a least-squares minimization method

We have determined the molar proportions of the MUC5AC and MUC6 mucus glycoproteins (mucins) in mucus from the normal and pathological human gastric antrum using a least-squares minimization analysis applied to amino acid compositions. We noted that the content of MUC5AC mucin in mucus from individuals without gastroduodenal disease was very high, suggesting that the integrity and barrier properties of the adherent gastric mucus layer are normally maintained by building-block structures formed from this mucin alone. We observed that the molar content of MUC6 mucin doubled (without significance) in mucus from patients with duodenal ulcer, and increased five times (with high significance) in mucus from patients with gastric ulcer, when compared with that in mucus from individuals without gastroduodenal disease.

Estimation of depth of buried conductive sphere from electromagnetic induction anomaly data using linearization process

In this paper, we have developed a least-squares minimization method to estimate the depth of a buried conducting sphere using electromagnetic induction (EMI) data. This approach is basically based on the solving a set of algebraic linear equations to estimate the depth of sphere embedded in an insulating media. In electromagnetic induction method, the transmitter coil produces the incident magnetic and electric fields that obey the Maxwell’s equations. In the receiver coil, the received response is created in two modes—eddy-current mode (Vec) derived from the perfectly conductor placed in the shallow depth and another mode called current-channeling response (Vcc) which depends on the conductivity of the medium. As expected, these responses differ depending on the direction of the incident field related to the receiver coil’s axis. In our case, the transmitter coil’s axis is parallel to the ground surface, and only the eddy-current response is measured in the receiver coil. The validity of this new method is demonstrated through studying and analyzing synthetic EMI anomalies, using simulated data generated from a known model with different random error components and a known statistical distribution.

EEG Inverse Problem Solution Using a Selection Procedure on a High Number of Electrodes With Minimal Influence of Conductivity

The uncertain conductivity value of skull and brain tissue influences the accuracy of the electroencephalogram (EEG) inverse problem solution. Indeed, when the assumed conductivity in the numerical procedure is different from the actual conductivity then a source localization error is introduced. When using traditional least-squares minimization methods, the number of electrodes in the EEG cap does not influence the spatial resolution. A recently developed reduced conductivity dependence (RCD) methodology, based on the selection of electrodes, is able to increase the spatial resolution of the EEG inverse problem. This paper presents the implications of the RCD method when using a large number of electrodes in the EEG cap on the spatial resolution of the EEG inverse solutions. We show by means of numerical experiments that in contrast to traditional methods, the RCD method enables to increase the spatial resolution. The computations show that the EEG hardware should be modified with as large as possible electrodes.

Geometry Optimization with Multilayer Methods Using Least-Squares Minimization.

In this article, we introduce a least-squares minimization scheme for optimizing molecular structures with mixed quantum mechanics (QM) and molecular mechanics (MM) multilayer models. A mixed-coordinate optimization framework was developed. The QM and MM regions are modeled with redundant internal coordinates and Cartesian coordinates, respectively. Within this mixed-coordinate system, a least-squares minimization method using the quasi-Newton step as the evaluation of error is constructed. The couplings between layers are treated rigidly in accordance with the mechanical embedding approach, and the MM Hessian is approximated as a scalar constant of the root-mean-square QM Hessian eigenvalues. Both two-layer and three-layer models were tested. The performance of the method developed herein shows consistently stable and fast convergence.

Implementation of a computationally efficient least‐squares algorithm for highly under‐determined three‐dimensional diffuse optical tomography problems

Three-dimensional (3D) diffuse optical tomography is known to be a nonlinear, ill-posed and sometimes under-determined problem, where regularization is added to the minimization to allow convergence to a unique solution. In this work, a generalized least-squares (GLS) minimization method was implemented, which employs weight matrices for both data-model misfit and optical properties to include their variances and covariances, using a computationally efficient scheme. This allows inversion of a matrix that is of a dimension dictated by the number of measurements, instead of by the number of imaging parameters. This increases the computation speed up to four times per iteration in most of the under-determined 3D imaging problems. An analytic derivation, using the Sherman-Morrison-Woodbury identity, is shown for this efficient alternative form and it is proven to be equivalent, not only analytically, but also numerically. Equivalent alternative forms for other minimization methods, like Levenberg-Marquardt (LM) and Tikhonov, are also derived. Three-dimensional reconstruction results indicate that the poor recovery of quantitatively accurate values in 3D optical images can also be a characteristic of the reconstruction algorithm, along with the target size. Interestingly, usage of GLS reconstruction methods reduces error in the periphery of the image, as expected, and improves by 20% the ability to quantify local interior regions in terms of the recovered optical contrast, as compared to LM methods. Characterization of detector photo-multiplier tubes noise has enabled the use of the GLS method for reconstructing experimental data and showed a promise for better quantification of target in 3D optical imaging. Use of these new alternative forms becomes effective when the ratio of the number of imaging property parameters exceeds the number of measurements by a factor greater than 2.

