van Naw Natal Riel

On the identifiability of pharmacokinetic parameters in dynamic contrast‐enhanced imaging

The so‐called “Kety model” is a two‐compartment pharmacokinetic model describing tumor perfusion kinetics. Its parameters, the transendothelial transfer constant (Ktrans), extravascular extracellular volume fraction (υe), and microvascular plasma volume fraction (υp), can be estimated with dynamic contrast‐enhanced magnetic resonance imaging (DCE‐MRI). However, the results obtained by current methods show large variation in predictability and reliability. Here, the aim was to examine which experimental conditions have to be fulfilled to avoid large uncertainties and mutual dependencies of the parameters. Using frequency response analysis and simulation, the identifiability of the model was examined. The requirements and influence of contrast enhancement measurements, such as temporal resolution, signal to noise ratio, and contrast injection rate, on the accuracy of the parameters were analyzed. Tissue response characteristics revealed a low‐frequency system with a cutoff frequency equal to Ktrans/υe, which confines the required temporal resolution. For malignant tissue with hyperpermeable vasculature (high Ktrans) a higher sampling frequency is required to accurately estimate Ktrans than for normal tissue. Too low sampling rates or too low injection rates resulted in inaccurate Ktrans values and hereby unreliable classification of malignant tissue. Magn Reson Med 58:425–429, 2007.

A Bayesian approach to targeted experiment design

Motivation: Systems biology employs mathematical modelling to further our understanding of biochemical pathways. Since the amount of experimental data on which the models are parameterized is often limited, these models exhibit large uncertainty in both parameters and predictions. Statistical methods can be used to select experiments that will reduce such uncertainty in an optimal manner. However, existing methods for optimal experiment design (OED) rely on assumptions that are inappropriate when data are scarce considering model complexity. Results: We have developed a novel method to perform OED for models that cope with large parameter uncertainty. We employ a Bayesian approach involving importance sampling of the posterior predictive distribution to predict the efficacy of a new measurement at reducing the uncertainty of a selected prediction. We demonstrate the method by applying it to a case where we show that specific combinations of experiments result in more precise predictions. Availability and implementation: Source code is available at: http://bmi.bmt.tue.nl/sysbio/software/pua.html Contact: j.vanlier@tue.nl; N.A.W.v.Riel@tue.nl Supplementary information: Supplementary data are available at Bioinformatics online.

An integrated strategy for prediction uncertainty analysis

Motivation: To further our understanding of the mechanisms underlying biochemical pathways mathematical modelling is used. Since many parameter values are unknown they need to be estimated using experimental observations. The complexity of models necessary to describe biological pathways in combination with the limited amount of quantitative data results in large parameter uncertainty which propagates into model predictions. Therefore prediction uncertainty analysis is an important topic that needs to be addressed in Systems Biology modelling. Results: We propose a strategy for model prediction uncertainty analysis by integrating profile likelihood analysis with Bayesian estimation. Our method is illustrated with an application to a model of the JAK-STAT signalling pathway. The analysis identified predictions on unobserved variables that could be made with a high level of confidence, despite that some parameters were non-identifiable. Availability and implementation: Source code is available at: http://bmi.bmt.tue.nl/sysbio/software/pua.html. Contact: j.vanlier@tue.nl Supplementary information: Supplementary data are available at Bioinformatics online.

System identification theory in pharmacokinetic modeling of dynamic contrast‐enhanced MRI: Influence of contrast injection

Optimization of experimental settings of dynamic contrast‐enhanced magnetic resonance imaging (DCE‐MRI), like the contrast administration protocol, is of great importance for reliable quantification of the microcirculatory properties, such as the volume transfer‐constant Ktrans. Using system identification theory and computer simulations, the confounding effects of volume, rate and multiplicity of a contrast injection on the reliability of Ktrans estimation was assessed. A new tracer‐distribution model (TDM), based on in vivo data from rectal cancer patients, served to describe the relationship between the contrast agent injection and the blood time‐course. A pharmacokinetic model (PKM) was used to describe the relation between the blood and tumor tissue time‐courses. By means of TDM and PKM in series, the tissue‐transfer function of the PKM was analyzed. As both the TDM and PKM represented low‐frequency‐pass filters, the energy‐density at low frequencies of the blood and tissue time‐courses was larger than at high frequencies. The simulations, based on measurements in humans, predict that the Ktrans is most reliable with a high injection volume administered in a single injection, where high rates only modestly improve Ktrans. Magn Reson Med 59:1111–1119, 2008.

