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.

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.

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.

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.

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.

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.

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.

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.

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.

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.