An Inverse Modeling Approach to Estimate Three-Dimensional Aortic Valve Interstitial Cell Stress Fiber Force Levels.

Within the aortic valve (AV) leaflet exists a population of interstitial cells (AVICs) that maintain the constituent tissues by extracellular matrix (ECM) secretion, degradation, and remodeling. AVICs can transition from a quiescent, fibroblast-like phenotype to an activated, myofibroblast phenotype in response to growth or disease. AVIC dysfunction has been implicated in AV disease processes, yet our understanding of AVIC function remains quite limited. A major characteristic of the AVIC phenotype is its contractile state, driven by contractile forces generated by the underlying stress fibers (SF). However, direct assessment of the AVIC SF contractile state and structure within physiologically mimicking three-dimensional environments remains technically challenging, as the size of single SFs are below the resolution of light microscopy. Therefore, in the present study, we developed a three-dimensional (3D) computational approach of AVICs embedded in 3D hydrogels to estimate their SF local orientations and contractile forces. One challenge with this approach is that AVICs will remodel the hydrogel, so that the gel moduli will vary spatially. We thus utilized our previous approach (Khang et al. 2023, "Estimation of Aortic Valve Interstitial Cell-Induced 3D Remodeling of Poly (Ethylene Glycol) Hydrogel Environments Using an Inverse Finite Element Approach," Acta Biomater., 160, pp. 123-133) to define local hydrogel mechanical properties. The AVIC SF model incorporated known cytosol and nucleus mechanical behaviors, with the cell membrane assumed to be perfectly bonded to the surrounding hydrogel. The AVIC SFs were first modeled as locally unidirectional hyperelastic fibers with a contractile force component. An adjoint-based inverse modeling approach was developed to estimate local SF orientation and contractile force. Substantial heterogeneity in SF force and orientations were observed, with the greatest levels of SF alignment and contractile forces occurring in AVIC protrusions. The addition of a dispersed SF orientation to the modeling approach did not substantially alter these findings. To the best of our knowledge, we report the first fully 3D computational contractile cell models which can predict locally varying stress fiber orientation and contractile force levels.

Responses of Photochemical Air Pollution in California's San Joaquin Valley to Spatially and Temporally Resolved Changes in Precursor Emissions.

Ground-level ozone adversely affects human health and ecosystems. The effectiveness of control programs depends on which precursor(s) are controlled, by how much, and where and when emission reductions occur. We use the adjoint of the Community Multiscale Air Quality model to investigate odd oxygen (Ox ≡ O3 + NO2) sensitivities in California's San Joaquin Valley (SJV) to precursor emissions from local and upwind sources. Sensitivities are mapped and disaggregated by hour and day. Taken together, impacts of precursor emissions in the San Francisco Bay area and Sacramento Valley are similar in magnitude to impacts of local SJV emissions. Same-day emission sensitivities are mostly attributable to local sources, with the most influential anthropogenic emissions of VOCs (volatile organic compounds) and NOx (nitrogen oxides) occurring in the morning (9-11 am) and early afternoon hours (1-3 pm), respectively. For the northernmost SJV receptor, the influence from Sacramento Valley emissions peaks 5-6 h later than Bay area emissions; this difference diminishes for SJV receptors located further downwind. Results show a shift toward more NOx-sensitive conditions in the afternoon with all but the southernmost receptor shifting from VOC- to NOx-sensitive conditions. We also evaluate opportunities to control pollution through shifts in precursor emission location and timing.

Predicting Influenza Epidemic for United States.

Influenza causes repeat epidemics and huge loss of lives and properties. To predict influenza epidemics, we proposed an infectious disease dynamic prediction model with control variables (SEIR-CV), which considers the characteristics of the influenza epidemic transmission, seasonal impacts, and the intensity changes of control measures over time. The critical parameters of the model were inversed using an adjoint method. When using the surveillance data of the past 15 weeks to invert the parameters, the epidemic in the next 3 weeks in the United States can be accurately predicted. In addition, roll predictions from 26 September 2016 to 27 September 2018 were implemented. The correlation coefficient between the predicted values and the surveillance values was greater than 0.975, and the overall relative error of the predictions was less than 10%. These good model performances demonstrated the practicability and feasibility of SEIR-CV for influenza and corresponding infectious disease prediction.