Acid–base properties of humic substances from composted and thermally-dried sewage sludges and amended soils as determined by potentiometric titration and the NICA-Donnan model

The acid–base properties of humic acids (HAs) and fulvic acids (FAs) isolated from composted sewage sludge (CS), thermally-dried sewage sludge (TS), soils amended with either CS or TS at a rate of 80 t ha −1 y −1 for 3 y and the corresponding unamended soil were investigated by use of potentiometric titrations. The non-ideal competitive adsorption (NICA)-Donnan model for a bimodal distribution of proton binding sites was fitted to titration data by use of a least-squares minimization method. The main fitting parameters of the NICA-Donnan model obtained for each HA and FA sample included site densities, median affinity constants and widths of affinity distributions for proton binding to low and high affinity sites, which were assumed to be, respectively, carboxylic- and phenolic-type groups. With respect to unamended soil HA and FA, the HAs and FAs from CS, and especially TS, were characterized by smaller acidic functional group contents, larger proton binding affinities of both carboxylic- and phenolic-type groups, and smaller heterogeneity of carboxylic and phenolic-type groups. Amendment with CS or TS led to a decrease of acidic functional group contents and a slight increase of proton binding affinities of carboxylic- and phenolic-type groups of soil HAs and FAs. These effects were more evident in the HA and FA fractions from CS-amended soil than in those from TS-amended soil.

Optimizing the incoherent pump spectrum of low-gain-ripple distributed fiber Raman amplifier for a given main pump wavelength

The method for designing the incoherent pump spectrum for the distributed fiber Raman amplifiers (DFRAs) of low gain ripple is studied, in which the wavelength of the maximum power spectral density can be assigned. The assigned wavelength is called the main pump wavelength. Incoherent pump spectrum is described with the power spectral density function (PSDF) that comprises a set of piece-wise continuous functions. PSDF is optimized for the minimum gain ripple with the least-square minimization method. An extremum pump wavelength condition is applied to PSDF. A proper initial trial PSDF is given so that the optimized PSDF converges to the desired result and the power spectral density at the extremum pump wavelength is the maximum. With this design method, we show the optimized PSDFs for the DFRAs using backward pumping and bidirectional pumping. The gain ripples of considered DFRAs are less than 0.1 dB for 20-dB ON-OFF Raman gain over 70-nm bandwidth. The reduction of average effective noise figure with shorter main pump wavelength is shown and investigated.

An inverse problem for the recovery of active faults from surface observations

We discuss in this paper the possibility of detecting slow slip events (such as silent earthquakes, or earthquake nucleation phases) in the vicinity of geological faults, and the possible localization of those faults from GPS observations. An eigenvalue problem (of Steklov type), modelling the slow evolution of the slip, is stated as a direct problem. The recovery of an active fault from surface observations is formulated as the related inverse problem.We use an asymptotic formula for the observed surface displacement to infer two inversion techniques for the recovery of faults from surface observations. The first one involves a least-square minimization method; the second one uses the momentum method. The recovered information contains only the depth of the fault, its horizontal position and the ‘normalized seismic moment’, which is related to the fault shape. We test the two inversion methods for line segment faults in numerical simulations. We are led to conclude that the momentum method gives a very good initial guess for the least-square minimization method, which turns out to be sharp, robust and computationally inexpensive. Unexpectedly, the latter method is also very efficient for faults that are close to the observation surface, despite the fact that our asymptotic approximation may not be valid in that region. Finally we assess how our method for detecting active faults is affected by the sensitivity of the observation apparatus and the stepsize for the grid of surface observation points. The maximum permissible stepsize for such a grid is computed for different values of fault depth and orientation.

