Estimating the COVID-19 prevalence from wastewater.

Wastewater based epidemiology has become a widely used tool for monitoring trends of concentrations of different pathogens, most notably and widespread of SARS-CoV-2. Therefore, in 2022, also in Rhineland-Palatinate, the Ministry of Science and Health has included 16 wastewater treatment sites in a surveillance program providing biweekly samples. However, the mere viral load data is subject to strong fluctuations and has limited value for political deciders on its own. Therefore, the state of Rhineland-Palatinate has commissioned the University Medical Center at Johannes Gutenberg University Mainz to conduct a representative cohort study called SentiSurv, in which an increasing number of up to 12,000 participants have been using sensitive antigen self-tests once or twice a week to test themselves for SARS-CoV-2 and report their status. This puts the state of Rhineland-Palatinate in the fortunate position of having time series of both, the viral load in wastewater and the prevalence of SARS-CoV-2 in the population. Our main contribution is a calibration study based on the data from 2023-01-08 until 2023-10-01 where we identified a scaling factor ( 0.208 ± 0.031 ) and a delay ( 5.07 ± 2.30 days) between the virus load in wastewater, normalized by the pepper mild mottle virus (PMMoV), and the prevalence recorded in the SentiSurv study. The relation is established by fitting an epidemiological model to both time series. We show how that can be used to estimate the prevalence when the cohort data is no longer available and how to use it as a forecasting instrument several weeks ahead of time. We show that the calibration and forecasting quality and the resulting factors depend strongly on how wastewater samples are normalized.

Hierarchical Multicriteria Optimization of Molecular Models of Water.

Many widely used molecular models of water are built from a single Lennard-Jones site on which three point charges are positioned, one negative and two positive ones. Models from that class, denoted LJ3PC here, are computationally efficient, but it is well known that they cannot represent all relevant properties of water simultaneously with good accuracy. Despite the importance of the LJ3PC water model class, its inherent limitations in simultaneously describing different properties of water have never been studied systematically. This task can only be solved by multicriteria optimization (MCO). However, due to its computational cost, applying MCO to molecular models is a formidable task. We have recently introduced the reduced units method (RUM) to cope with this problem. In the present work, we apply the RUM in a hierarchical scheme to optimize LJ3PC water models taking into account five objectives: the representation of vapor pressure, saturated liquid density, self-diffusion coefficient, shear viscosity, and relative permittivity. Of the six parameters of the LJ3PC models, five were varied; only the H-O-H bond angle, which is usually chosen based on physical arguments, was kept constant. Our hierarchical RUM-based approach yields a Pareto set that contains attractive new water models. Furthermore, the results give an idea of what can be achieved by molecular modeling of water with models from the LJ3PC class.

Statistical analysis of three data sources for Covid-19 monitoring in Rhineland-Palatinate, Germany.

In Rhineland-Palatinate, Germany, a system of three data sources has been established to track the Covid-19 pandemic. These sources are the number of Covid-19-related hospitalizations, the Covid-19 genecopies in wastewater, and the prevalence derived from a cohort study. This paper presents an extensive comparison of these parameters. It is investigated whether wastewater data and a cohort study can be valid surrogate parameters for the number of hospitalizations and thus serve as predictors for coming Covid-19 waves. We observe that this is possible in general for the cohort study prevalence, while the wastewater data suffer from a too large variability to make quantitative predictions by a purely data-driven approach. However, the wastewater data and the cohort study prevalence are able to detect hospitalizations waves in a qualitative manner. Furthermore, a detailed comparison of different normalization techniques of wastewater data is provided.

Multicriteria Optimization of Molecular Models of Water Using a Reduced Units Approach.

Multicriteria optimization (MCO) is used to parametrize molecular models of water. The set of the best possible compromises between different objectives, the Pareto set, is determined. Calculating Pareto sets for optimization problems involving molecular simulations is computationally expensive. Therefore, we use a novel, highly efficient method, which is based on the fact that numerical results from molecular simulations can be interpreted as dimensionless numbers. Hence, they carry information on an entire class of models in physical units. This approach was applied here for the MCO of water models of the "one-center Lennard-Jones + point charge" type, in which the objectives were the quality of the description of the vapor pressure, liquid density, and enthalpy of vaporization. The results were compared to models from the literature. Significant improvements were observed. The new optimization method for the development of molecular models is efficient, robust, and broadly applicable.