The use of a reference tissue arterial input function with low-temporal-resolution DCE-MRI data

Pharmacokinetic modeling is a promising quantitative analysis technique for cancer diagnosis. However, diagnostic dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) of the breast is commonly performed with low temporal resolution. This limits its clinical utility. We investigated for a range of temporal resolutions whether pharmacokinetic parameter estimation is impacted by the use of data-derived arterial input functions (AIFs), obtained via analysis of dynamic data from a reference tissue, as opposed to the use of a standard AIF, often obtained from the literature. We hypothesized that the first method allows the use of data at lower temporal resolutions than the second method. Test data were obtained by downsampling high-temporal-resolution rodent data via a k-space-based strategy. To fit the basic Tofts model, either the data-derived or the standard AIF was used. The resulting estimates of K(trans) and v(e) were compared with the standard estimates obtained by using the original data. The deviations in K(trans) and v(e), introduced when lowering temporal resolution, were more modest using data-derived AIFs compared with using a standard AIF. Specifically, lowering the resolution from 5 to 60 s, the respective changes in K(trans) were 2% (non-significant) and 18% (significant). Extracting the AIF from a reference tissue enables accurate pharmacokinetic parameter estimation for low-temporal-resolution data.

Modeling glucose and water dynamics in human skin.

BACKGROUND Glucose is heterogeneously distributed in the different physiological compartments in the human skin. Therefore, for the development of a noninvasive measurement method, both a good quantification of the different compartments of human skin and an understanding of glucose transport processes are important. METHODS The composition of human skin was quantified by histology research. Based on this information a mathematical model was developed to simulate glucose dynamics in human skin. RESULTS The model predicts dynamically glucose concentrations in the different layers of the skin as a result of changes in blood glucose concentration. The model was validated with published time course data of blood and interstitial fluid glucose during a clamp study with three different set points for blood glucose, and model outcomes were compared to measurements for the lag time and gradient. According to the model, glucose in the interstitial fluid of the dermis best matches the amplitude and dynamics of blood glucose. CONCLUSIONS The new data obtained from quantitative histology appeared crucial for the model. The proposed model was successfully validated. This result was obtained without tuning or fitting of any parameter. It was shown how the model can be used to set standards for measurements and to define the best measurement depth for noninvasive glucose monitoring.

Mathematical modelling of the calcium-left ventricular pressure relationship in the intact diabetic rat heart

Aim:  The objective was to characterize cross‐bridge kinetics from the cytoplasmic calcium ion concentration ([Ca2+]i) and the left ventricular pressure (LVP) in the early‐stage diabetic rat heart under baseline conditions and upon β‐adrenergic stimulation.

Qualitative analysis of nonlinear biochemical networks with piecewise-affine functions

Nonlinearities and the lack of accurate quantitative information considerably hamper modeling and system analysis of biochemical networks. Here we propose a procedure for qualitative mathematical analysis of piecewise-affine (PWA) approximations of these networks. First the biochemical model size was reduced with quasi-steady state approaches by taking a priori information into account. Second, a conversion of a nonlinear model into a PWA approximation and subsequent qualitative analysis of this model was performed. This resulted in different sets of transition graphs that depend on the parameter values, which enables reduction of the parameter search space.

Identifiability analysis of the standard pharmacokinetic models in DCE MR imaging of tumours

The usage of dynamic contrast-enhanced MRI (DCE-MRI) as a clinical tool is still widely assessed. Application of the standard pharmacokinetic models to obtain physiologically relevant parameter values using DCE-MRI in tumours is not trivial, when the temporal resolution is low. Mathematical analysis and analysis by simulation of the identifiability for the generalized and extended Kety models was executed. Parameter estimation was executed using synthetic data sets and maximum likelihood estimation (MLE). The influence of temporal resolution was examined. The generalized and extended Kety model showed a large bias in the parameter estimates (10-120%) for sampling times >4 s, although the estimated variance was relatively low (<1%). This was in accordance with the generated contour plots of the hyperplane of the MLE cost-function. The influence of measurement noise on the input and output turned out to be less significant than the temporal resolution.

Analysis of the transforming growth factor-/spl beta//sub 1/ pathway and extracellular matrix formation as a hybrid system

It is generally accepted that aging of the vascular system plays an important role in cardiovascular disease (CVD). Recent experimental findings have indicated the involvement of the cytokine transforming growth factor-/spl beta//sub 1/ (TGF-/spl beta//sub 1/) in these vascular aging processes. This cytokine is, after binding to a cell receptor, associated with numerous cellular processes, including formation of the extracellular matrix (ECM, the biomolecular network that surrounds the cell). We implemented TGF-/spl beta//sub 1/ signaling and its effect on ECM formation with piecewise-linear differential equations (PLDEs), which have several advantageous properties over traditional continuous modeling. Aging of the system was simulated as a reduction in cell sensitivity for TGF-/spl beta//sub 1/. The model predicted a disturbed ECM balance during aging, which corresponds well to findings from the literature. The outcome of this hybrid approach was satisfactory and, therefore, we will continue modeling of various aging-related pathways with PLDEs in future research.