Perturbation Monte Carlo Method Research Articles

Cable Angle and Minimum Resultant Force Response Analysis of Lower Limb Traction Device for Rehabilitation Robot With Interval Parameters

Abstract This paper proposes a hybrid uncertainty analysis method (HUAM) based on the first-order interval perturbation method (FIPM) and Monte Carlo method (MCM) for minimum resultant force response analysis of the lower limb traction device (LLTD) of a hybrid-driven parallel waist rehabilitation robot (HDPWRR) with interval parameters. Based on the analysis of cable angles by using the interval algorithm, the problem of non-uniqueness of the force solution in redundant constraint mechanisms is solved. The force response domain prediction with interval parameters on rehabilitation patients is estimated by using the HUAM which combining the first-order interval perturbation technique with direct Monte Carlo method in different stages, and it reduces the calculation amount. First, the kinematic and static models of the LLTD with deterministic information are established according to its work principle. Then, the interval matrices with interval parameters are calculated by using the FIPM and the response of cable angles is combined with the static model. Third, by numerical examples, the accuracy and efficiency of the HUAM for solving the force response domain problem with interval parameters are verified. The bounds of cable angle response domain of the interval LLTD model are determined. Finally, the minimum resultant force response domain prediction with interval parameters on rehabilitation patients is estimated by combining the FIPM and MCM.

Perturbation Monte Carlo Method for Quantitative Photoacoustic Tomography.

Quantitative photoacoustic tomography aims at estimating optical parameters from photoacoustic images that are formed utilizing the photoacoustic effect caused by the absorption of an externally introduced light pulse. This optical parameter estimation is an ill-posed inverse problem, and thus it is sensitive to measurement and modeling errors. In this work, we propose a novel way to solve the inverse problem of quantitative photoacoustic tomography based on the perturbation Monte Carlo method. Monte Carlo method for light propagation is a stochastic approach for simulating photon trajectories in a medium with scattering particles. It is widely accepted as an accurate method to simulate light propagation in tissues. Furthermore, it is numerically robust and easy to implement. Perturbation Monte Carlo maintains this robustness and enables forming gradients for the solution of the inverse problem. We validate the method and apply it in the framework of Bayesian inverse problems. The simulations show that the perturbation Monte Carlo method can be used to estimate spatial distributions of both absorption and scattering parameters simultaneously. These estimates are qualitatively good and quantitatively accurate also in parameter scales that are realistic for biological tissues.

Development of perturbation Monte Carlo methods for polarized light transport in a discrete particle scattering model

We present a polarization-sensitive, transport-rigorous perturbation Monte Carlo (pMC) method to model the impact of optical property changes on reflectance measurements within a discrete particle scattering model. The model consists of three log-normally distributed populations of Mie scatterers that approximate biologically relevant cervical tissue properties. Our method provides reflectance estimates for perturbations across wavelength and/or scattering model parameters. We test our pMC model performance by perturbing across number densities and mean particle radii, and compare pMC reflectance estimates with those obtained from conventional Monte Carlo simulations. These tests allow us to explore different factors that control pMC performance and to evaluate the gains in computational efficiency that our pMC method provides.

Fast Perturbation Monte Carlo simulation for heterogeneous medium and its utilization in functional near-infrared spectroscopy

In near-infrared spectroscopy, fiber optic probe is usually applied to incident light into the bio-sample and detect the spatial and temporal resolved optical signal re-emitted from the turbid medium. In this point-source-point-detector measurement system, seed Perturbation Monte Carlo (Pmc) method is an effective model to perform the forward simulation. In our study, the integration of parallel computing with graphics processing units(GPU) into the existing seed Pmc method substantially accelerate the speed of the original simulation. The GPU based seed Pmc provide an excellent solution for the application of fiber optic probe in both homogeneous a heterogeneous turbid medium.