Dose-guided patient positioning in proton radiotherapy using multicriteria-optimization.

Proton radiotherapy (PT) requires accurate target alignment before each treatment fraction, ideally utilizing 3D in-room X-ray computed tomography (CT) imaging. Typically, the optimal patient position is determined based on anatomical landmarks or implanted markers. In the presence of non-rigid anatomical changes, however, the planning scenario cannot be exactly reproduced and positioning should rather aim at finding the optimal position in terms of the actually applied dose. In this work, dose-guided patient alignment, implemented as multicriterial optimization (MCO) problem, was investigated in the scope of intensity-modulated and double-scattered PT (IMPT and DSPT) for the first time. A method for automatically determining the optimal patient position with respect to pre-defined clinical goals was implemented. Linear dose interpolation was used to access a continuous space of potential patient shifts. Fourteen head and neck (H&N) and eight prostate cancer patients with up to five repeated CTs were included. Dose interpolation accuracy was evaluated and the potential dosimetric advantages of dose-guided over bony-anatomy-based patient alignment investigated by comparison of clinically relevant target and organ-at-risk (OAR) dose-volume histogram (DVH) parameters. Dose interpolation was found sufficiently accurate with average pass-rates of 90% and 99% for an exemplary H&N and prostate patient, respectively, using a 2% dose-difference criterion. Compared to bony-anatomy-based alignment, the main impact of automated MCO-based dose-guided positioning was a reduced dose to the serial OARs (spinal cord and brain stem) for the H&N cohort. For the prostate cohort, under-dosage of the target structures could be efficiently diminished. Limitations of dose-guided positioning were mainly found in reducing target over-dosage due to weight loss for H&N patients, which might require adaptation of the treatment plan. Since labor-intense online quality-assurance is not required for dose-guided patient positioning, it might, nevertheless, be considered an interesting alternative to full online re-planning for initially mitigating the effects of anatomical changes.

Multi-criterial patient positioning based on dose recalculation on scatter-corrected CBCT images.

BACKGROUND AND PURPOSE: Our aim was to evaluate the feasibility and potential advantages of dose guided patient positioning based on dose recalculation on scatter corrected cone beam computed tomography (CBCT) image data. MATERIAL AND METHODS: A scatter correction approach has been employed to enable dose calculations on CBCT images. A recently proposed tool for interactive multicriterial dose-guided patient positioning which uses interpolation between pre-calculated sample doses has been utilized. The workflow was retrospectively evaluated for two head and neck patients with a total of 39 CBCTs. Dose-volume histogram (DVH) parameters were compared to rigid image registration based isocenter corrections (clinical scenario). RESULTS: The accuracy of the dose interpolation was found sufficient, facilitating the implementation of dose guided patient positioning. Compared to the clinical scenario, the mean dose to the parotid glands could be improved for 2 out of 5 fractions for the first patient while other parameters were preserved. For the second patient, the mean coverage over all fractions of the high dose PTV could be improved by 4%. For this patient, coverage improvements had to be traded against organ at risk (OAR) doses within their clinical tolerance limits. CONCLUSIONS: Dose guided patient positioning using in-room CBCT data is feasible and offers increased control over target coverage and doses to OARs.

A novel method for interactive multi-objective dose-guided patient positioning.

