A theoretical study of the multigrid three-dimensional variational data assimilation scheme using a simple bilinear interpolation algorithm

In order to solve the so-called ＂bull-eye＂ problem caused by using a simple bilinear interpolation as an observational mapping operator in the cost function in the multigrid three-dimensional variational （3DVAR） data assimilation scheme, a smoothing term, equivalent to a penalty term, is introduced into the cost function to serve as a means of troubleshooting. A theoretical analysis is first performed to figure out what on earth results in the issue of ＂bull-eye＂, and then the meaning of such smoothing term is elucidated and the uniqueness of solution of the multigrid 3DVAR with the smoothing term added is discussed through the theoretical deduction for one-dimensional （1D） case, and two idealized data assimilation experiments （one- and two-dimensional （2D） cases）. By exploring the relationship between the smoothing term and the recursive filter theoretically and practically, it is revealed why satisfied analysis results can be achieved by using such proposed solution for the issue of the multigrid 3DVAR.

Application of a Recursive Filter to a Three-Dimensional Variational Ocean Data Assimilation System

In order to improve the efficiency of the Ocean Variational Assimilation System （OVALS）, which has been widely used in various applications, an improved OVALS （OVALS2） is developed based on the recursive filter （RF） algorithm. The first advantage of OVALS2 is that memory storage can be substantially reduced in practice because it implicitly computes the background error covariance matrix; the second advantage is that there is no inversion of the background error covariance by preconditioning the control variable. For comparing the effectiveness between OVALS2 and OVALS, a set of experiments was implemented by assimilating expendable bathythermograph （XBT） and ARGO data into the Tropical Pacific circulation model. The results show that the efficiency of OVALS2 is much higher than that of OVALS. The computational time and the computer storage in the assimilation process were reduced by 83% and 77%, respectively. Additionally, the corresponding results produced by the RF are almost as good as those obtained by OVALS. These results prove that OVALS2 is suitable for operational numerical oceanic forecasting.

Three-dimensional limit variation analysis on the ultimate pullout capacity of the anchor cables based on the Hoek-Brown failure criterion

Only simplified two-dimensional model and a single failure mode are adopted to calculate the ultimate pullout capacity(UPC)of anchor cables in most previous research.This study focuses on a more comprehensive combination failure mode that consists of bond failure of an anchorage body and failure of an anchored rock mass.The three-dimensional ultimate pullout capacity of the anchor cables is calculated based on the Hoek-Brown failure criterion and variation analysis method.The numerical solution for the curvilinear function in fracture plane is obtained based on the finite difference theory,which more accurately reflects the failure state of the anchor cable,as opposed to that being assumed in advance.The results reveal that relying solely on a single failure mode for UPC calculations has limitations,as changes in parameter values not only directly impact the UPC value but also can alter the failure model and thus the calculation method.

Construction and application of a three-dimensional vascular variation-based nephrometry scoring system for completely endophytic renal tumors

Background:Completely endophytic renal tumors(CERT)pose significant challenges due to their anatomical complexity and loss of visual clues about tumor location.A facile scoring model based on three-dimensional(3D)reconstructed images will assist in better assessing tumor location and vascular variations.Methods:In this retrospective study,80 patients diagnosed with CERT were included.Forty cases underwent preoperative assessment using 3D reconstructed imaging(3D-Cohort),while the remaining 40 cases were assessed using two-dimensional imaging(2D-Cohort).Vascular variations were evaluated by ascertaining the presence of renal arteries>1,prehilar branching arteries,and arteries anterior to veins.The proposed scoring system,termed RAL,encompassed three critical components:(R)adius(maximal tumor diameter in cm),(A)rtery(occurrence of arterial variations),and(L)ocation relative to the polar line.Comparison of the RAL scoring system was made with established nephrometry scoring systems.Results:A total of 48(60%)patients exhibited at least one vascular variation.In the 2D-Cohort,patients with vascular variations experienced significantly prolonged operation time,increased bleeding volume,and extended warm ischemia time compared with those without vascular variations.Conversely,the presence of vascular vari-ations did not significantly affect operative parameters in the 3D-Cohort.Furthermore,the 2D-Cohort demon-strated a notable decline in both short-and long-term estimated glomerular filtration rate(eGFR)changes com-pared with the 3D-Cohort,a trend consistent across patients with warm ischemia time≥25 min and those with vascular variations.Notably,the 2D-Cohort exhibited a larger margin of normal renal tissue compared with the 3D-Cohort.Elevated RAL scores correlated with larger tumor size,prolonged operation time,extended warm is-chemia time,and substantial postoperative eGFR decrease.The RAL scoring system displayed superior predictive capabilities in assessing postoperative eGFR changes compared with conventional nephrometry scoring systems.Conclusions:Our proposed 3D vascular variation-based nephrometry scoring system offers heightened proficiency in preoperative assessment,precise prediction of surgical complexity,and more accurate evaluation of postoper-ative renal function in CERT patients.

