Continuous Time Scale Research Articles

Efficient designs for three-sequence stepped wedge trials with continuous recruitment.

The standard approach to designing stepped wedge trials that recruit participants in a continuous stream is to divide time into periods of equal length. But the choice of design in such cases is infinitely more flexible: each cluster could cross from the control to the intervention at any point on the continuous time-scale. We consider the case of a stepped wedge design with clusters randomised to just three sequences (designs with small numbers of sequences may be preferred for their simplicity and practicality) and investigate the choice of design that minimises the variance of the treatment effect estimator under different assumptions about the intra-cluster correlation. We make some simplifying assumptions in order to calculate the variance: in particular that we recruit the same number of participants, , from each cluster over the course of the trial, and that participants present at regularly spaced intervals. We consider an intra-cluster correlation that decays exponentially with separation in time between the presentation of two individuals from the same cluster, from a value of for two individuals who present at the same time, to a value of for individuals presenting at the start and end of the trial recruitment interval. We restrict attention to three-sequence designs with centrosymmetry - the property that if we reverse time and swap the intervention and control conditions then the design looks the same. We obtain an expression for the variance of the treatment effect estimator adjusted for effects of time, using methods for generalised least squares estimation, and we evaluate this expression numerically for different designs, and for different parameter values. There is a two-dimensional space of possible three-sequence, centrosymmetric stepped wedge designs with continuous recruitment. The variance of the treatment effect estimator for given and can be plotted as a contour map over this space. The shape of this variance surface depends on and on the parameter , but typically indicates a broad, flat region of close-to-optimal designs. The 'standard' design with equally spaced periods and 1:1:1 allocation rarely performs well, however. In many different settings, a relatively simple design can be found (e.g. one based on simple fractions) that offers close-to-optimal efficiency in that setting. There may also be designs that are robustly efficient over a wide range of settings. Contour maps of the kind we illustrate can help guide this choice. If efficiency is offered as one of the justifications for using a stepped wedge design, then it is worth designing with optimal efficiency in mind.

Dynamics of task preparation processes revealed by effect course analysis on response times and error rates

Cuing or executing a task impacts processing pathways for task-relevant information. While there is ample evidence that processing associated with task execution changes with practice, such evidence regarding cue-induced task preparation is scarce. Here we explored practice-related changes of processing pathways by task cuing in order to assess the plasticity of task preparation. We first developed and validated a new method for the study of practice-related changes, the effect course analysis. The effect course analysis is a model-free, non-parametric method designed to reveal effect changes within an experimental session on a continuous time scale. Then we applied this method to a new study in which cued task sets were supposed to remain activated during assessment of task-relevant pathways, as potential task execution was postponed at the end of the trial. The results showed that, with little practice, task cuing amplified task-relevant pathways, whereas this effect vanished with practice, suggesting that practice prompts fundamental changes of how task cues are used for task preparation. Hence, if one cannot be certain that cognitive processing is stationary, investigating the time course of experimental effects appears to be crucial to determine how cognitive processing is influenced by practice.

Multiproxy bioarchaeological data reveals interplay between growth, diet and population dynamics across the transition to farming in the central Mediterranean

The transition to farming brought on a series of important changes in human society, lifestyle, diet and health. The human bioarchaeology of the agricultural transition has received much attention, however, relatively few studies have directly tested the interrelationship between individual lifestyle factors and their implications for understanding life history changes among the first farmers. We investigate the interplay between skeletal growth, diet, physical activity and population size across 30,000 years in the central Mediterranean through a ‘big data’ cross-analysis of osteological data related to stature (n = 361), body mass (n = 334) and long bone biomechanics (n = 481), carbon (δ13C) and nitrogen (δ15N) stable isotopes (n = 1986 human, n = 475 animal) and radiocarbon dates (n = 5263). We present the observed trends on a continuous timescale in order to avoid grouping our data into assigned ‘time periods’, thus achieving greater resolution and chronological control over our analysis. The results identify important changes in human life history strategies associated with the first farmers, but also highlight the long-term nature of these trends in the millennia either side of the agricultural transition. The integration of these different data is an important step towards disentangling the complex relationship between demography, diet and health, and reconstruct life history changes within a southern European context. We believe the methodological approach adopted here has broader global implications for bioarchaeological studies of human adaptation more generally.

