With the advancement of science and technology, the development and application of unmanned mobile vehicles (UMVs) have emerged as topics of crucial concern in the global industry. The development goals and directions of UMVs vary according to their industrial uses, which include navigation, autonomous driving, and environmental recognition; these uses have become the priority development goals of researchers in various fields. UMVs employ sensors to collect environmental data for environmental analysis and path planning. However, the analysis function of a single sensor is generally affected by natural environmental factors, resulting in poor identification results. Therefore, this study introduces fusion technology that employs heterogeneous sensors in the Ackerman UMV, leveraging the advantages of each sensor to enhance accuracy and stability in environmental detection and identification. This study proposes a fusion technique involving heterogeneous imaging and LiDAR  sensors in an Ackerman UMV. A camera is used to obtain real-time images, and YOLOv4-tiny and simple online real-time tracking are then employed to detect the location of objects and conduct object classification and object tracking. LiDAR is simultaneously used to obtain real-time distance information of detected objects. An inertial measurement unit is used to gather odometry information to determine the position of the Ackerman UMV. Static maps are created using simultaneous localization and mapping. When the user commands the Ackerman UMV to move to the target point, the vehicle control center composed of the robot operating system activates the navigation function through the navigation control module. The Ackerman UMV can reach the destination and instantly identify obstacles and pedestrians when in motion. With the advancement of science and technology, the development and application of unmanned mobile vehicles (UMVs) have emerged as topics of crucial concern in the global industry. The development goals and directions of UMVs vary according to their industrial uses, which include navigation, autonomous driving, and environmental recognition; such uses have become priority development goals for researchers in various fields. UMVs recognize the external environment through sensors, which each have different advantages and disadvantages . VariousCamera sensors easily identify objects using high-resolution color information. Gradual advancements in image processing technology have contributed to the rapid development of the deep learning field. Researchers have widely employed convolutional neural networks (CNNs) to achieve satisfactory results in various vision applications. Girshick  proposedRadar sensors obtain information about the physical environment, such as the relative speed, distance, angle, and direction of motion of high-precision targets. Valtl et al.  proposedAlthough LiDAR and radar operate similarly, LiDAR emits laser light instead of millimeter waves. LiDAR resolution is inferior to that of cameras, but it can obtain clearer object outlines compared with radar. Mihai et al.  proposedThe mainstream research of UMV systems focuses on the combined use of multiple sensors to exploit their complementary advantages and disadvantages. Potdar et al.  proposedNavigational algorithms have been widely employed in UMVs. Dijkstra  proposed❖A fusion technique involving heterogeneous imaging and LiDAR sensors is proposed.❖YOLOv4-tiny and simple online real-time tracking (SORT) are used to detect the location of objects and perform object classification and tracking to ensure that the objects encountered by vehicles are pedestrians or static obstacles.❖LiDAR is employed to obtain real-time distance information of detected objects. Compared with other sensors , LiDAR is less affected by the environment and has high precision.❖The vehicle control center (VCC) activates the navigation control module based on heterogeneous sensors in real time. The VCC vehicle can perform obstacle avoidance and navigation functions, allowing the vehicle to reach its destination.❖The experimental results indicated an average distance error of 0.03 m and an average error of the entire motion path of 0.357 m when using LiDAR in the Ackerman UMV.Most of the literature emphasizes the design of navigation algorithms and obstacle avoidance methods for Ackerman unmanned vehicles. However, many dynamic obstacles in the real environment are not considered. If obstacles and pedestrians can be effectively identified, collisions between vehicles and pedestrians can be avoided. Furthermore, most of these methods rely on a single sensor , which leads to the poor robustness of Ackermann UGV. To improve those shortcomings, this study proposes a fusion technique with heterogeneous imaging and LiDAR sensors in an Ackerman UMV. The major contributions of this study are as follows:This paper is organized as follows. This study developed an Ackerman UMV system with heterogeneous sensors. The proposed system architecture is presented in During system operation, the camera obtains real-time images; it then employs YOLOv4-tiny to determine the position, classification, and movement of objects. LiDAR simultaneously gathers real-time distance information. To avoid delays caused by excessive image data and point cloud data, this system uses the NVIDIA AGX Jetson Xavier embedded system for calculation. An inertial measurement unit (IMU) is used to collect odometry information to calculate the position of the Ackerman UMV. Static maps are created using simultaneous localization and mapping (SLAM). When the user issues a command to the Ackerman UMV to move to the target point, the VCC composed of the robot operating system (ROS) uses the navigation control module to activate the navigation function and simultaneously identifies obstacles and pedestrians in real time. The system flowchart and pseudocode are presented in The Ackerman UMV is composed of sensors, computing devices, controllers, and a vehicle chassis. The vehicle chassis includes the steering system, the power transmission system, and the frame. The VCC is the control terminal, and the AGX embedded system acts as the computing device. The AGX collects sensor information, makes decisions, and issues commands to the VCC to control the power