A Dimension-Splitting Variational Multiscale Element-Free Galerkin Method for Three-Dimensional Singularly Perturbed Convection-Diffusion Problems

By introducing the dimensional splitting(DS)method into the multiscale interpolating element-free Galerkin(VMIEFG)method,a dimension-splitting multiscale interpolating element-free Galerkin(DS-VMIEFG)method is proposed for three-dimensional(3D)singular perturbed convection-diffusion(SPCD)problems.In the DSVMIEFG method,the 3D problem is decomposed into a series of 2D problems by the DS method,and the discrete equations on the 2D splitting surface are obtained by the VMIEFG method.The improved interpolation-type moving least squares(IIMLS)method is used to construct shape functions in the weak form and to combine 2D discrete equations into a global system of discrete equations for the three-dimensional SPCD problems.The solved numerical example verifies the effectiveness of the method in this paper for the 3D SPCD problems.The numerical solution will gradually converge to the analytical solution with the increase in the number of nodes.For extremely small singular diffusion coefficients,the numerical solution will avoid numerical oscillation and has high computational stability.

Assimilation of Total Lightning Data Using the Three-Dimensional Variational Method at Convection-Allowing Resolution

A large number of observational analyses have shown that lightning data can be used to indicate areas of deep convection. It is important to assimilate observed lightning data into numerical models, so that more small-scale information can be incorporated to improve the quality of the initial condition and the subsequent forecasts. In this study, the empirical relationship between flash rate, water vapor mixing ratio, and graupel mixing ratio was used to adjust the model relative humidity, which was then assimilated by using the three-dimensional variational data assimilation system of the Weather Research and Forecasting model in cycling mode at 10-min intervals. To find the appropriate assimilation time-window length that yielded significant improvement in both the initial conditions and subsequent forecasts, four experiments with different assimilation time-window lengths were conducted for a squall line case that occurred on 10 July 2007 in North China. It was found that 60 min was the appropriate assimilation time-window length for this case, and longer assimilation window length was unnecessary since no further improvement was present. Forecasts of 1-h accumulated precipitation during the assimilation period and the subsequent 3-h accumulated precipitation were significantly improved compared with the control experiment without lightning data assimilation. The simulated reflectivity was optimal after 30 min of the forecast, it remained optimal during the following 42 min, and the positive effect from lightning data assimilation began to diminish after 72 min of the forecast. Overall,the improvement from lightning data assimilation can be maintained for about 3 h.

A theory for three-dimensional response of micropolar plates

Through combined applications of the transfer-matrix method and asymptotic expansion technique,we formulate a theory to predict the three-dimensional response of micropolar plates.No ad hoc assumptions regarding through-thickness assumptions of the field variables are made,and the governing equations are two-dimensional,with the displacements and microrotations of the mid-plane as the unknowns.Once the deformation of the mid-plane is solved,a three-dimensional micropolar elastic field within the plate is generated,which is exact up to the second order except in the boundary region close to the plate edge.As an illustrative example,the bending of a clamped infinitely long plate caused by a uniformly distributed transverse force is analyzed and discussed in detail.