Inverse design of the thermal environment in an airplane cockpit using the adjoint method with the momentum method.

Currently, the thermal environment in airplane cockpits is unsatisfactory and pilots often complain about a strong draft sensation in the cockpit. It is caused by the unreasonable air supply diffusers design. One of the best approaches to design a better cockpit environment is the adjoint method. The method can simultaneously and efficiently identify the number, size, location, and shape of air supply inlets, and the air supply parameters. However, the real air diffuser needed to design often have grilles, especially in the airplane cockpit, and the current method can only design the inlet as an opening. This study combined the adjoint method with the momentum method to directly identify the optimal air supply diffusers with grilles to create optimal thermal environment in an airplane cockpit (1) under ideal conditions and (2) with realistic constraints. Under the ideal conditions, the resulting design provides an optimal thermal environment for the cockpit, but it might not be feasible in practice. The design with realistic constraints provides acceptable thermal comfort in the cockpit, but it is not optimal. Thus, there is an engineering trade-off between design feasibility and optimization. All in all, the adjoint method with the momentum method can be effectively used to identify real air supply diffusers.

Expansion of the Nodal-Adjoint Method for Simple and Efficient Computation of the 2D Tomographic Imaging Jacobian Matrix.

This paper focuses on the construction of the Jacobian matrix required in tomographic reconstruction algorithms. In microwave tomography, computing the forward solutions during the iterative reconstruction process impacts the accuracy and computational efficiency. Towards this end, we have applied the discrete dipole approximation for the forward solutions with significant time savings. However, while we have discovered that the imaging problem configuration can dramatically impact the computation time required for the forward solver, it can be equally beneficial in constructing the Jacobian matrix calculated in iterative image reconstruction algorithms. Key to this implementation, we propose to use the same simulation grid for both the forward and imaging domain discretizations for the discrete dipole approximation solutions and report in detail the theoretical aspects for this localization. In this way, the computational cost of the nodal adjoint method decreases by several orders of magnitude. Our investigations show that this expansion is a significant enhancement compared to previous implementations and results in a rapid calculation of the Jacobian matrix with a high level of accuracy. The discrete dipole approximation and the newly efficient Jacobian matrices are effectively implemented to produce quantitative images of the simplified breast phantom from the microwave imaging system.

Inverse design of an indoor environment using a filter-based topology method with experimental verification.

In order to create a healthy, comfortable, productive, and energy-efficient indoor environment, the computational fluid dynamics (CFD)-based adjoint method with an area-constrained topology method can be used to inversely design the optimal number, size, location, and shape of air supply inlets and air supply parameters. However, this method is not very mature, and the distribution of retained inlets is always scattered. To solve that problem, this investigation introduced a filter method that smooths the intermediate results during the inverse design process. Using a three-dimensional, non-isothermal, asymmetrical office with pre-set air supply inlets as an example, this study verified the performance of the proposed filter-based topology method. The verified method was then used to solve a multi-objective design problem and design an optimal indoor environment for a room. The results indicate that the proposed method was able to find the optimal number, location, and shape of air supply inlets and the optimal air supply temperature, velocity, and angle that led to a thermally comfortable, healthy, productive, and energy-efficient indoor environment. Finally, this investigation installed the optimal inlets in an environmental chamber to mimic the room. The measured air temperature, velocity, and mean age of air in several typical locations in the environmental chamber matched the CFD simulation results very closely.

Inverse design of indoor environment using an adjoint RNG k-ε turbulence model.

The adjoint method can determine design variables of an indoor environment according to the optimal design objective, such as minimal predicted mean vote (PMV) for thermal comfort. The method calculates the gradient of the objective function over the design variables so that the objective function can be minimized along the fastest direction using an optimization algorithm. Since the objective function is controlled by the Reynolds-averaged Navier-Stokes (RANS) equations with the RNG k-ε model during the optimization process, all the corresponding adjoint equations should be solved, rather than the "frozen turbulence" assumption used in previous studies. This investigation developed adjoint equations for the RNG k-ε turbulence model and applied it to a two-dimensional ventilated cavity and a three-dimensional, two-person office. Design processes with the adjoint RNG k-ε turbulence model led to a near-zero design function for the two cases, while those with the "frozen turbulence" assumption did not. This investigation has successfully used the new method to design a two-person office with optimal thermal comfort level around the two occupants.

