## 1 Introduction
The so-called primary or independent parameters include plasma volume, plasma flow, interstitial volume and permeability product [9]. Based on these attributes, one may derive dependent parameters, i.e., the extraction fraction and the volume transfer constant. The latter, denoted as \(K^{trans}\), characterizes regional renal filtration, as it measures the ratio of plasma flow that is transferred from the glomerular capillary bed into the Bowman's space. \(K^{trans}\) multiplied by the kidney volume leads to an estimate of the glomerular filtration rate, and is therefore a central descriptor in quantifying kidney function. In this study, we propose to use a multi-layer perceptron (MLP) network for PK model parameter estimation, instead of the non-linear least-squares curve-fitting method. The rationale behind this concept arises from the fact that the results of the iterative methods may be located in a local and--in general--suboptimal solution. Thus, the outcome depends largely on the initial choice of parameter values. Moreover, one usually has to establish constraints on the expected parameter values, so that the result falls into a physiologically feasible range. Bounds that are too narrow, however, may prevent the fitting algorithm from finding an optimum. Contrary to NLLS, MLP does not require that one provides the initial parameter values; moreover, it ensures the optimal solution when properly trained. Although MLP networks could be regarded as a legacy method, they are still in use, and prove efficient in complex non-linear regression problems [11; 12]. Moreover, according to the universal approximation theorem, an artificial neural network with at least one hidden layer of nonpolynomial activation (such as sigmoid or rectified linear) can model any measurable function that maps one finite-dimensional space to another, provided the hidden layers contain enough units [13]. Therefore, MLP seems to be particularly usefully in its application to the specific problem of PK model parameter estimation in renal DCE-MRI examinations. Also, the reliability of the fitted PK model parameters is conditioned by--among other factors--the determination of the arterial input function (AIF), i.e., the tracer concentration's time course in the feeding artery. The standard way of annotating AIF consists of estimating it for each patient. However, other approaches are accepted if patient-specific AIF measurements are not possible. Such problems can arise due to data acquisition constraints or the lack of a suitable artery within the imaging field of view. In the alternative strategy, one either utilizes a population-based mean AIF [14] (calculated for a cohort of studies, where it is feasible to do so) or defines its parameterized functional form [15]. In this study, we implicitly follow the population-based approach. The neural network is trained using a pool of AIFs automatically derived for a subset of available DCE images. Then, the GFR for an individual test case is estimated without the need to determine the case-specific AIF. To sum up, the main contribution of this paper is the establishment of the architecture of an MLP network for estimating parameters of the 2 CFM, based solely on image intensity time courses in the kidney region. Additionally, a side-contribution is the introduction of the algorithm for automatic determination of the AIF in DCE-MRI examinations. The latter achievement was needed in order to construct the data set for MLP training, but the algorithm can be equally used in standard approaches to PK modeling.