Predefined-time synchronization for competitive neural networks with different time scales and external disturbances

This paper presents a study on the predefined-time (PdT) and practical PdT synchronization of competitive neural networks (CNN) in the presence of different time scales and external disturbances. Two types of external disturbances, which satisfy Lipschitz or bounded conditions, are investigated respectively. The new PdT and practical PdT stability theorems are derived in singularly perturbed systems, where the final residual set is given in detail. By employing the newly derived stability theorems, novel autonomous controllers are designed without relying on a continuous linear term and time scale parameters, while enabling PdT or practical PdT synchronization for drive-response CNNs. Additionally, upper bounds for the settling time are estimated, allowing for adjusting the predefined synchronization times regardless of the initial conditions. Finally, numerical simulations are conducted to demonstrate the effectiveness of the main results.

Controllability of consensus of multi-agent networks over heterogeneous dynamics

This work investigates controllability issues under the leader–follower framework of consensus problem on multi-agent networks where its agents exhibit the heterogeneous dynamics involving first-, second-, and third-order integrator agents on a continuous time-scale. The communication topology is directed, time-invariant, and the reliability of all interactions are unity. We employ two kinds of consensus protocols that are linear and distributed. The necessary and sufficient criteria for the controllability of followers’ dynamics through the selected leaders are obtained in terms of matrix-rank conditions. We also obtain some necessary conditions of controllability involving eigenvectors of system matrices. It is verified that, if either of the first-, second-, or third-order integrator agents are absent, then the controllability of the network becomes equivalent to the controllability of the communication topology just like those of the networks with homogeneous dynamic agents. Obtained results are verified with illustrative examples.

Using Wearable Passive Sensing to Predict Binge Eating in Response to Negative Affect Among Individuals With Transdiagnostic Binge Eating: Protocol for an Observational Study.

Binge eating (BE), characterized by eating a large amount of food accompanied by a sense of loss of control over eating, is a public health crisis. Negative affect is a well-established antecedent for BE. The affect regulation model of BE posits that elevated negative affect increases momentary risk for BE, as engaging in BE alleviates negative affect and reinforces the behavior. The eating disorder field's capacity to identify moments of elevated negative affect, and thus BE risk, has exclusively relied on ecological momentary assessment (EMA). EMA involves the completion of surveys in real time on one's smartphone to report behavioral, cognitive, and emotional symptoms throughout the day. Although EMA provides ecologically valid information, EMA surveys are often delivered only 5-6 times per day, involve self-report of affect intensity only, and are unable to assess affect-related physiological arousal. Wearable, psychophysiological sensors that measure markers of affect arousal including heart rate, heart rate variability, and electrodermal activity may augment EMA surveys to improve accurate real-time prediction of BE. These sensors can objectively and continuously measure biomarkers of nervous system arousal that coincide with affect, thus allowing them to measure affective trajectories on a continuous timescale, detect changes in negative affect before the individual is consciously aware of them, and reduce user burden to improve data completeness. However, it is unknown whether sensor features can distinguish between positive and negative affect states, given that physiological arousal may occur during both negative and positive affect states. The aims of this study are (1) to test the hypothesis that sensor features will distinguish positive and negative affect states in individuals with BE with >60% accuracy and (2) test the hypothesis that a machine learning algorithm using sensor data and EMA-reported negative affect to predict the occurrence of BE will predict BE with greater accuracy than an algorithm using EMA-reported negative affect alone. This study will recruit 30 individuals with BE who will wear Fitbit Sense 2 wristbands to passively measure heart rate and electrodermal activity and report affect and BE on EMA surveys for 4 weeks. Machine learning algorithms will be developed using sensor data to distinguish instances of high positive and high negative affect (aim 1) and to predict engagement in BE (aim 2). This project will be funded from November 2022 to October 2024. Recruitment efforts will be conducted from January 2023 through March 2024. Data collection is anticipated to be completed in May 2024. This study is anticipated to provide new insight into the relationship between negative affect and BE by integrating wearable sensor data to measure affective arousal. The findings from this study may set the stage for future development of more effective digital ecological momentary interventions for BE. DERR1-10.2196/47098.