In intensity-modulated radiation therapy (IMRT), 3D in-room imaging data is typically utilized for accurate patient alignment on the basis of anatomical landmarks. In the presence of non-rigid anatomical changes, it is often not obvious which patient position is most suitable. Thus, dose-guided patient alignment is an interesting approach to use available in-room imaging data for up-to-date dose calculation, aimed at finding the position that yields the optimal dose distribution. This contribution presents the first implementation of dose-guided patient alignment as multi-criteria optimization problem. User-defined clinical objectives are employed for setting up a multi-objective problem. Using pre-calculated dose distributions at a limited number of patient shifts and dose interpolation, a continuous space of Pareto-efficient patient shifts becomes accessible. Pareto sliders facilitate interactive browsing of the possible shifts with real-time dose display to the user. Dose interpolation accuracy is validated and the potential of multi-objective dose-guided positioning demonstrated for three head and neck (H&N) and three prostate cancer patients. Dose-guided positioning is compared to replanning for all cases. A delineated replanning CT served as surrogate for in-room imaging data. Dose interpolation accuracy was high. Using a [Formula: see text] dose difference criterion, a median pass-rate of 95.7% for H&N and 99.6% for prostate cases was determined in a comparison to exact dose calculations. For all patients, dose-guided positioning allowed to find a clinically preferable dose distribution compared to bony anatomy based alignment. For all H&N cases, mean dose to the spared parotid glands was below [Formula: see text] (up to [Formula: see text] with bony alignment) and clinical target volume (CTV) [Formula: see text] above 99.1% (compared to 95.1%). For all prostate patients, CTV [Formula: see text] was above 98.9% (compared to 88.5%) and [Formula: see text] to the rectum below [Formula: see text] (compared to 56.1%). Replanning yielded improved results for the H&N cases. For the prostate cases, differences to dose-guided positioning were minor.

A new mathematical approach for handling DVH criteria in IMRT planning.

The appropriate handling of planning criteria on the cumulative dose-volume histogram (DVH) is a highly problematic issue in intensity-modulated radiation therapy (IMRT) plan optimization. The nonconvexity of DVH criteria and globality of the resulting optimization problems complicate the design of suitable optimization methods, which feature numerical efficiency, reliable convergence and optimality of the results. This work examines the mathematical structure of DVH criteria and proves the valuable properties of isotonicity/antitonicity, connectedness, invexity and sufficiency of the KKT condition. These properties facilitate the use of efficient and goal-oriented optimization methods. An exemplary algorithmic realization with feasible direction methods gives rise to a functional framework for interactive IMRT planning on DVH criteria. Numerical examples on real world planning cases prove its practical capability.

Analyzing the quality robustness of chemotherapy plans with respect to model uncertainties.

Mathematical models of chemotherapy planning problems contain various biomedical parameters, whose values are difficult to quantify and thus subject to some uncertainty. This uncertainty propagates into the therapy plans computed on these models, which poses the question of robustness to the expected therapy quality. This work introduces a combined approach for analyzing the quality robustness of plans in terms of dosing levels with respect to model uncertainties in chemotherapy planning. It uses concepts from multi-criteria decision making for studying parameters related to the balancing between the different therapy goals, and concepts from sensitivity analysis for the examination of parameters describing the underlying biomedical processes and their interplay. This approach allows for a profound assessment of a therapy plan, how stable its quality is with respect to parametric changes in the used mathematical model.

Breast cancer therapy planning - a novel support concept for a sequential decision making problem.

Breast cancer is the most common carcinosis with the largest number of mortalities in women. Its therapy comprises a wide spectrum of different treatment modalities a breast oncologist decides about for the individual patient case. These decisions happen according to medical guide lines, current scientific publications and experiences acquired in former cases. Clinical decision making therefore involves the time-consuming search for possible therapy options and their thorough testing for applicability to the current patient case.This research work addresses breast cancer therapy planning as a multi-criteria sequential decision making problem. The approach is based on a data model for patient cases with therapy descriptions and a mathematical notion for therapeutic relevance of medical information. This formulation allows for a novel decision support concept, which targets at eliminating observed weaknesses in clinical routine of breast cancer therapy planning.

The critical spot eraser-a method to interactively control the correction of local hot and cold spots in IMRT planning.

Common problems in inverse radiotherapy planning are localized dose insufficiencies like hot spots in organs at risk or cold spots inside targets. These are hard to correct since the optimization is based on global evaluations like maximum/minimum doses, equivalent uniform doses or dose-volume constraints for whole structures. In this work, we present a new approach to locally correct the dose of any given treatment plan. Once a treatment plan has been found that is acceptable in general but requires local corrections, these areas are marked by the planner. Then the system generates new plans that fulfil the local dose goals. Consequently, it is possible to interactively explore all plans between the locally corrected plans and the original treatment plan, allowing one to exactly adjust the degree of local correction and how the plan changes overall. Both the amount (in Gy) and the size of the local dose change can be navigated. The method is introduced formally as a new mathematical optimization setting, and is evaluated using a clinical example of a meningioma at the base of the skull. It was possible to eliminate a hot spot outside the target volume while controlling the dose changes to all other parts of the treatment plan. The proposed method has the potential to become the final standard step of inverse treatment planning.