and steering systems. This study employed NVIDIA Jetson AGX Xavier as a computing device; it collects sensor information, makes decisions, and sends commands to the onboard controller to operate the power and steering systems. The operating system is Ubuntu 18.04. ROS provides common functions, management of functional blocks, communication between blocks (publish/subscribe), and device controls. The camera, a Logitech C925e with a 45° horizontal field of view, is installed on the front center of the vehicle. The camera is used to input real-time images to analyze the identification process of obstacles in front of the vehicle, such as pedestrians. The LiDAR sensor, which uses a Velodyne VLP-16 with a 360° horizontal viewing angle, is mounted on the front center of the vehicle above the camera. The sensor is used to construct maps and obtain real-time distance information. The IMU uses a Bosch imu_bno055, which can calculate the acceleration relative to the three axes as an input of the odometry information.The steering system of the UMV adopts Ackermann steering. The servo motor is connected to and fixed on the Ackermann lock point, converting the rotational motion of the motor into linear motion. The steering rod is used to pull the steering column and change the direction of the tires. The transmission mode is designed to drive the rear wheels. The gears of the gearbox are driven by the motor, and the decelerated power is transmitted to the transmission shaft to directly control the rear wheels.SLAM enables the Ackerman UMV to start from an unknown location in an unknown environment, identify its own position through repeatedly observed map features during movement, and construct a map based on its position. Cartographer, a real-time indoor SLAM method developed by Google, supports multi-sensor mapping. This study employed Cartographer to construct a static map for the input of the system navigation module.Navigation control is a crucial system function used to determine the best route and avoid collisions. First, global navigation is employed to establish a predetermined path, and then local navigation is used to correct and optimize the path through a cost map. The path with the highest score is converted into linear and angular velocities and commands the Ackerman UMV to move. The result of the final navigation is then completed. The cost map is constructed with the static map, dynamic map (including map and obstacles), and odometry information. Cartographer provides simultaneous 2-D and 3-D localization and mapping in real time. This study employed Cartographer to obtain a static map; adaptive Monte Carlo localization is used to locate the Ackerman UMV on the map. LiDAR is employed to obtain angular distances around the Ackerman UMV. The IMU is used to obtain the odometry information, which includes the position of the Ackerman UMV  and speed (including linear speed and steering speed). Global navigation uses Dijkstra’s algorithm to identify the shortest path, and local navigation implements the TEB algorithm to optimize the path given to global navigation. Dijkstra’s algorithm starts at the source node and analyzes the graph to find the shortest path between that node and all the other nodes in the graph. If the shortest path between the source node and another node is found, that node is marked as “visited” and added to the path. The process continues until all the nodes in the graph have been added to the path. Then the shortest path can be obtained. Finally, the motion path of the Ackerman UMV is determined.In the Ackerman UMV system, the YOLOv4-tiny network model is used to detect obstacles and pedestrians. YOLOv4-tiny, a lightweight network simplified from YOLOv4, uses the CSPDarknet53-tiny network to extract object features. UpSampling and Concat are used to merge previous features to expand feature information and improve detection performance. In this network, predictions use scale sizes of 13 × 13 and 26 × 26. If the direction of pedestrian travel can be determined, the probability of collision with the Ackerman UMV can be reduced. Therefore, this study implemented correlation matching of detected objects in different image frames to determine whether detected objects were new. SORT  was usedX-axis ratio of the center point to the pixel identifies the corresponding angle from the DI. Each laser layer of LiDAR can return 897 distance points and be evenly distributed in 360°. To determine the distance between the obstacle and the vehicle in the image recognition system, the camera view angle and the LiDAR sensor must be matched. DI is the distance between the red point and LiDAR; the distance (Dis) formula can be expressed as follows:The corresponding value of the To obtain the point cloud and image comparison, a LiDAR and image integration method is used to cut the point cloud and implement point cloud analysis of the camera visual angle range. x, y, z, I) about a point, where x, y, z are the coordinates corresponding to each axis, and I is the intensity of the laser reflection. In x and y coordinates, the angle (θ) and distance (D) between the point and the LiDAR sensor are calculated; the formulas are represented as follows:When the LiDAR sensor scans a circle, it obtains point cloud data. The data contain information , moving distance, and time of the Ackerman UMV were recorded.3 (O1), 58 × 30 × 30 cm3 (O2), and 63 × 43 × 43 cm3 (O3). This study developed a short-distance assessment to evaluate the obstacle avoidance ability of the Ackerman UMV. Three obstacles were placed in the path of the Ackerman UMV on the way to its destination. Cardboard boxes placed crosswise were used as obstacles. The length, width, and height of the three cartons were 50 × 29 × 25 cmDijkstra’s algorithm determines the shortest path based on the cost map of the original map and between the starting point and the target point, but it does not consider real-time changes in the map. The study then assessed the ability of the Ackerman UMV to avoid dynamic obstacles. An experiment was implemented in which two pedestrians passed in front of the moving vehicle. One pedestrian passed from left to right; the other passed from right to left. YOLOv4-tiny and SORT are used to track the movement trajectory of the center point of the dynamic