Oxygen tension modulates cell function in an in vitro three-dimensional glioblastoma tumor model

Hypoxia is a typical feature of the tumor microenvironment,one of the most critical factors affecting cell behavior and tumor progression.However,the lack of tumor models able to precisely emulate natural brain tumor tissue has impeded the study of the effects of hypoxia on the progression and growth of tumor cells.This study reports a three-dimensional(3D)brain tumor model obtained by encapsulating U87MG(U87)cells in a hydrogel containing type I collagen.It also documents the effect of various oxygen concentrations(1%,7%,and 21%)in the culture environment on U87 cell morphology,proliferation,viability,cell cycle,apoptosis rate,and migration.Finally,it compares two-dimensional(2D)and 3D cultures.For comparison purposes,cells cultured in flat culture dishes were used as the control(2D model).Cells cultured in the 3D model proliferated more slowly but had a higher apoptosis rate and proportion of cells in the resting phase(G0 phase)/gap I phase(G1 phase)than those cultured in the 2D model.Besides,the two models yielded significantly different cell morphologies.Finally,hypoxia(e.g.,1%O2)affected cell morphology,slowed cell growth,reduced cell viability,and increased the apoptosis rate in the 3D model.These results indicate that the constructed 3D model is effective for investigating the effects of biological and chemical factors on cell morphology and function,and can be more representative of the tumor microenvironment than 2D culture systems.The developed 3D glioblastoma tumor model is equally applicable to other studies in pharmacology and pathology.

Three-dimensional cell-based strategies for liver regeneration

Liver regeneration and the development of effective therapies for liver failure remain formidable challenges in modern medicine.In recent years,the utilization of 3D cell-based strategies has emerged as a promising approach for addressing these urgent clinical requirements.This review provides a thorough analysis of the application of 3D cell-based approaches to liver regeneration and their potential impact on patients with end-stage liver failure.Here,we discuss various 3D culture models that incorporate hepatocytes and stem cells to restore liver function and ameliorate the consequences of liver failure.Furthermore,we explored the challenges in transitioning these innovative strategies from preclinical studies to clinical applications.The collective insights presented herein highlight the significance of 3D cell-based strategies as a transformative paradigm for liver regeneration and improved patient care.

The combined application of stem cells and three-dimensional bioprinting scaffolds for the repair of spinal cord injury

Spinal cord injury is considered one of the most difficult injuries to repair and has one of the worst prognoses for injuries to the nervous system.Following surgery,the poor regenerative capacity of nerve cells and the generation of new scars can make it very difficult for the impaired nervous system to restore its neural functionality.Traditional treatments can only alleviate secondary injuries but cannot fundamentally repair the spinal cord.Consequently,there is a critical need to develop new treatments to promote functional repair after spinal cord injury.Over recent years,there have been seve ral developments in the use of stem cell therapy for the treatment of spinal cord injury.Alongside significant developments in the field of tissue engineering,three-dimensional bioprinting technology has become a hot research topic due to its ability to accurately print complex structures.This led to the loading of three-dimensional bioprinting scaffolds which provided precise cell localization.These three-dimensional bioprinting scaffolds co uld repair damaged neural circuits and had the potential to repair the damaged spinal cord.In this review,we discuss the mechanisms underlying simple stem cell therapy,the application of different types of stem cells for the treatment of spinal cord injury,and the different manufa cturing methods for three-dimensional bioprinting scaffolds.In particular,we focus on the development of three-dimensional bioprinting scaffolds for the treatment of spinal cord injury.