Balancing control and simplicity: A variable aggregation method in intensity modulated radiation therapy planning.

It is commonly believed that not all degrees of freedom are needed to produce good solutions for the treatment planning problem in intensity modulated radiation therapy (IMRT). However, typical methods to exploit this fact either increase the complexity of the optimization problem or are heuristic in nature. In this work we introduce a technique based on adaptively refining variable clusters to successively attain better treatment plans. The approach creates approximate solutions based on smaller models that may come arbitrarily close to the optimal solution. Although the method is illustrated using a specific treatment planning model, the components constituting the variable clustering and the adaptive refinement are independent of the particular optimization problem.

A new concept for interactive radiotherapy planning with multicriteria optimization: first clinical evaluation.

BACKGROUND AND PURPOSE: Currently, inverse planning for intensity-modulated radiotherapy (IMRT) can be a time-consuming trial and error process. This is because many planning objectives are inherently contradictory and cannot reach their individual optimum all at the same time. Therefore in clinical practice the potential of IMRT cannot be fully exploited for all patients. Multicriteria (multiobjective) optimization combined with interactive plan navigation is a promising approach to overcome these problems. PATIENTS AND METHODS: We developed a new inverse planning system called "Multicriteria Interactive Radiotherapy Assistant (MIRA)". The optimization result is a database of patient specific, Pareto-optimal plan proposals. The database is explored with an intuitive user interface that utilizes both a new interactive element for plan navigation and familiar dose visualizations in form of DVH and isodose projections. Two clinical test cases, one paraspinal meningioma case and one prostate case, were optimized using MIRA and compared with the clinically approved planning program KonRad. RESULTS: Generating the databases required no user interaction and took approx. 2-3h per case. The interactive exploration required only a few minutes until the best plan was identified, resulting in a significant reduction of human planning time. The achievable plan quality was comparable to KonRad with the additional benefit of having plan alternatives at hand to perform a sensitivity analysis or to decide for a different clinical compromise. CONCLUSIONS: The MIRA system provides a complete database and interactive exploration of the solution space in real time. Hence, it is ideally suited for the inherently multicriterial problem of inverse IMRT treatment planning.

IMRT planning on adaptive volume structures--a decisive reduction in computational complexity.

The objective of radiotherapy planning is to find a compromise between the contradictive goals of delivering a sufficiently high dose to the target volume while widely sparing critical structures. The search for such a compromise requires the computation of several plans, which mathematically means solving several optimization problems. In the case of intensity modulated radiotherapy (IMRT) these problems are large-scale, hence the accumulated computational expense is very high. The adaptive clustering method presented in this paper overcomes this difficulty. The main idea is to use a preprocessed hierarchy of aggregated dose-volume information as a basis for individually adapted approximations of the original optimization problems. This leads to a decisively reduced computational expense: numerical experiments on several sets of real clinical data typically show computation times decreased by a factor of about 10. In contrast to earlier work in this field, this reduction in computational complexity will not lead to a loss in accuracy: the adaptive clustering method produces the optimum of the original optimization problem.

Characterization of dose distributions through the max and mean dose concept.

A new approach for the determination of the equivalent uniform dose (EUD) for inhomogeneously irradiated normal organs is developed and tested. The EUD is calculated as a linear combination of the maximum and the mean dose: EUD = alphaDmax + (1 - alpha)D. We call this the max & mean model. The values of alpha are determined by a fit to the Emami tables for complication levels of 5% and 50%. The predictions of the max & mean model are compared with the Emami tables for different treatment volume fractions. The quality of the fit is also compared with the well-known power-law EUD model. The max & mean model makes it possible to make useful predictions of the EUD for organs having an organization anywhere between serial and parallel. The model can be fitted to the Emami tables within the same error range as the widely used power-law model (about 10%) and can be integrated into linear multicriteria optimization algorithms for planning of intensity-modulated radiotherapy.