Perturbation Monte Carlo methods for tissue structure alterations

This paper describes an extension of the perturbation Monte Carlo method to model light transport when the phase function is arbitrarily perturbed. Current perturbation Monte Carlo methods allow perturbation of both the scattering and absorption coefficients, however, the phase function can not be varied. The more complex method we develop and test here is not limited in this way. We derive a rigorous perturbation Monte Carlo extension that can be applied to a large family of important biomedical light transport problems and demonstrate its greater computational efficiency compared with using conventional Monte Carlo simulations to produce forward transport problem solutions. The gains of the perturbation method occur because only a single baseline Monte Carlo simulation is needed to obtain forward solutions to other closely related problems whose input is described by perturbing one or more parameters from the input of the baseline problem. The new perturbation Monte Carlo methods are tested using tissue light scattering parameters relevant to epithelia where many tumors originate. The tissue model has parameters for the number density and average size of three classes of scatterers; whole nuclei, organelles such as lysosomes and mitochondria, and small particles such as ribosomes or large protein complexes. When these parameters or the wavelength is varied the scattering coefficient and the phase function vary. Perturbation calculations give accurate results over variations of ∼15-25% of the scattering parameters.

Probabilistic Interval Perturbation Methods for Hybrid Uncertain Acoustic Field Prediction

For the hybrid uncertain acoustic field prediction with random and interval variables, the random interval dynamic equilibrium equation is established and two hybrid probabilistic interval perturbation methods, named as hybrid perturbation Monte Carlo method (HPMCM) and hybrid perturbation vertex method (HPVM), are present. In HPMCM, the intervals of expectation and variance of sound pressure are calculated by a combination of the random interval matrix perturbation method, the random interval moment method and Monte Carlo method. In HPVM, the intervals of expectation and variance of sound pressure are calculated by a combination of the random interval matrix perturbation method, the random interval moment method and the vertex method. Numerical results on a 2D acoustic tube, the 2D acoustic cavity of a car and a 3D acoustic cavity verify the effectiveness and the high efficiency of HPVM when compared with HPMCM. HPVM can be considered as an effective engineering method to quantify the effects of parametric uncertainty on the sound pressure response.

Hybrid uncertain analysis for structural–acoustic problem with random and interval parameters

In this paper, hybrid perturbation Monte–Carlo method (HPMCM) and hybrid perturbation vertex method (HPVM) are developed for the hybrid uncertain structural–acoustic problem with random and interval variables. The random variables are used to treat the uncertain parameters with sufficient information; whereas, the interval variables are used to treat the uncertain parameters with limited information. In HPMCM, the intervals of expectation and variance of the frequency response vector are calculated by a combination of random interval matrix perturbation method, random interval moment method and Monte–Carlo method. In HPVM, a monotonicity analysis is conducted for the frequency response vector based on the random interval matrix perturbation method; and then the intervals of expectation and variance of the frequency response vector are calculated by employing the random interval moment method and the vertex method. Numerical results on a shell structural–acoustic problem verify the effectiveness and high efficiency of HPVM compared with HPMCM.

Hybrid method for fast Monte Carlo simulation of diffuse reflectance from a multilayered tissue model with tumor-like heterogeneities

We present a hybrid method that combines a multilayered scaling method and a perturbation method to speed up the Monte Carlo simulation of diffuse reflectance from a multilayered tissue model with finite-size tumor-like heterogeneities. The proposed method consists of two steps. In the first step, a set of photon trajectory information generated from a baseline Monte Carlo simulation is utilized to scale the exit weight and exit distance of survival photons for the multilayered tissue model. In the second step, another set of photon trajectory information, including the locations of all collision events from the baseline simulation and the scaling result obtained from the first step, is employed by the perturbation Monte Carlo method to estimate diffuse reflectance from the multilayered tissue model with tumor-like heterogeneities. Our method is demonstrated to shorten simulation time by several orders of magnitude. Moreover, this hybrid method works for a larger range of probe configurations and tumor models than the scaling method or the perturbation method alone.