Three-Dimensional Sound Source Location Algorithm for Subsea Leakage Using Hydrophone

Leakages from subsea oil and gas equipment cause substantial economic losses and damage to marine ecosystem,so it is essential to locate the source of the leak.However,due to the complexity and variability of the marine environment,the signals collected by hydrophone contain a variety of noises,which makes it challenging to extract useful signals for localization.To solve this problem,a hydrophone denoising algorithm is proposed based on variational modal decomposition(VMD)with grey wolf optimization.First,the average envelope entropy is used as the fitness function of the grey wolf optimizer to find the optimal solution for the parameters K andα.Afterward,the VMD algorithm decomposes the original signal parameters to obtain the intrinsic mode functions(IMFs).Subsequently,the number of interrelationships between each IMF and the original signal was calculated,the threshold value was set,and the noise signal was removed to calculate the time difference using the valid signal obtained by reconstruction.Finally,the arrival time difference is used to locate the origin of the leak.The localization accuracy of the method in finding leaks is investigated experimentally by constructing a simulated leak test rig,and the effectiveness and feasibility of the method are verified.

Variational Reconstruction and Simulation Experiments of Sea Surface Wind Field for Ocean Data Buoy

The sea surface wind field is an important physical parameter in oceanography and meteorology.With the continuous refinement of numerical weather prediction,air-sea interface materials,energy exchange,and other studies,three-dimensional(3D)wind field distribution at local locations on the sea surface must be measured accurately.The current in-situ observation of sea surface wind parameters is mainly achieved through the installation of wind sensors on ocean data buoys.However,the results obtained from this single-point measurement method cannot reflect wind field distribution in a vertical direction above the sea surface.Thus,the present paper proposes a theoretical framework for the optimal inversion of the 3D wind field structure variation in the area where the buoy is located.The variation analysis method is first used to reconstruct the wind field distribution at different heights of the buoy,after which theoretical analysis verification and numerical simulation experiments are conducted.The results indicate that the use of variational methods to reconstruct 3D wind fields is significantly effective in eliminating disturbance errors in observations,which also verifies the correctness of the theoretical analysis of this method.The findings of this article can provide a reference for the layout optimization design of wind measuring instruments in buoy observation systems and also provide theoretical guidance for the design of new observation buoys in the future.

A new two-step variational model for multiplicative noise removal with applications to texture images

Multiplicative noise removal problems have attracted much attention in recent years.Unlike additive noise,multiplicative noise destroys almost all information of the original image,especially for texture images.Motivated by the TV-Stokes model,we propose a new two-step variational model to denoise the texture images corrupted by multiplicative noise with a good geometry explanation in this paper.In the first step,we convert the multiplicative denoising problem into an additive one by the logarithm transform and propagate the isophote directions in the tangential field smoothing.Once the isophote directions are constructed,an image is restored to fit the constructed directions in the second step.The existence and uniqueness of the solution to the variational problems are proved.In these two steps,we use the gradient descent method and construct finite difference schemes to solve the problems.Especially,the augmented Lagrangian method and the fast Fourier transform are adopted to accelerate the calculation.Experimental results show that the proposed model can remove the multiplicative noise efficiently and protect the texture well.

Development of a toroidal soft x-ray imaging system and application for investigating three-dimensional plasma on J-TEXT

A toroidal soft x-ray imaging(T-SXRI)system has been developed to investigate threedimensional(3D)plasma physics on J-TEXT.This T-SXRI system consists of three sets of SXR arrays.Two sets are newly developed and located on the vacuum chamber wall at toroidal positionsφof 126.4°and 272.6°,respectively,while one set was established previously atφ=65.50.Each set of SXR arrays consists of three arrays viewing the plasma poloidally,and hence can be used separately to obtain SXR images via the tomographic method.The sawtooth precursor oscillations are measured by T-SXRI,and the corresponding images of perturbative SXR signals are successfully reconstructed at these three toroidal positions,hence providing measurement of the 3D structure of precursor oscillations.The observed 3D structure is consistent with the helical structure of the m/n=1/1 mode.The experimental observation confirms that the T-SXRI system is able to observe 3D structures in the J-TEXT plasma.