Structural optimization for nonlinear dynamic response.

Much is known about the nonlinear resonant response of mechanical systems, but methods for the systematic design of structures that optimize aspects of these responses have received little attention. Progress in this area is particularly important in the area of micro-systems, where nonlinear resonant behaviour is being used for a variety of applications in sensing and signal conditioning. In this work, we describe a computational method that provides a systematic means for manipulating and optimizing features of nonlinear resonant responses of mechanical structures that are described by a single vibrating mode, or by a pair of internally resonant modes. The approach combines techniques from nonlinear dynamics, computational mechanics and optimization, and it allows one to relate the geometric and material properties of structural elements to terms in the normal form for a given resonance condition, thereby providing a means for tailoring its nonlinear response. The method is applied to the fundamental nonlinear resonance of a clamped-clamped beam and to the coupled mode response of a frame structure, and the results show that one can modify essential normal form coefficients by an order of magnitude by relatively simple changes in the shape of these elements. We expect the proposed approach, and its extensions, to be useful for the design of systems used for fundamental studies of nonlinear behaviour as well as for the development of commercial devices that exploit nonlinear behaviour.

On the utilization of the adjoint method in microwave tomography.

In microwave imaging, the adjoint method is widely used for the efficient calculation of the update direction, which is then used to update the unknown model parameter. However, the utilization and the formulation of the adjoint method differ significantly depending on the imaging scenario and the applied optimization algorithm. Because of the problem-specific nature of the adjoint formulations, the dissimilarities between the adjoint calculations may be overlooked. Here, we have classified the adjoint method formulations into two groups: the direct and indirect methods. The direct method involves calculating the derivative of the cost function, whereas, in the indirect method, the derivative of the predicted data is calculated. In this review, the direct and indirect adjoint methods are presented, compared, and discussed. The formulations are explicitly derived using the two-dimensional wave equation in frequency and time domains. Finite-difference time-domain simulations are conducted to show the different uses of the adjoint methods for both single source-multiple receiver, and multiple transceiver scenarios. This study demonstrated that an appropriate adjoint method selection is significant to achieve improved computational efficiency for the applied optimization algorithm.

Sensitivities of ozone to its precursors during heavy ozone pollution events in the Yangtze River Delta using the adjoint method.

Although the concentrations of five basic ambient air pollutants in the Yangtze River Delta (YRD) have been reduced since the implementation of the "Air Pollution Prevention and Control Action Plan" in 2013, the ozone concentrations still increase. In order to explore the causes of ozone pollution in YRD, we use the GEOS-Chem and its adjoint model to study the sensitivities of ozone to its precursor emissions from different source regions and emission sectors during heavy ozone pollution events under typical circulation patterns. The Multi-resolution Emission Inventory for China (MEIC) of Tsinghua University and 0.25° × 0.3125° nested grids are adopted in the model. By using the T-mode principal component analysis (T-PCA), the circulation patterns of heavy ozone pollution days (observed MDA8 O3 concentrations ≥160 µg m-3) in Nanjing located in the center area of YRD from 2013 to 2019 are divided into four types, with the main features of Siberian Low, Lake Balkhash High, Northeast China Low, Yellow Sea High, and southeast wind at the surface. The adjoint results show that the contributions of emissions emitted from Jiangsu and Zhejiang are the largest to heavy ozone pollution in Nanjing. The 10 % reduction of anthropogenic NOx and NMVOCs emissions in Jiangsu, Zhejiang and Shanghai could reduce the ozone concentrations in Nanjing by up to 3.40 µg m-3 and 0.96 µg m-3, respectively. However, the reduction of local NMVOCs emissions has little effect on ozone concentrations in Nanjing, and the reduction of local NOx emissions would even increase ozone pollution. For different emissions sectors, industry emissions account for 31 %-74 % of ozone pollution in Nanjing, followed by transportation emissions (18 %-49 %). This study could provide the scientific basis for forecasting ozone pollution events and formulating accurate strategies of emission reduction.