Controllability of consensus heterogeneous multi-agent networks over continuous time scale

Abstract The research, presented in this paper, concernes the controllability of a multi-agent network with a directed, unweighted, cooperative, and time-invariant communication topology. The network’s agents follow linear and heterogeneous dynamics, encompassing first-order, second-order, and third-order differential equations over continuous time. Two classes of neighbour-based linear distributed control protocols are considered: the first one utilises average feedback from relative velocities/relative accelerations, and the second one utilises feedback from absolute velocities/absolute accelerations. Under both protocols, the network’s agents achieve consensus in their states asymptotically. We observe that both of the considered dynamical rules exploit the random-walk normalised Laplacian matrix of the network’s graph. By categorising the agents of the network into leaders and followers, with leaders serving as exogenous control inputs, we analyse the controllability of followers within their state space through the influence of leaders. Specifically, matrix-rank conditions are established to evaluate the leader–follower controllability of the network under both control protocols. These matrix-rank conditions are further refined in terms of the system matrices’ eigenvalues and eigenvectors. The inference diagrams presented in this work provide deeper insights into how leader–follower interactions impact the network controllability. The efficacy of the theoretical findings is validated through numerical examples.

Cyclostratigraphic correlation of Middle–Late Ordovician sedimentary successions between the South China Block and Tarim Basin with paleoclimatic and geochronological implications

The Middle−Late Ordovician transition was one of the most critical periods throughout the Earth's history, and it involved paleoclimate changes and biological turnover. Here, we conducted cyclostratigraphic analysis on the magnetic susceptibility (MS) from the Kuniutan and Miaopo formations in the Zhenjin section and the Pagoda and Linhsiang formations in the Puxihe section in Yichang, South China. We constructed an astronomical time scale to understand the astronomically forced paleoclimate changes during this key interval. Spectral analyses on the MS series show that the thickness ratios of different sedimentary cycles in the studied sections are consistent with those of Milankovitch cycles during the Middle and Late Ordovician. The floating astronomical time scale of the studied sections was constructed based on astronomical tuning to 405-kyr eccentricity cycles, providing an estimated duration of ∼0.82 Myr for the Guttenberg isotopic carbon excursion (GICE). A high-precision and continuous astronomical time scale has previously been established in the Ordovician marine sediments in the Tarim Basin. The cyclostratigraphic correlation of sedimentary successions between the South China Block and Tarim Basin reveals that the duration of the Middle Ordovician gap in South China is ∼1.38 Myr. Alignment of the maxima of the ∼1.2-Myr obliquity cycle and the 405-kyr eccentricity cycle may have resulted in increased weathering inputs and prolonged periods of ocean anoxia, pacing the enhanced organic carbon burials and the positive isotopic carbon excursion during the middle Darriwilian isotope carbon excursion (MDICE) and GICE.

Towards a consensus on a continuous coordinated universal time

This paper explains the considerations that were important in 1972, when the current leap second procedure was adopted, to maintain a close connection between UTC, the international reference time scale, and UT1—a time scale based on the rotation of the Earth. Although some of these considerations are still relevant, the procedure for adding leap seconds creates difficulties in many modern applications that require a continuous and monotonic time scale. We present the advantages and disadvantages of the leap second procedure, and some of the problems foreseen if it is not reconsidered. We suggest the general outline of a way forward, which addresses the deficiencies in the current leap second system, and which will ensure that UTC remains an international standard that is useful and appropriate for all time and frequency applications. Further discussion and evaluation of the impact of any changes is required.

The floating astronomical time scale for the terrestrial Early Permian Fengcheng Formation from the Junggar Basin and its stratigraphic and palaeoclimate implications

The Permian Fengcheng Formation of the Mahu Sag in the Jungar Basin is one of the most important hydrocarbon source rocks in Xinjiang oil field. The preservation of the geological records of Milankovitch cycles can be studied to understand the history of the Earth's evolution and sedimentary processes, and high‐resolution astronomical time scales (ATS) can be obtained by analysing (quasi) periodic sedimentary signals in geological records. In this study, the natural gamma ray (GR) and density (DEN) logging data are used to carry out a detailed spectrum analysis, including 2π‐Multi‐taper Method (MTM), Evolutive Harmonic Analysis (EHA), Correlation coefficient method (COCO) and DYNOT simulation. GR and DEN data analysis results show sedimentary cycles of 39.3, 9.1 m, 3.6–2.7 m and 2.1–1.7 m, 37.5, 9.7, 3.7 m and 2.4–1.9 m in MY‐1 well; MH‐15 well recorded the significant peaks at 81, 20, 8.6 m and 3.6–3.4 m and 66, 17.6, 6.8 m and 3.3–2.7 m; FN‐14 well revealed high‐confidence level frequencies with wavelength of 97, 23, 8.8 and 3.9 m and 88, 22, 8.5 m and 4–3.4 m respectively. The average sediment accumulation rates (SAR) are estimated at 9–9.7 cm/kyr for MY‐1, 14.5–19 cm/kyr for MH‐15, 13.5–14.5 cm/kyr for FN‐14 by using the COCO. In addition, we construct a continuous time scale for Fengcheng Formation, yielding a deposition duration of about 3.5 ± 0.2 Myr for these three drilling cores. Finally, we used the DYNOT sea‐level change model to analyse the GR and DEN logging series of three wells, for reconstructing the lake‐level changes of the Fengcheng Formation in the Junggar Basin.