obstacle  and judge the moving direction of the obstacle. The tracking results of dynamic obstacles are presented in In this subsection we will discuss the differences between single-sensor and multi-sensor fusion methods. Recently, multi-sensor fusion technology has been applied in unmanned vehicle systems. Caltagirone  developeA total of 500 point cloud data points and camera photos were collected, including trees and stone objects. This experiment compared the performance of single camera image, single LiDAR image, and LiDAR camera image fusion methods in object detection. The object detection results are shown in This study proposed a fusion technique with heterogeneous imaging and LiDAR sensors in an Ackerman UMV. The major contributions of this study consist of the following: (1) The proposed system uses a camera to obtain real-time images, and YOLOv4-tiny and SORT are employed to classify, track, and detect the location of objects. (2) LiDAR is employed to obtain real-time distance information of detected objects which also combines camera images to improve detection accuracy. (3) The experimental results indicated an average distance error of 0.03 m using LiDAR and an average error of the entire motion path of 0.357 m. (4) The proposed Ackerman UMV successfully reaches its destination and instantly identifies static obstacles and pedestrians when in motion.The proposed Ackerman UMV employs two heterogeneous sensors to detect obstacles. The control center collects a large amount of real-time data from these sensors, resulting in a long calculation time and subsequent system delay. Future research will implement an algorithm of the collected images and point cloud data using a field-programmable gate array to achieve real-time operation.


Credit risk analysis (CRA) quantum algorithms aim at providing a quadratic speedup over classical analogous methods. Despite this, experts in the business domain have identified significant limitations in the existing approaches. Thus, we proposed a new variant of the CRA quantum algorithm to address these limitations. In particular, we improved the risk model for each asset in a portfolio by enabling it to consider multiple systemic risk factors, resulting in a more realistic and complex model for each asset’s default probability. Additionally, we increased the flexibility of the loss-given-default input by removing the constraint of using only integer values, enabling the use of real data from the financial sector to establish fair benchmarking protocols. Furthermore, all proposed enhancements were tested both through classical simulation of quantum hardware and, for this new version of our work, also using QPUs from IBM Quantum Experience in order to provide a baseline for future research. Our proposed variant of the CRA quantum algorithm addresses the significant limitations of the current approach and highlights an increased cost in terms of circuit depth and width. In addition, it provides a path to a substantially more realistic software solution. Indeed, as quantum technology progresses, the proposed improvements will enable meaningful scales and useful results for the financial sector. This paper is intended as an extension of previous work . In partThe field of quantum finance aims to use quantum computing to solve a variety of computational problems in finance more effectively than classical methods ,3. In reHowever, Monte Carlo simulations are computationally expensive due to the rare-event simulation problems inherent in credit risk evaluation . AdditioTo overcome these limitations, researchers have explored new methods, such as those based on quantum computing, which can naturally generate true random samples due to the probabilistic nature of qubits . MoreoveHowever, the existing quantum algorithm for CRA  is basedAdditionally, we presented a solution to encode non-integer values for the loss-given-default input parameter to use real-world data and provide a fair comparison with traditional benchmarks.We are now able to provide experimental results for the enhanced version of the original quantum algorithm, not only through classical simulation of quantum hardware but also from cloud access to IBM QPUs with 7 and 27 superconducting qubits.Researchers program [pay-as-you-go service [In the following sections, we first introduce the use of quantum amplitude estimation for CRA. We then present the proposed modifications to the existing algorithm to address outstanding issues, including the Basel II model’s limitations and the encoding of non-integer values. Lastly, we present the new results of simulation experiments and of executions on real quantum devices obtained by running the experiments on IBM devices from the  program  and from service .n assets is the sum of each exposure’s expected loss.As described in , credit The expected loss is already taken into account in financial reports for financial institutions, so it is subtracted from the VaR and thus not factored into the EC. Therefore, the economic capital is used to measure unexpected or extreme values of losses rather than average losses.The quantum amplitude estimation (QAE) algorithm  providesa. The reader can refer to [In order to exploit the speedup guaranteed by the QAE algorithm, the problem under consideration has to be mapped to a Hermitian operator refer to ,12,18 foIn prior research , QAE hasx.To map the CDF of the total loss to a Hermitian operator Operator k to default is the probability that z, the Bernoulli random variables z while F represents the CDF of the standard normal distribution, and For what concerns the default model, the framework implemented in  is similgiven byPDk(z)=FFIn the original single-factor model presented in , the defduced in .The original implementation also makes use of a register with posed in . In thisAs stated in R risk factors considered.In the proposed implementation of the model described above, each risk factor nsidered . TherefoFrom a practical standpoint, this model comprises multiple latent random variables whose realizations, when appropriately combined, determine the probability of default for each asset.However, with increased complexity comes the need for alternative approaches to implement a quantum multi-factor version of the canonical uncertainty model. To