Intraoperative application of three-dimensional printed guides in total hip arthroplasty: A systematic review

BACKGROUND Acetabular component positioning in total hip arthroplasty(THA)is of key importance to ensure satisfactory post-operative outcomes and to minimize the risk of complications.The majority of acetabular components are aligned freehand,without the use of navigation methods.Patient specific instruments(PSI)and three-dimensional(3D)printing of THA placement guides are increasingly used in primary THA to ensure optimal positioning.AIM To summarize the literature on 3D printing in THA and how they improve acetabular component alignment.METHODS PubMed was used to identify and access scientific studies reporting on different 3D printing methods used in THA.Eight studies with 236 hips in 228 patients were included.The studies could be divided into two main categories;3D printed models and 3D printed guides.RESULTS 3D printing in THA helped improve preoperative cup size planning and post-operative Harris hip scores between intervention and control groups(P=0.019,P=0.009).Otherwise,outcome measures were heterogeneous and thus difficult to compare.The overarching consensus between the studies is that the use of 3D guidance tools can assist in improving THA cup positioning and reduce the need for revision THA and the associated costs.CONCLUSION The implementation of 3D printing and PSI for primary THA can significantly improve the positioning accuracy of the acetabular cup component and reduce the number of complications caused by malpositioning.

Computer-assisted three-dimensional individualized extreme liver resection for hepatoblastoma in proximity to the major liver vasculature

BACKGROUND The management of hepatoblastoma(HB)becomes challenging when the tumor remains in close proximity to the major liver vasculature(PMV)even after a full course of neoadjuvant chemotherapy(NAC).In such cases,extreme liver resection can be considered a potential option.AIM To explore whether computer-assisted three-dimensional individualized extreme liver resection is safe and feasible for children with HB who still have PMV after a full course of NAC.METHODS We retrospectively collected data from children with HB who underwent surgical resection at our center from June 2013 to June 2023.We then analyzed the detailed clinical and three-dimensional characteristics of children with HB who still had PMV after a full course of NAC.RESULTS Sixty-seven children diagnosed with HB underwent surgical resection.The age at diagnosis was 21.4±18.8 months,and 40 boys and 27 girls were included.Fifty-nine(88.1%)patients had a single tumor,39(58.2%)of which was located in the right lobe of the liver.A total of 47 patients(70.1%)had PRE-TEXT III or IV.Thirty-nine patients(58.2%)underwent delayed resection.After a full course of NAC,16 patients still had close PMV(within 1 cm in two patients,touching in 11 patients,compressing in four patients,and showing tumor thrombus in three patients).There were 6 patients of tumors in the middle lobe of the liver,and four of those patients exhibited liver anatomy variations.These 16 children underwent extreme liver resection after comprehensive preoperative evaluation.Intraoperative procedures were performed according to the preoperative plan,and the operations were successfully performed.Currently,the 3-year event-free survival of 67 children with HB is 88%.Among the 16 children who underwent extreme liver resection,three experienced recurrence,and one died due to multiple metastases.CONCLUSION Extreme liver resection for HB that is still in close PMV after a full course of NAC is both safe and feasible.This approach not only reduces the necessity for liver transplantation but also results in a favorable prognosis.Individualized three-dimensional surgical planning is beneficial for accurate and complete resection of HB,particularly for assessing vascular involvement,remnant liver volume and anatomical variations.

Three-dimensional numerical analysis of plant-soil hydraulic interactions on pore water pressure of vegetated slope under different rainfall patterns

Understanding the pore water pressure distribution in unsaturated soil is crucial in predicting shallow landslides triggered by rainfall,mainly when dealing with different temporal patterns of rainfall intensity.However,the hydrological response of vegetated slopes,especially three-dimensional(3D)slopes covered with shrubs,under different rainfall patterns remains unclear and requires further investigation.To address this issue,this study adopts a novel 3D numerical model for simulating hydraulic interactions between the root system of the shrub and the surrounding soil.Three series of numerical parametric studies are conducted to investigate the influences of slope inclination,rainfall pattern and rainfall duration.Four rainfall patterns(advanced,bimodal,delayed,and uniform)and two rainfall durations(4-h intense and 168-h mild rainfall)are considered to study the hydrological response of the slope.The computed results show that 17%higher transpiration-induced suction is found for a steeper slope,which remains even after a short,intense rainfall with a 100-year return period.The extreme rainfalls with advanced(PA),bimodal(PB)and uniform(PU)rainfall patterns need to be considered for the short rainfall duration(4 h),while the delayed(PD)and uniform(PU)rainfall patterns are highly recommended for long rainfall durations(168 h).The presence of plants can improve slope stability markedly under extreme rainfall with a short duration(4 h).For the long duration(168 h),the benefit of the plant in preserving pore-water pressure(PWP)and slope stability may not be sufficient.