Generation of realistic synthetic data using Multimodal Neural Ordinary Differential Equations

Individual organizations, such as hospitals, pharmaceutical companies, and health insurance providers, are currently limited in their ability to collect data that are fully representative of a disease population. This can, in turn, negatively impact the generalization ability of statistical models and scientific insights. However, sharing data across different organizations is highly restricted by legal regulations. While federated data access concepts exist, they are technically and organizationally difficult to realize. An alternative approach would be to exchange synthetic patient data instead. In this work, we introduce the Multimodal Neural Ordinary Differential Equations (MultiNODEs), a hybrid, multimodal AI approach, which allows for generating highly realistic synthetic patient trajectories on a continuous time scale, hence enabling smooth interpolation and extrapolation of clinical studies. Our proposed method can integrate both static and longitudinal data, and implicitly handles missing values. We demonstrate the capabilities of MultiNODEs by applying them to real patient-level data from two independent clinical studies and simulated epidemiological data of an infectious disease.

Dynamic optimization of a cogeneration plant for an industrial application with two different hydrogen embedding solutions

Seasonal storage of hydrogen is a valuable option today increasingly considered in order to optimize cogeneration plants under continuous operation in an incentive framework where electricity sale to the national grids is becoming less economically profitable than in the past. The paper concerns the numerical study and optimization of a cogeneration plant installed in an industrial site having an availability of hydrogen over a continuous time scale, to meet the energy needs and mitigating the environmental impact of the plant operation by reducing the energy withdrawal from traditional sources. Two alternatives are analyzed into detail: the former regards energy production through an internal combustion engine, this last properly controlled to be fueled with blends of natural gas and increasing percentages of hydrogen, the latter concerning the addition of fuel cells to the proposed layout to further reduce the electricity integration by the grid. The dynamic response of the cogeneration system under examination is dynamically evaluated to efficiently fulfill the industrial loads to be fulfilled. First, optimization is performed by implementing a PID controller to better track the industrial demand of electric energy. The main results of this solution reveal a −81% reduction of excess electricity, a −7% reduction of natural gas consumed but a 47% raise of CO 2 emissions due to the increase in thermal integration. Then, an additional energy generation from fuel cells is assumed. An economic analysis is carried out for each of the implemented configurations. The adoption of fuel cells, despite requiring a greater initial investment, allows obtaining a SPB of 1,4 years (− 16%), 1,17 Mln € of avoided costs (− 18,5%) and 1320 t/year of CO 2 emissions avoided (− 95%) with respect to the initial layout. • Seasonal storage of hydrogen is considered in an industrial cogeneration plant. • Electricity generation by hydrogen-NG blends powering an internal combustion engine or by fuel cells. • Design and optimization are conducted by dynamic modelling in TRNSYS. • The internal combustion engine is optimally calibrated under various fuel blends powering. • An economic and environmental analysis is carried out through an advanced engine model.

Automation of Life Data Analysis Processes

Life data analysis is an effective statistical process to gain information on the reliability of technical facilities. The Weibull analysis is a widely-used method for modeling the probabilities of different functional failures. For its application in modern manufacturing and maintenance processes, an automation of this analysis is expedient. An exemplary process of data collection and fitting of a parametric model with continuous time scale is analyzed in this article. Its automation with different statistic software tools is described and comparatively evaluated. With the ambition of minimizing manual effort in the process, a highly automated solution was developed in this research. We describe this self-implemented solution in “R” and justify that this procedure automatizes the process more than the examined commercial implementations. The here presented work proves to be a practical real-time assistance, right now applied in aircraft maintenance.