Weighted least-squares phase unwrapping algorithm based on derivative variance correlation map

Among different phase unwrapping approaches, the weighted least-squares minimization methods are gaining attention. In these algorithms, weighting coefficient is generated from a quality map. The intrinsic drawbacks of existing quality maps constrain the application of these algorithms. They often fail to handle wrapped phase data contains error sources, such as phase discontinuities, noise and undersampling. In order to deal with those intractable wrapped phase data, a new weighted least-squares phase unwrapping algorithm based on derivative variance correlation map is proposed. In the algorithm, derivative variance correlation map, a novel quality map, can truly reflect wrapped phase quality, ensuring a more reliable unwrapped result. The definition of the derivative variance correlation map and the principle of the proposed algorithm are present in detail. The performance of the new algorithm has been tested by use of a simulated spherical surface wrapped data and an experimental interferometric synthetic aperture radar (IFSAR) wrapped data. Computer simulation and experimental results have verified that the proposed algorithm can work effectively even when a wrapped phase map contains intractable error sources.

Design of the pump power spectrum for the distributed fiber Raman amplifiers using incoherent pumping

The method to design the incoherent pump power spectrum described with a set of piece-wise continuous functions (PWCFs) for the distributed fiber Raman amplifier (DFRA) is presented. The pump power spectrum is divided into a number of sub-bands, in which each sub-band is described with a polynomial. The power spectral density function (PSDF) is the absolute value of the set of PWCFs, in which the polynomial coefficients are optimized with the least-square minimization method for reducing the signal gain ripple. Two 100-km TW-Reach DFRAs using backward pumping and bidirectional pumping respectively are taken as examples. The numerical results show that the gain ripple of less than 0.02 dB over 70-nm bandwidth can be achieved. The spectral characteristics of the optimized PSDF for the ultra-low gain ripple are investigated. The optimized PSDF can be synthesized with multiple incoherent pumps. The synthesis examples using the multiple Gaussian incoherent pumps are shown, in which the gain ripples are increased to 0.3 dB due to the discrepancy between the optimized PSDF and the synthesized PSDF. The gain ripples can be reduced to 0.05 dB by further optimizing the parameters of the multiple Gaussian incoherent pumps.

Soil moisture estimates from TRMM Microwave Imager observations over the Southern United States

The lack of continuous soil moisture fields at large spatial scales, based on observations, has hampered hydrologists from understanding its role in weather and climate. The most readily available observations from which a surface wetness state could be derived is the Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI) observations at 10.65 GHz. This paper describes the first attempt to map daily soil moisture from space over an extended period of time. Methods to adjust for diurnal changes associated with this temporal variability and how to mosaic these orbits are presented. The algorithm for deriving soil moisture and temperature from TMI observations is based on a physical model of microwave emission from a layered soil–vegetation–atmosphere medium. An iterative, least-squares minimization method, which uses dual polarization observations at 10.65 GHz, is employed in the retrieval algorithm. Soil moisture estimates were compared with ground measurements over the U.S. Southern Great Plains (SGP) in Oklahoma and the Little River Watershed, Georgia. The soil moisture experiment in Oklahoma was conducted in July 1999 and Little River in June 2000. During both the experiments, the region was dry at the onset of the experiment, and experienced moderate rainfall during the course of the experiment. The regions experienced a quick dry-down before the end of the experiment. The estimated soil moisture compared well with the ground observations for these experiments (standard error of 2.5%). The TMI-estimated soil moisture during 6–22 July over Southern U.S. was analyzed and found to be consistent with the observed meteorological conditions.

Defining Triangular Probability Distributions from Historical Cost Data

During the development of an automated cost estimating system, several factors led to the selection of the triangular probability-density function to model historical construction costs. The triangular-density function is customarily used when function parameters are directly estimated by experts. A typical example is for estimating activity durations by identifying a minimum value, a most likely value, and a maximum value. These values are then used to construct triangular-density functions to represent uncertain activity durations. For this work, however, it was necessary to estimate parameters of the triangular-density function using historical cost data. A methodology was developed to generate test data and compare three methods of parameter estimation—maximum likelihood, moment matching, and least-squares curve-fitting techniques. It is concluded that optimized moment matching and least-squares techniques produce more accurate parameter estimates, while maximum likelihood estimation yields less accurate results. It is further concluded that the least-squares minimization method always performed as well as or better than the optimized moment matching technique and was therefore selected as the method of choice for the project.

Shape and depth solutions from moving average residual gravity anomalies

The least-squares minimization method can be used to determine the depth of a buried structure from moving average residual gravity anomalies separated from observed data using regionals of successive windows (Abdelrahman and El-Araby, 1993a). In the present study, we show that this method can be applied not only to extract depth, but also to simultaneously define the shape of the buried structure. For a fixed window length, the depth is determined for each shape factor. The computed depths are plotted against the shape factor representing a continuous window curve. The solution for the shape and depth of the buried structure is read at the common intersection of window curves. The method is tested on two theoretical examples and a field example from the United states.