STRONGLY CONVERGENT INERTIAL FORWARD-BACKWARD-FORWARD ALGORITHM WITHOUT ON-LINE RULE FOR VARIATIONAL INEQUALITIES

This paper studies a strongly convergent inertial forward-backward-forward algorithm for the variational inequality problem in Hilbert spaces.In our convergence analysis,we do not assume the on-line rule of the inertial parameters and the iterates,which have been assumed by several authors whenever a strongly convergent algorithm with an inertial extrapolation step is proposed for a variational inequality problem.Consequently,our proof arguments are different from what is obtainable in the relevant literature.Finally,we give numerical tests to confirm the theoretical analysis and show that our proposed algorithm is superior to related ones in the literature.

Influence of sampling on three-dimensional surface shape measurement

In order to accurately measure an object’s three-dimensional surface shape,the influence of sampling on it was studied.First,on the basis of deriving spectra expressions through the Fourier transform,the generation of CCD pixels was analyzed,and its expression was given.Then,based on the discrete expression of deformation fringes obtained after sampling,its Fourier spectrum expression was derived,resulting in an infinitely repeated"spectra island"in the frequency domain.Finally,on the basis of using a low-pass filter to remove high-order harmonic components and retaining only one fundamental frequency component,the inverse Fourier transform was used to reconstruct the signal strength.A method of reducing the sampling interval,i.e.,reducing the number of sampling points per fringe,was proposed to increase the ratio between the sampling frequency and the fundamental frequency of the grating.This was done to reconstruct the object’s surface shape more accurately under the condition of m>4.The basic principle was verified through simulation and experiment.In the simulation,the sampling intervals were 8 pixels,4 pixels,2 pixels,and 1 pixel,the maximum absolute error values obtained in the last three situations were 88.80%,38.38%,and 31.50%in the first situation,respectively,and the corresponding average absolute error values are 71.84%,43.27%,and 32.26%.It is demonstrated that the smaller the sampling interval,the better the recovery effect.Taking the same four sampling intervals in the experiment as in the simulation can also lead to the same conclusions.The simulated and experimental results show that reducing the sampling interval can improve the accuracy of object surface shape measurement and achieve better reconstruction results.

An efficient parallel algorithm of variational nodal method for heterogeneous neutron transport problems

The heterogeneous variational nodal method(HVNM)has emerged as a potential approach for solving high-fidelity neutron transport problems.However,achieving accurate results with HVNM in large-scale problems using high-fidelity models has been challenging due to the prohibitive computational costs.This paper presents an efficient parallel algorithm tailored for HVNM based on the Message Passing Interface standard.The algorithm evenly distributes the response matrix sets among processors during the matrix formation process,thus enabling independent construction without communication.Once the formation tasks are completed,a collective operation merges and shares the matrix sets among the processors.For the solution process,the problem domain is decomposed into subdomains assigned to specific processors,and the red-black Gauss-Seidel iteration is employed within each subdomain to solve the response matrix equation.Point-to-point communication is conducted between adjacent subdomains to exchange data along the boundaries.The accuracy and efficiency of the parallel algorithm are verified using the KAIST and JRR-3 test cases.Numerical results obtained with multiple processors agree well with those obtained from Monte Carlo calculations.The parallelization of HVNM results in eigenvalue errors of 31 pcm/-90 pcm and fission rate RMS errors of 1.22%/0.66%,respectively,for the 3D KAIST problem and the 3D JRR-3 problem.In addition,the parallel algorithm significantly reduces computation time,with an efficiency of 68.51% using 36 processors in the KAIST problem and 77.14% using 144 processors in the JRR-3 problem.