Source term estimation for continuous plume dispersion in Fusion Field Trial-07: Bayesian inference probability adjoint inverse method.

In scenarios involving sudden releases of unidentified gases or concealed pollution emergencies, source control emerges as a critical procedure to safeguard residential air quality. Appropriate inverse source tracking methodology depending on diverse measurement data could be utilized to promptly identify pollutant source parameters. In this study, source term estimation (STE) method, i.e., jointly combining probability adjoint method with the Bayesian inference method, has been proposed. General form of the pollutant inverse transport equation was firstly established. Subsequently, the pollution source information, assumed from single continuous point releases during Fusion Field Trials 2007 under an unsteady wind field, was identified using the Bayesian inference probability adjoint inverse method. Metropolis-Hastings Markov Chain Monte Carlo (MH-MCMC) and Differential Evolution Markov Chain Monte Carlo (DE-MCMC) were then compared as sampling methods for Bayesian inference. Results indicated that the DE-MCMC algorithm has superior convergence and could present higher accuracy of pollutant source information than that of MH-MCMC algorithm, particularly for highly nonlinear and multi-modal distribution systems. Furthermore, the integration of Union standard Adjoint Location Probability (UALP) as prior information into the Bayesian inference probability adjoint inverse method effectively narrowed the sampling range, enhancing both the accuracy and robustness of the proposed approach. Finally, the impact of the covariance matrix on the inverse identification accuracy was explored. Overall, this research has provided insights into the future applicability of this Bayesian inference inversion technique for point source identification.

An adjoint-based method for the computation of gradients in coagulation schemes.

An adjoint-based methodology is proposed to compute the gradient of the outcomes of mathematical models for the coagulation cascade. The method is first exposed and validated by considering a simple, analytically tractable case involving only 3 species. Its potential is further illustrated by considering a detailed model for the extrinsic pathway involving 34 chemical species interacting through 45 chemical reactions and for which the gradient of Endogeneous Thrombin Potential, clotting time, maximum rate and peak value of thrombin with respect to the initial concentrations and reactions rates are computed. It is shown that the method produces gradients estimates that are fully consistent with the finite differences approximation used so far in the literature, but at a much lower computational cost.

Modelling the spatial spread of COVID-19 in a German district using a diffusion model.

In this study, we focus on modeling the local spread of COVID-19 infections. As the pandemic continues and new variants or future pandemics can emerge, modelling the early stages of infection spread becomes crucial, especially as limited medical data might be available initially. Therefore, our aim is to gain a better understanding of the diffusion dynamics on smaller scales using partial differential equation (PDE) models. Previous works have already presented various methods to model the spatial spread of diseases, but, due to a lack of data on regional or even local scale, few actually applied their models on real disease courses in order to describe the behaviour of the disease or estimate parameters. We use medical data from both the Robert-Koch-Institute (RKI) and the Birkenfeld district government for parameter estimation within a single German district, Birkenfeld in Rhineland-Palatinate, during the second wave of the pandemic in autumn 2020 and winter 2020-21. This district can be seen as a typical middle-European region, characterized by its (mainly) rural nature and daily commuter movements towards metropolitan areas. A basic reaction-diffusion model used for spatial COVID spread, which includes compartments for susceptibles, exposed, infected, recovered, and the total population, is used to describe the spatio-temporal spread of infections. The transmission rate, recovery rate, initial infected values, detection rate, and diffusivity rate are considered as parameters to be estimated using the reported daily data and least square fit. This work also features an emphasis on numerical methods which will be used to describe the diffusion on arbitrary two-dimensional domains. Two numerical optimization techniques for parameter fitting are used: the Metropolis algorithm and the adjoint method. Two different methods, the Crank-Nicholson method and a finite element method, which are used according to the requirements of the respective optimization method are used to solve the PDE system. This way, the two methods are compared and validated and provide similar results with good approximation of the infected in both the district and the respective sub-districts.

Identifying spatiotemporal information of the point pollutant source indoors based on the adjoint-regularization method.