A review for comparing SWAT and SWAT coupled models and its applications

The continuous time scale model SWAT was established to determine the stream flow discharge, nutrient loads of water quality and reservoir sediment loads in the watershed. Due to its limitation on estimating groundwater recharge, optimum water allocation, and instantaneous peak flow in the river and groundwater discharge during low flow period become the prime cause for the enhancement of the coupled SWAT model. According to the objective and state of the problem, the integrated SWAT model was established and applied for the watershed scenarios. Coupled SWAT-MODFLOW applied to determine the recharge rate and groundwater parameters. The integrated SWAT-TOP defines the topographic index and its detailed hydrological processes. SWAT-MODSIM and SWAT-WEAP allows to estimate the optimum water allocation for the present and future demand in the watershed. In this study, the following integrated models SWAT-MODFLOW, SWAT-MODSIM, SWAT-TOP, and coupled SWAT machine learning techniques were interpreted and its application was evaluated to determine its limitations for the future scope of research.

Discrete-time survival data with longitudinal covariates.

Survival analysis has been conventionally performed on a continuous time scale. In practice, the survival time is often recorded or handled on a discrete scale; when this is the case, the discrete-time survival analysis would provide analysis results more relevant to the actual data scale. Besides, data on time-dependent covariates in the survival analysis are usually collected through intermittent follow-ups, resulting in the missing and mismeasured covariate data. In this work, we propose the sufficient discrete hazard (SDH) approach to discrete-time survival analysis with longitudinal covariates that are subject to missingness and mismeasurement. The SDH method employs the conditional score idea available for dealing with mismeasured covariates, and the penalized least squares for estimating the missing covariate value using the regression spline basis. The SDH method is developed for the single event analysis with the logistic discrete hazard model, and for the competing risks analysis with the multinomial logit model. Simulation results revel good finite-sample performances of the proposed estimator and the associated asymptotic theory. The proposed SDH method is applied to the scleroderma lung study data, where the time to medication withdrawal and time to death were recorded discretely in months, for illustration.

Temporally coherent cardiac motion tracking from cine MRI: Traditional registration method and modern CNN method.

PurposeCardiac motion tracking enables quantitative evaluation of myocardial strain, which is clinically interesting in cardiovascular disease research. However, motion tracking is difficult to perform manually. In this paper, we aim to develop and compare two fully automated motion tracking methods for the steady state free precession (SSFP) cine magnetic resonance imaging (MRI), and explore their use in real clinical scenario with different patient groups.MethodsWe proposed two automated cardiac motion tracking method: (a) a traditional registration‐based method, named full cardiac cycle registration, which simultaneously tracks all cine frames within a full cardiac cycle by joint registration of all frames; and (b) a modern convolutional neural network (CNN)‐based method, named Groupwise MotionNet, which enhances the temporal coherence by fusing motion along a continuous time scale. Both methods were evaluated on the healthy volunteer data from the MICCAI 2011 STACOM Challenge, as well as on patient data including hypertrophic cardiomyopathy (HCM) and myocardial infarction (MI).ResultsThe full cardiac cycle registration method achieved an average end‐point error (EPE) 2.89 ± 1.57 mm for cardiac motion tracking, with computation time of around 9 min per short‐axis cine MRI (size 128 × 128, 30 cardiac phases). In comparison, the Groupwise MotionNet achieved an average EPE of 0.94 ± 1.59 mm, taking < 1 s for a full cardiac phases. Further experiments showed that registration method had stable performance, independent of patient cohort and MRI machine, while the CNN‐based method relied on the training data to deliver consistently accurate results.ConclusionBoth registration‐based and CNN‐based method can track the cardiac motion from SSFP cine MRI in a fully automated manner, while taking temporal coherence into account. The registration method is generic, robust, but relatively slow; the CNN‐based method trained with heterogeneous data was able to achieve high tracking accuracy with real‐time performance.

Neuroanatomical spread of amyloid β and tau in Alzheimer's disease: implications for primary prevention.

