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.

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.

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.

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.

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.

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.

Observations of ocean pollutants are usually spatiotemporally dispersive, while it is of great importance to obtain continuous distribution of ocean pollutants in a certain area. In this paper, a dynamically constrained interpolated methodology (DCIM) is proposed to interpolate surface nitrogen concentration (SNC) in the Bohai Sea. The DCIM takes the pollutant transport advection diffusion equation as a dynamic constraint to interpolate SNCs and optimizes the interpolation results with adjoint method. Feasibility and validity of the DCIM are testified by ideal twin experiments. In ideal experiments, mean absolute gross errors between interpolated observations and final interpolated SNCs are all no more than 0.03 mg/L, demonstrating that the DCIM can provide convincing results. In practical experiment, SNCs are interpolated and the final interpolated surface nitrogen distribution is acquired. Correlation coefficient between interpolated and observed SNCs is 0.77. In addition, distribution of the final interpolated SNCs shows a good agreement with the observed ones.

The adjoint method is an efficient way to obtain gradient information in a mantle convection model relative to past flow structure, allowing one to retrodict mantle flow from observations of the present-day mantle state. While adjoint equations for isochemical mantle flow have been derived for both incompressible and compressible flows, here we extend the method to thermochemical mantle flow models, and present thermochemical adjoint equations in the elastic-liquid approximation. We verify the method with twin experiments, and retrodict the flow history of a thermochemical reference model (reference twin) assuming for the final state, either a consistent thermochemical interpretation, using the thermochemical adjoint equations, or an inconsistent purely thermal interpretation, using the isochemical adjoint equations. The consistent simulation correctly retrodicts the flow evolution of the reference twin. The inconsistent case, instead, restores a false flow history whereby internal buoyancy forces and convectively maintained topography are overestimated. Because the cost function is reduced in either case, our results suggest that the adjoint method can be used to link assumptions on the role of chemical mantle heterogeneity to geologic inferences of dynamic topography, thus providing additional means to test hypotheses on mantle composition and dynamics.

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.

In myocardial infarction, muscle tissue of the heart is damaged as a result of ceased or severely impaired blood flow. Survivors have an increased risk of further complications, possibly leading to heart failure. Material properties play an important role in determining post-infarction outcome. Due to spatial variation in scarring, material properties can be expected to vary throughout the tissue of a heart after an infarction. In this study we propose a data assimilation technique that can efficiently estimate heterogeneous elastic material properties in a personalized model of cardiac mechanics. The proposed data assimilation is tested on a clinical dataset consisting of regional left ventricular strains and in vivo pressures during atrial systole from a human with a myocardial infarction. Good matches to regional strains are obtained, and simulated equi-biaxial tests are carried out to demonstrate regional heterogeneities in stress-strain relationships. A synthetic data test shows a good match of estimated versus ground truth material parameter fields in the presence of no to low levels of noise. This study is the first to apply adjoint-based data assimilation to the important problem of estimating cardiac elastic heterogeneities in 3-D from medical images.