Fast and accurate identification of the pollutant source location and release rate is important for improving indoor air quality. From the perspective of public health, identification of the airborne pathogen source in public buildings is particularly important for ensuring people's safety and health. The existing adjoint probability method has difficulty in distinguishing the temporal source, and the optimization algorithm can only analyze a few potential sources in space. This study proposed an algorithm combining the adjoint-pulse and regularization methods to identify the spatiotemporal information of the point pollutant source in an entire room space. We first obtained a series of source-receptor response matrices using the adjoint-pulse method in the room based on the validated CFD model, and then used the regularization method and composite Bayesian inference to identify the release rate and location of the dynamic pollutant source. The results showed that the MAPEs (mean absolute percentage errors) of estimated source intensities were almost less than 15%, and the source localization success rates were above 25/30 in this study. This method has the potential to be used to identify the airborne pathogen source in public buildings combined with sensors for disease-specific biomarkers.

Estimation of aortic valve interstitial cell-induced 3D remodeling of poly(ethylene glycol) hydrogel environments using an inverse finite element approach.

Aortic valve interstitial cells (AVICs) reside within the leaflet tissues of the aortic valve and maintain and remodel its extracellular matrix components. Part of this process is a result of AVIC contractility brought about by underlying stress fibers whose behaviors can change in various disease states. Currently, it is challenging to directly investigate AVIC contractile behaviors within dense leaflet tissues. As a result, optically clear poly (ethylene glycol) hydrogel matrices have been used to study AVIC contractility via 3D traction force microscopy (3DTFM). However, the local stiffness of the hydrogel is difficult to measure directly and is further confounded by the remodeling activity of the AVIC. Ambiguity in hydrogel mechanics can lead to large errors in computed cellular tractions. Herein, we developed an inverse computational approach to estimate AVIC-induced remodeling of the hydrogel material. The model was validated with test problems comprised of an experimentally measured AVIC geometry and prescribed modulus fields containing unmodified, stiffened, and degraded regions. The inverse model estimated the ground truth data sets with high accuracy. When applied to AVICs assessed via 3DTFM, the model estimated regions of significant stiffening and degradation in the vicinity of the AVIC. We observed that stiffening was largely localized at AVIC protrusions, likely a result of collagen deposition as confirmed by immunostaining. Degradation was more spatially uniform and present in regions further away from the AVIC, likely a result of enzymatic activity. Looking forward, this approach will allow for more accurate computation of AVIC contractile force levels. STATEMENT OF SIGNIFICANCE: The aortic valve (AV), positioned between the left ventricle and the aorta, prevents retrograde flow into the left ventricle. Within the AV tissues reside a resident population of aortic valve interstitial cells (AVICs) that replenish, restore, and remodel extracellular matrix components. Currently, it is technically challenging to directly investigate AVIC contractile behaviors within the dense leaflet tissues. As a result, optically clear hydrogels have been used to study AVIC contractility through means of 3D traction force microscopy. Herein, we developed a method to estimate AVIC-induced remodeling of PEG hydrogels. This method was able to accurately estimate regions of significant stiffening and degradation induced by the AVIC and allows a deeper understanding of AVIC remodeling activity, which can differ in normal and disease conditions.

Meta-Optics-Empowered Switchable Integrated Mode Converter Based on the Adjoint Method.

Monolithic integrated mode converters with high integration are essential to photonic integrated circuits (PICs), and they are widely used in next-generation optical communications and complex quantum systems. It is expected that PICs will become more miniaturized, multifunctional, and intelligent with the development of micro/nano-technology. The increase in design space makes it difficult to realize high-performance device design based on traditional parameter sweeping or heuristic design, especially in the optimal design of reconfigurable PIC devices. Combining the mode coupling theory and adjoint calculation method, we proposed a design method for a switchable mode converter. The device could realize the transmission of TE0 mode and the conversion from TE0 to TE1 mode with a footprint of 0.9 × 7.5 µm2 based on the phase change materials (PCMs). We also found that the mode purity could reach 78.2% in both states at the working wavelength of 1.55 µm. The designed method will provide a new impetus for programmable photonic integrated devices and find broad application prospects in communication, optical neural networks, and sensing.

A Differentiable Dynamic Model for Musculoskeletal Simulation and Exoskeleton Control.