address this challenge, we proposed two alternatives, each with unique advantages and limitations.first alternative for encoding systemic risk factors in quantum financial applications involves the use of multiple quantum registers. In this approach, each systemic risk factor, denoted as The K new controlled linear rotations. This increased number of gates is because each risk factor requires a separate register and rotation, which in turn requires additional controlled operations in the circuit.While this alternative only requires a limited number of extra qubits to represent the various risk factors, it does entail a significant increase in the number of gates required to implement the encoding process. Specifically, each additional risk factor considered will necessitate second alternative for implementing a quantum multi-factor version of the canonical uncertainty model involves a single quantum register encoding a random variable The However, since a single rotation is performed per asset, accounting for all the risk factors, the multivariate normal distribution, in this case, is non-standard. This is because it is not possible to encode the weights in the slope of the rotations. Instead, the covariance matrix of the distribution is used to encode the Despite this limitation, this approach reduces the circuit depth compared to the previous one, as only one rotation is required for encoding the asset’s default probability. However, the method incurs overhead in terms of the required qubits due to the presence of an extra sum register. Nevertheless, this overhead becomes negligible in a scenario with portfolios composed of thousands of assets.For a more detailed evaluation of the qubits and gates required by the various approaches, we refer the reader to Both multi-factor approaches provide an advantage over the Basel II single-factor model by using actual information about the point in time of the credit cycle. Uncertainties about the parameters needed for value-at-risk calculations in portfolio models can thus be reduced.One limitation of current implementations of quantum credit risk algorithms is the constraint on LGD parameters, which can only assume integer values due to the use of a weighted sum register in the operator WeightedAdder register provided by Qiskit [Here, y Qiskit ,25, whicn-qubit state. This new approach allows the operator to directly read defaulted qubits from the X-register and associate them with the corresponding total loss. The objective qubit is flipped only if the total loss is less than or equal to the given level x set by the current bisection search step. Essentially, the operator reads the X-register as a binary number, and then the specific total loss associated with that binary number is compared with x to determine if the objective qubit should be flipped.This constraint is particularly limiting considering the small number of currently available qubits. For instance, using three assets with LGD values in the order of plitudes ,26,27. TIn the next section, we apply this improved algorithm to an illustrative example using both classical simulations of quantum hardware and real quantum computers.In this section, we present the results of experiments conducted on toy models that illustrate the proposed improvements.The chosen numeric values for the LGD parameters demonstrate the increased flexibility allowed by our approach compared to the previous one. Each latent random variable The noiseless experiment utilized the multiple-rotations scheme with n Qiskit . We perfy Qiskit . The resThe experiments described in this section aimed to approach as closely as possible the practical implementation of the algorithm on actual quantum hardware. The results can provide a reference point for future research works that may want to evaluate technological improvements. For this reason, the data used were specifically generated by domain experts who took into account what realistic and reliable values for input measurements could be. All the relevant data are available in a public repository .For these experiments, we tested various configurations of the multiple-rotations model on several quantum processors. For each configuration, the experiment was executed both on the actual machine and classically via simulation of the machine’s noise model. This was done to understand the effect of the QPU’s quantum volume and of its topology on the output, as well as to validate the noise models through simulation. As expected, the circuit sizes  make the effects of decoherence on the results evident for all configurations, which hinders the proper extrapolation of the target measurement. Nevertheless, these findings allow for a baseline for future works focused on providing solutions in this regard, by reducing the circuit depth or exploiting more stable qubits.Ibm_perth and ibm_lagos, each with 7 qubits and a quantum volume of 32.Ibm_canberra and ibm_algiers, each with 27 qubits and quantum volumes of 32 and 128, respectively.The configurations considered involved 2 to 4 assets and 1 to 3 systemic risk factors. The required number of qubits varied from a minimum of 7 to a maximum of 13. The quantum processors used were as follows:The topology for these architectures is shown in The aggregate results of the simulated experiments are displayed in The complete and non-aggregate results, as well as the code used to generate them, are available in a public repository .Noise is one of the major challenges facing quantum computing, as it can cause errors in qubits. The sources of noise can vary, from environmental factors such as temperature and electromagnetic radiation to decoherence and imperfections in the hardware itself. As a result, researchers have been actively investigating ways to characterize and mitigate the impact of noise on qubits ,30,31,32What we observed, both by simulating quantum machines with their respective noise and by directly performing experiments on QPUs, was that the estimation of the expected total loss tended to converge towards half of the maximum possible loss see  regardleibm_algiers: this machine with a higher quantum volume (128) shows a greater variance around the central value, a potential indication of how the continuous improvement of this particular dimension suggests a future