With recent advances in our understanding of the continuous pathophysiological changes that begin many years prior to symptom onset, it is now apparent that Alzheimer’s disease cannot be adequately described by discrete clinical stages, but should also incorporate the continuum of biological changes that precede and underlie the clinical representation of the disease. By jointly considering longitudinal changes of all available biomarkers and clinical assessments, variation within individuals can be integrated into a single continuous measure of disease progression and used to identify the earliest pathophysiological changes. Disease time, a measure of disease severity, was estimated using a Bayesian latent time joint mixed-effects model applied to an array of imaging, biomarker and neuropsychological data. Trajectories of regional amyloid β and tau PET uptake were estimated as a function of disease time. Regions with early signs of elevated amyloid β uptake were used to form an early, focal composite and compared to a commonly used global composite, in a separate validation sample. Disease time was estimated in 279 participants (183 cognitively unimpaired individuals, 61 mild cognitive impairment and 35 Alzheimer’s disease dementia patients) with available amyloid β and tau PET data. Amyloid β PET uptake levels in the posterior cingulate and precuneus start high and immediately increase with small increases of disease time. Early elevation in tau PET uptake was found in the inferior temporal lobe, amygdala, banks of the superior temporal sulcus, entorhinal cortex, middle temporal lobe, inferior parietal lobe and the fusiform gyrus. In a separate validation sample of 188 cognitively unimpaired individuals, the early, focal amyloid β PET composite showed a 120% increase in the accumulation rate of amyloid β compared to the global composite (P < 0.001), resulting in a 60% increase in the power to detect a treatment effect in a primary prevention trial design. Ordering participants on a continuous disease time scale facilitates the inspection of the earliest signs of amyloid β and tau pathology. To detect early changes in amyloid β pathology, focusing on the earliest sites of amyloid β accumulation results in more powerful and efficient study designs in early Alzheimer’s disease. Targeted composites could be used to re-examine the thresholds for amyloid β-related study inclusion, especially as the field shifts to focus on primary and secondary prevention. Clinical trials of anti-amyloid β treatments may benefit from the use of focal composites when estimating drug effects on amyloid β and tau changes in populations with minimal amyloid β and tau pathology and limited expected short-term accumulation.

An Experiment in Weather Prediction for North East and South West Monsoon Over Chennai

There is a growing demand for spot specific forecast. Presently this has to be extracted from the regional forecast based on synoptic models. Synoptic models require input from various observatories of regions or the country and the central analysis centre is required for generating the synoptic charts. But recently the authors have established the potential of local data alone as a continuous time scale for use in effective local forecast using data mining techniques. Following the same association rule mining and classifier approach is tried for the forecast of wet and dog days on North East Monsoon and South West Monsoon months for the Chennai region with Latitude 13°11' N and Longitude 80°11' E, a coastal station over Bay of Bengal in South India and results are presented.

Introduction, analysis and asymptotic behavior of a multi-level manpower planning model in a continuous time setting under potential department contraction

A mathematical model in a multi-level manpower planning setting is developed and analyzed incorporating the divisions of an organization’s personnel into several homogeneous groups. The proposed framework builds upon recent research to develop, via the continuous time scale, a departmental model encompassing employees flows within departments (intra-departmental transitions), as well as transfers among departments (inter-departmental transitions). Management-wise, this is a common practice under certain conditions as in restructuring and rightsizing ventures both in private industries and in the public sector. After establishing the baseline differential equations of the system, an investigation follows regarding the system’s limiting behavior integrating the concept of department contraction which can be seen as an indirect and mild control that can be exercised on the manpower system. It is proved that under a set of conditions, the system’s limiting structure exists and is specified. The aforementioned asymptotic analysis can be utilized to predict, in the long run, future stock structures of departments and thus, in the case where these structures diverge from the desired ones, identify departments that could be considered as candidates for probable rightsizing or mergers. The paper concludes with a numerical illustration and some concluding remarks.

Bolus arrival time estimation in dynamic contrast-enhanced magnetic resonance imaging of small animals based on spline models

Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) is used to quantify perfusion and vascular permeability. In most cases a bolus arrival time (BAT) delay exists between the arterial input function (AIF) and the contrast agent arrival in the tissue of interest which needs to be estimated. Existing methods for BAT estimation are tailored to tissue concentration curves, which have a fast upslope to the peak as frequently observed in patient data. However, they may give poor results for curves that do not have this characteristic shape such as tissue concentration curves of small animals. In this paper, we propose a method for BAT estimation of signals that do not have a fast upslope to their peak. The model is based on splines which are able to adapt to a large variety of concentration curves. Furthermore, the method estimates BATs on a continuous time scale. All relevant model parameters are automatically determined by generalized cross validation. We use simulated concentration curves of small animal and patient settings to assess the accuracy and robustness of our approach. The proposed method outperforms a state-of-the-art method for small animal data and it gives competitive results for patient data. Finally, it is tested on in vivo acquired rat data where accuracy of BAT estimation was also improved upon the state-of-the-art method. The results indicate that the proposed method is suitable for accurate BAT estimation of DCE-MRI data, especially for small animals.