An exoskeleton, a wearable device, was designed based on the user's physical and cognitive interactions. The control of the exoskeleton uses biomedical signals reflecting the user intention as input, and its algorithm is calculated as an output to make the movement smooth. However, the process of transforming the input of biomedical signals, such as electromyography (EMG), into the output of adjusting the torque and angle of the exoskeleton is limited by a finite time lag and precision of trajectory prediction, which result in a mismatch between the subject and exoskeleton. Here, we propose an EMG-based single-joint exoskeleton system by merging a differentiable continuous system with a dynamic musculoskeletal model. The parameters of each muscle contraction were calculated and applied to the rigid exoskeleton system to predict the precise trajectory. The results revealed accurate torque and angle prediction for the knee exoskeleton and good performance of assistance during movement. Our method outperformed other models regarding the rate of convergence and execution time. In conclusion, a differentiable continuous system merged with a dynamic musculoskeletal model supported the effective and accurate performance of an exoskeleton controlled by EMG signals.

Reconstruction of vascular blood flow in a vessel from tomographic projections.

In this work, we study the measurement of blood velocity with contrast enhanced computed tomography. The reconstruction is based on CT projections perpendicular to the main axis of the vessel and on a partial differential equation describing the propagation of the contrast agent. The inverse problem is formulated as an optimal control problem with the transport equation as constraint. The velocity field is obtained with stationary and unstationary Navier-Stokes equations and it is reconstructed with the adjoint method. The velocity and the density of the contrast agent are well reconstructed. The reconstruction results obtained are better for the axial component of the velocity than for transverse components.

Sources of black carbon during severe haze events in the Beijing-Tianjin-Hebei region using the adjoint method.

The Beijing-Tianjin-Hebei (BTH) region in China has been frequently suffering from severe haze events (observed daily mean surface fine particulate matter PM2.5 concentrations larger than 150 µg m-3) partially caused by certain types of large-scale synoptic patterns. Black carbon (BC), as an important PM2.5 component and a primarily emitted species, is a good tracer for investigating sources and formation mechanisms leading to severe haze pollutions. We apply GEOS-Chem model and its adjoint to quantify the source contributions to BC concentrations at the surface and at the top of the planetary boundary layer (PBL) during typical types of severe haze events for April 2013-2017 in BTH. Four types of severe haze events, mainly occurred in December-January-February (DJF, 62.3%) and in September-October-November (SON, 26.3%), are classified based on the associated synoptic weather patterns using principal component analysis. Model results reasonably capture the daily variations of BC measurements at three ground sites in BTH. The adjoint method attributes BC concentrations to emissions from different source sectors and from local versus regional transport at the model spatial and temporal resolutions. By source sectors, the adjoint method attributes the daily BC concentrations during typical severe haze events (in winter heating season) in Beijing largely to residential emissions (48.1-62.0%), followed by transportation (16.8-25.9%) and industry (19.1-29.5%) sectors. In terms of regionally aggregated source influences, local emissions in Beijing (59.6-79.5%) predominate the daily surface BC concentrations, while contributions of emissions from Beijing, Hebei, and outside BTH regions are comparable to the daily BC concentrations at the top of PBL (~200-400 m). Our adjoint analyses would provide a scientific support for joint regional and targeted control policies on effectively mitigating the particulate pollutions when the dominant synoptic weather patterns are predicted.

Application of the Spline Interpolation in Simulating the Distribution of Phytoplankton in a Marine NPZD Type Ecosystem Model.

The available observations for the model are usually sparse and uneven. The application of interpolation methods help researchers obtain an approximate form of the original data. A marine nutrient, phytoplankton, zooplankton and detritus (NPZD) type ecosystem model is applied to simulate the distribution of phytoplankton combined with the spline interpolation (SI) and the Cressman interpolation (CI). In the idealized twin experiments, the performance of these two interpolation methods is validated through the analysis of several quantitative metrics, which show the minor error and high efficiency when using the SI. Namely, the given distributions can be better inverted with the SI. The actual distribution of phytoplankton in the Bohai Sea is interpolated in the practical experiment, where a satisfactory simulation result is obtained by the model with the SI. The model experiments and results verify the feasibility and effectiveness of SI.