successful application of this and other algorithms on quantum machines.A potentially interesting aspect that emerges from the analysis concerns K and R, this advantage disappears when the algorithm scales to a realistic setting with thousands of assets and tens of factors. At this scaling, the overhead derived from the presence of the sum register becomes negligible, as the number of qubits it requires scales logarithmically as LinearAmplitudeFunction register [K that approaches While the proposed multiple-rotations variant of the quantum model presents an advantage over the original implementation  in termsregister  requiresation in . MoreoveRegarding algorithm complexity, the iterative QAE introduced in  and usedThe main advantage of IQAE is that it does not increase the number of required qubits, as it does not require performing quantum phase estimation and still provides convergence proofs .K uncontrolled Y-rotations followed by w times. Multiple copies of Z allow us to parallelize the preparation of the qubits representing the counterparties, achieving a depth of For what concerns the uncertainty model, extrapolating from , the staeader to  and parteader to , which cLinearAmplitudeFunction class. This circuit uses controlled linear rotations and comparator registers to implement the piecewise linear function on qubit amplitudes [LinearAmplitudeFunction.For our implementations, we highlight the increase in terms of gates needed due to the use of the plitudes . The numular, in , the autular, in , a novelIn this paper, we offered solutions to address the limitations of the quantum credit risk analysis algorithm, making it a more effective tool for future advancements in quantum computing technology. We illustrated our proposal and presented the results of several tests  that show the capabilities of our approach and the remaining challenges in terms of scalability and execution on actual QPUs.The analysis highlights the need for further improvements in qubit coherence since our proposed measures require significantly more gates and qubits at scale than the previous implementation.Thanks to the improvements proposed, our architecture can take non-integer values for the LGD vector, increasing input flexibility and allowing the use of real-world data. Additionally, our new uncertainty model with multiple risk factors corresponds to the framework most commonly used by big entities in the financial sector ,37. ThesIn conclusion, it is important to mention that while the proposed quantum credit risk model has the potential to improve the classical CRA process, its integration into production environments will require further research and development. In particular, the integration with existing data pipelines and possibly the design of an end-to-end digital twin will be necessary to evaluate the performance of the quantum model. Additionally, new regulations and legal requirements may be needed for the adoption of quantum algorithms in sensitive financial applications. These considerations highlight the importance of continued collaboration between researchers, financial institutions, and regulatory bodies to ensure the responsible and effective deployment of quantum technologies in the financial industry.


Fresh-frozen allograft is the gold-standard bone graft material used during revision hip arthroplasty. However, new technology has been developed to manufacture decellularised bone with potentially better graft incorporation. As these grafts cost more to manufacture, the aim of this cost-effectiveness study was to estimate whether the potential health benefit of decellularised bone allograft outweighs their increased cost.A Markov model was constructed to estimate the costs and the quality-adjusted life years of impaction bone grafting during a revision hip arthroplasty.This study took the perspective of the National Health Service in the UK.The Markov model includes patients undergoing a revision hip arthroplasty in the UK.Impaction bone grafting during a revision hip arthroplasty using either decellularised bone allograft or fresh-frozen allograft.Outcome measures included: total costs and quality-adjusted life years of both interventions over the lifetime of the model; and incremental cost-effectiveness ratios for both graft types, using base case parameters, univariate sensitivity analysis and probabilistic analysis.The incremental cost-effectiveness ratio for the base case model was found to be £270 059 per quality-adjusted life year. Univariate sensitivity analysis found that changing the discount rate, the decellularised bone graft cost, age of the patient cohort and the revision rate all had a significant effect on the incremental cost-effectiveness ratio.As there are no clinical studies of impaction bone grafting using a decellularised bone allograft, there is a high level of uncertainty around the costs of producing a decellularised bone allograft and the potential health benefits. However, if a decellularised bone graft was manufactured for £2887 and lowered the re-revision rate to less than 64 cases per year per 10 000 revision patients, then it would most likely be cost-effective compared with fresh-frozen allograft. By using the widely used Markov model, this study captured the dynamic nature of revision hip arthroplasty outcomes and estimated the costs and quality-adjusted life years over the lifetime of the patient.The study included sensitivity analyses that assessed the variability and uncertainty of the findings by exploring the impact of key variables on the cost-effectiveness of the grafts used.The use of the stochastic modelling with 10 000 simulations provides a strong evaluation of the estimates made by accounting for parameter variability.One potential limitation is the lack of clinical data meaning the study relies on assumptions and extrapolation from studies involving different graft types for the decellularised graft revision rates.Another potential limitation is the use of costs from a variety of sources which may not accurately reflect the costs paid by the National Health Service in 2022.In the UK, there are approximately 8000 revision hip arthroplasties (RHAs) each year;7Decellularisation is a novel technology that removes cells and DNA from tissue while preserving the underlying tissue