Comparison of Monte Carlo methods for fluorescence molecular tomography-computational efficiency

The Monte Carlo method is an accurate model for time-resolved quantitative fluorescence tomography. However, this method suffers from low computational efficiency due to the large number of photons required for reliable statistics. This paper presents a comparison study on the computational efficiency of three Monte Carlo-based methods for time-domain fluorescence molecular tomography. The methods investigated to generate time-gated Jacobians were the perturbation Monte Carlo (pMC) method, the adjoint Monte Carlo (aMC) method and the mid-way Monte Carlo (mMC) method. The effects of the different parameters that affect the computation time and statistics reliability were evaluated. Also, the methods were applied to a set of experimental data for tomographic application. In silico results establish that, the investigated parameters affect the computational time for the three methods differently (linearly, quadratically, or not significantly). Moreover, the noise level of the Jacobian varies when these parameters change. The experimental results in preclinical settings demonstrates the feasibility of using both aMC and pMC methods for time-resolved whole body studies in small animals within a few hours. Among the three Monte Carlo methods, the mMC method is a computationally prohibitive technique that is not well suited for time-domain fluorescence tomography applications. The pMC method is advantageous over the aMC method when the early gates are employed and large number of detectors is present. Alternatively, the aMC method is the method of choice when a small number of source-detector pairs are used.

Fast perturbation Monte Carlo method for photon migration in heterogeneous turbid media

We present a two-step Monte Carlo (MC) method that is used to solve the radiative transfer equation in heterogeneous turbid media. The method exploits the one-to-one correspondence between the seed value of a random number generator and the sequence of random numbers. In the first step, a full MC simulation is run for the initial distribution of the optical properties and the "good" seeds (the ones leading to detected photons) are stored in an array. In the second step, we run a new MC simulation with only the good seeds stored in the first step, i.e., we propagate only detected photons. The effect of a change in the optical properties is calculated in a short time by using two scaling relationships. By this method we can increase the speed of a simulation up to a factor of 1300 in typical situations found in near-IR tissue spectroscopy and diffuse optical tomography, with a minimal requirement for hard disk space. Potential applications of this method for imaging of turbid media and the inverse problem are discussed.

Hybrid probabilistic interval analysis of bar structures with uncertainty using a mixed perturbation Monte-Carlo method

This paper presents a mixed perturbation Monte-Carlo method for static and reliability analysis of structural systems with a mixture of random and interval parameters/loadings. Using a combination of the Taylor expansion, matrix perturbation theory and random interval moment method, the expressions for the mean value and standard deviation of random interval structural responses are developed. The Monte-Carlo simulation method is employed to determine the lower and upper bounds of the mean values and standard deviations of structural displacements and stresses. The structural reliability is not a deterministic value but an interval as the structural stress responses are random interval variables. The lower and upper bounds of probability of failure and reliability of structural elements and systems are investigated based on the first-order second-moment reliability method and interval approach. Three numerical examples are used to illustrate the effectiveness of the proposed method.

Experimental investigation of perturbation Monte-Carlo based derivative estimation for imaging low-scattering tissue

Experimental results for imaging the low-scattering tissue phantoms based on the derivative estimation through perturbation Monte-Carlo (pMC) method are presented. It is proven that pMC-based methods give superior reconstructions compared to diffusion-based reconstruction methods. An easy way to estimate the Jacobian using analytical expression obtained from perturbation Monte-Carlo method is employed. Simulation studies on the same objects, considered in the experiment, are performed and corresponding results are found to be in reasonable agreement with the experimental studies. It is shown that inter-parameter cross talk in diffusion based methods lead to false results for the low-scattering tissue, where as the pMC-based method gives accurate results.

Perturbation Monte Carlo methods to solve inverse photon migration problems in heterogeneous tissues

We introduce a novel and efficient method to provide solutions to inverse photon migration problems in heterogeneous turbid media. The method extracts derivative information from a single Monte Carlo simulation to permit the rapid determination of rates of change in the detected photon signal with respect to perturbations in background tissue optical properties. We then feed this derivative information to a nonlinear optimization algorithm to determine the optical properties of the tissue heterogeneity under examination. We demonstrate the use of this approach to solve rapidly a two-region inverse problem of photon migration in the transport regime, for which diffusion-approximation-based approaches are not applicable.