matrix.10However, the overall costs of an RHA with decellularised allograft are £39 017, compared with the overall cost of fresh-frozen allograft IBG: £16 343, there is an increase of £22 674 per surgery. Therefore, any potential health benefit from decellularisation needs to be evaluated against the potential increase in cost. In this study, a cost-effectiveness analysis was conducted to compare the novel decellularised allograft with the current most common bone graft option  for acetabular IBG during an RHA. The costs and health benefits of both bone graft choices were estimated and compared using a Markov model from the perspective of the UK National Health Service (NHS).11A decision tree and Markov modelTo compare the two bone graft choices, an incremental cost-effectiveness ratio (ICER) was used. The ICER is calculated by:C1 is the cost and E1 is the effectiveness of the new intervention with C0 and E0 being the cost and effectiveness of the original intervention.12where To find the cost of each bone graft choice, the cost of an RHA was combined with the cost of each bone graft . The ind10.1136/bmjopen-2022-067876.supp1Supplementary dataThe costs of the reagents used for the decellularisation process were obtained from a variety of suppliers . The cos15For this analysis, QALYs are used as the indicator of effectiveness and health benefit. QALYs incorporate the impact of a disease and treatment on both the quantity and quality of life and are the recommended outcome measure in the UK.The transition probability is the probability that a patient will move from one health state to another during each period of the model (1 year). R) and transition probabilities (TP) were calculated by:It was assumed that the risk of needing an RHA is the same for all health states for each bone graft choice. For the fresh-frozen allograft, the risk of re-revision was calculated from the studies summarised in et alTo date, there have not yet been any clinical studies using decellularised bone as an IBG during RHA.The transition from the health states to the ‘death’ state is based on the mean age of the patients in the model. The starting age used for the model was 71 years, this is the average age of RHA patients in the UK National Joint Registry.To test which of the parameters affect the results of the model, a univariate sensitivity analysis was used. One variable in the model was changed to an extreme value and a new ICER was calculated. As suggested in the NICE guide for technology appraisal,Many of the parameters used in the Markov model have varying levels of uncertainty; therefore, distributions of potential values were found using the mean and SD of each parameter . To testPatients or the public were not involved in the design, or conduct, or reporting, or dissemination plans of our research.For the base case parameters in this model, the overall revision surgery costs for the decellularised allograft were £39 017 per patient and the costs for the fresh-frozen allograft were £16 343 per patient. The QALYs calculated for the decellularised allograft choice were 6.93 per patient with the fresh-frozen allograft providing 6.86 QALYs per patient. To determine the cost-effectiveness of treatment options, the total costs and health benefits of each graft choice model are compared. For the base values in this model, neither bone graft option was found to be dominant, with the decellularised allograft costing more but providing an increase in QALYs . For the base model, the ICER of decellularised allograft was calculated as £270 059 per QALY, which is £240 059 higher than the NICE £30 000 per QALY guidance.12As can be seen in Calculated from the results of the randomly generated models, the percentage of models in which the decellularised graft was cheaper than fresh-frozen was 11.1% and the percentage in which the decellularised graft was more effective was 51.2%; this is highlighted in The aim of this study was to evaluate the cost-effectiveness of using a decellularised bone allograft for IBG during an RHA from the perspective of the NHS. For the NICE £30 000 per QALY guidance, both base case and stochastic modelling indicated that fresh-frozen allograft is more likely to be cost-effective than the decellularised graft. However, although the favoured bone graft choice stayed the same throughout the univariate sensitivity analysis, there were large changes to the ICER when the patient cohort age was changed, indicating how substantial any potential uncertainty around the input parameter values could be. However, the stochastic model should effectively capture parameter uncertainty by collating the results of numerous simulations, enhancing the reliability of cost-effectiveness estimates.Logically, if the cost of producing a decellularised graft was reduced, this would increase the probability of the graft being cost-effective. The current model assumes a large cost of retrieval of the femoral head bone graft  prices, these assumptions may not accurately reflect the 2022 costs spent by the NHS. Moreover, the use of the good outcome care costs from Arden An alternative to decellularised allograft is washed bone. Studies have found that allograft bone that undergoes a washing process to remove bone marrow possesses similar mechanical properties to fresh-frozen allografts and the removal of immunogenic material could minimise immune reaction and increase bone regeneration.The results of this cost-effectiveness analysis suggest that using the current manual manufacturing method, decellularised bone grafts are unlikely to be cost-effective compared with the current fresh-frozen allograft choice. However, if the purchase price of a decellularised bone allograft was below £2887 (71.2% reduction of the current price) and the graft adequately lowered the re-revision rate of hip arthroplasty to 64 re-revisions per year per 10 000 patients as estimated, the ICER would be below the lower NICE guideline of £30 000 per QALY and the graft likely to be cost-effective. In conclusion, the model-based economic evaluation undertaken in this study suggests that if the cost of manufacturing decellularised bone allograft could be reduced, this would warrant exploration into the effectiveness of these grafts through a randomised clinical trial of IBG during RHA.


Spatial frequency domain imaging (SFDI) is well established in biology and medicine for non-contact, wide-field imaging of optical properties and 3D topography. Especially for turbid media with displaced, tilted or irregularly shaped surfaces, the reliable quantitative measurement of diffuse reflectance requires efficient calibration and correction methods. In this work, we present the implementation of a generic and hardware independent calibration routine for SFDI setups based on the so-called pinhole camera model for both projection and detection. Using a two-step geometric and intensity calibration, we obtain an imaging model that efficiently and accurately determines 3D topography and diffuse reflectance for subsequently measured samples, taking into account their relative distance and orientation to the camera and projector, as well as the distortions of the optical system. Derived correction procedures for position- and orientation-dependent changes in spatial frequency and intensity allow the determination of the effective scattering coefficient  Spatial frequency domain imaging (SFDI) is a non-contact and fast measurement method to determine both the 3D shape and optical properties of scattering samples. A major advantage is the high lateral resolution that can be achieved to quantitatively map, for example, the effective volume scattering coefficient meter rs ,2. The tmeter rs ,5. The mmeter rs . Other mmeter rs ,8. In bometer rs . Based oequation ,11. In aequation ,13,14. Hequation . This raIn the simplified case of a flat sample, the diffuse reflectance can be corrected by measuring a reference sample with known optical properties at exactly the same position . For morIn this paper, we present a two-step calibration routine for SFDI systems: geometric calibration involves measuring a calibration target with a circular grid at different positions to determine the imaging characteristics and distortion of the projector and camera using the pinhole camera model. After transformation to a uniform coordinate system, the geometry of the projector-camera system can be described consistently, which is used to calculate a 3D map of the sample surface using a nonlinear phase distance model. Thus, for each 3D point, the relative distance to the camera and the projector as well as the projection and acquisition angle can be specified in cylindrical coordinates. Knowledge of the distortion parameters allows for their correction after image acquisition and the calculation of pre-distorted phase images, which produce sinusoidal patterns of high homogeneity when projected onto a reference plane for a given working distance. If the sample surface deviates from the reference surface, the resulting local change in spatial frequency can be quantified geometrically. The second calibration step uses a calibration sample with known optical properties to characterize the MTF of the system and the heterogeneous intensity distribution within the calibrated volume. By parameterization and interpolation within the entire calibrated volume, the model provides the system MTF and reference intensity as a look-up table for subsequent measurements. Optical phantoms were measured for validation, showing how the information from both calibration steps can be efficiently used for post-processing the data without the need for further measurements. In particular, The aim of this work was to develop a generic and hardware-independent calibration routine for SFDI setups based on the so-called pinhole camera model for projection and detection. Through a two-step geometric and intensity calibration, we obtain an imaging model that can be used to accurately determine the diffuse reflectance of turbid media with displaced or irregular surfaces. In particular, we present correction methods to account for position- and orientation-dependent changes in the spatial frequency and intensity, which are validated by measuring Calibration and subsequent measurements were performed using a multispectral SFDI system schematically shown in r et al. .s, the camera intrinsic matrix A and the extrinsic rotation-translation matrix t and rotation R into the local camera coordinate system. Especially for systems consisting of several cameras or projectors, this allows the corresponding coordinates of the subsystems to be correlated. The camera intrinsic matrixThe basis for calibration is an appropriate model that describes the imaging process, in the most general case as a mapping of a ray from 3D space to a 2D pixel. Depending on the imaging system, there are both parameterized and non-parameterized models, e.g., for pinhole cameras, stereo cameras, fisheye cameras or catadioptric cameras, as shown in detail by Ramalingam  and Gros1 and p2 .There are several implementations of this parameterized pinhole camera model for general calibration purposes, such as the Python module Camera Calibration and 3D Reconstruction from the open source computer vision library (openCV) , which wThe calibration of the SFDI system is divided into two parts: the first calibration routine uses a circular grid to characterize the imaging properties of the camera and projector based on the pinhole camera model , while afterwards, a calibration standard with known reflectance properties is used for intensity calibration.a), which will be referred to as object points in the following. After capturing the calibration target in different positions, an image processing algorithm recognizes the individual marker structures in each of the resulting camera images. Their pixel coordinates are referred to as image points in the following and, together with the corresponding object points, serve as input parameters for the actual modeling. Estimating the pose of the camera based on a set of 2D points and their corresponding 3D points is also known as the perspective-n-point problem [The aim of geometric calibration is to determine the extrinsic and intrinsic parameters using the pinhole camera model for both the camera and the projection system. If we first restrict ourselves to camera calibration, according to Zhang , it is s problem . The sol problem , uses a The procedure described for a single camera can be extended to the calibration of a projector using the same pinhole camera model, but with reversed conceptualization. The main difference is the determination of the image points, which are not directly accessible with the projector in contrast to the camera. Instead, phase images are projected onto the calibration target, allowing the pixel rows and columns of the projector chip to be encoded onto the measurement plane. By evaluating the unique phase at each marker structure, the required correspondence can thus be found indirectly. In this work, the phase is determined using the phase shift method, which is based on the demodulation of at least three sequentially recorded sinusoidal patterns, each shifted by a. In step ➂, the pixel positions in the camera image, i.e., the camera image points, are determined for each marker. In step ➃, n different positions, but at least three times. The camera pinhole model is then determined separately for the camera and projector image points of all n positions with their respective object points, resulting in their intrinsic and extrinsic parameters. Although this technically completes the geometric calibration, there are some useful post-processing steps. In step ➄, we define, without a loss of generality, a global coordinate system by transforming the projector coordinates into the camera coordinate system. The transformation matrix is obtained by transforming To better illustrate the combined calibration of the camera and projector, an overview of the processing steps for the geometric calibration is shown in Equation  yields tGeometric calibration allows a 3D point cloud to be determined by triangulation using the phase information. This means that for a given camera pixel, the measured global phase is directly linked to a unique 3D coordinate. Instead of a strictly geometric determination, in this work, we applied a parameterized approach using the presented pinhole camera model, as reported by Lu . For thisolution , which wFor the further post-processing of the point cloud, the open source library Open3D  was usedAs shown in f. Thus, for each camera pixel , we obtain When determining the absolute diffuse reflectance, the inhomogeneous intensity distribution and the MTF of the system, which were neglected so far during the geometric calibration, must also be taken into account. For this purpose, the intensity calibration is performed in a second step using a reference standard of known diffuse reflectance After measuring a sample such as an optical phantom, we repeat the evaluation steps shown so far. The geometric calibration provides a 3D model of the sample surface with corrected spatial frequencies To evaluate the optical properties of the measured sample, we use an analytical solution of the radiative transfer equation based on the pagation ,37,38. TOptical phantoms made of epoxy resin with additional scattering particles (titanium dioxide) and a mineral absorber (hematite) were used for the validation measurements. The geometry and surface properties of the phantoms can be controlled by molding or mechanical finishing. In the present case, flat cylindrical phantoms and spherical caps of different sizes were used. The reference values of their optical properties were determined with an integrating sphere .For the geometric calibration of the SFDI device, an aluminum plate with a printed grid of Compared to the real SFDI setup, some of these parameters can be directly validated, e.g., the size of the camera field of view in the reference plane can be easily measured and checked with a ruler. Regarding the illumination field, it should be noted that the DMD chip may not be fully illuminated and its margins are usually obscured by parts of the projection optics. The fact that the illumination field is significantly larger than the camera image serves to avoid marginal light propagation effects. The relative position of the camera, projector and reference plane could also be roughly confirmed with a tape measure, although the model parameters do not necessarily reflect the exact setup geometry. In particular, the virtual camera and projector centers are not characteristic or distinctive points of the real optical system. Strictly speaking, their specification is only meaningful if the entire set of model parameters is taken into account.The geometric calibration allows the translation of the measured and unwrapped phase directly into a distance Equation . To deteEquation , the uniEquation , the corEquation . Due to To illustrate the determination of the projection and detection angles, a custom-made planar phantom with a central spherical cap with a diameter of approximately 10 mm was measured. f. The outset on the right shows three intensity profiles as a function of For the intensity calibration, a white coated, highly scattered aluminum plate with known reflectance properties was used as a reference target for further intensity calibration. It was measured at six different positions in the calibrated volume, each at nine spatial frequencies ranging from To evaluate the influence of frequency and intensity corrections on the determination of optical properties, another custom-made hemispherical phantom with a radius of curvature of 40 mm was measured at three different positions in the calibrated volume. The SFD measurement was performed at all nine available wavelengths recording six spatial frequencies between The presented approach of a two-step geometry and intensity calibration allows a comprehensive and coherent description of the entire SFDI system with a large set of internal and external parameters obtained both for the projector and camera. In combination with the 3D topography of the sample, available through the phase information, local changes in spatial frequency or intensity can be determined directly from the displacement or tilt of the sample surface and taken into account in a further analysis. This allows the investigation and further development of correction methods that require virtually no prior knowledge of the setup. The parameterized approach to phase–distance conversion and intensity correction using rays associated with an individual camera and projector pixels provides an efficient and insightful representation of the measurement process and subsequent data processing. A general drawback, however, is the extensive algorithms that must be developed and implemented once for post-processing.Overall, the results of the calibration, i.e., the characterization of the geometric imaging properties, including realistic distortions and inhomogeneous intensity distributions, can be further used to establish a digital twin of the setup. A future goal is therefore to simulate the entire measurement process with forward calculations using numerical methods such as the Monte Carlo method ,41. ThisFrom an application perspective, the calibration model can provide advantages in various fields, such as medical imaging. After the one-time calibration, which does not require any prior knowledge of the specific hardware used in the application, comprehensive information on the distance and relative orientation of different image areas of the examined specimen is available in addition to the diffuse reflectance. A major advantage is that no additional image acquisition is required for their determination, i.e., the measurement time remains unchanged. In addition to the presented quantitative approach for the determination of scattering and absorption properties, applications in the field of machine learning are becoming more and more important. For example, in the automated classification of tissue types based on reflectance properties, additional knowledge of their relative position and distance to the camera and projector could enable more stable prediction models.