Parameter estimation for linear compartmental models--a sensitivity analysis approach

Mathematical Models for FDG Kinetics in Cancer: A Review

Compartmental analysis is the mathematical framework for the modelling of tracer kinetics in dynamical Positron Emission Tomography. This paper provides a review of how compartmental models are constructed and numerically optimized. Specific focus is given on the identifiability and sensitivity issues and on the impact of complex physiological conditions on the mathematical properties of the models.

The role of endoplasmic reticulum in in vivo cancer FDG kinetics

A recent result obtained by means of an in vitro experiment with cancer cultured cells has configured the endoplasmic reticulum as the preferential site for the accumulation of 2-deoxy-2-[¹⁸F]fluoro-D-glucose (FDG). Such a result is coherent with cell biochemistry and is made more significant by the fact that the reticular accumulation rate of FDG is dependent upon extracellular glucose availability. The objective of the present paper is to confirm in vivo the result obtained in vitro concerning the crucial role played by the endoplasmic reticulum in FDG cancer metabolism. This study utilizes data acquired by means of a Positron Emission Tomography scanner for small animals in the case of CT26 models of cancer tissues. The recorded concentration images are interpreted within the framework of a three-compartment model for FDG kinetics, which explicitly assumes that the endoplasmic reticulum is the dephosphorylation site for FDG in cancer cells. The numerical reduction of the compartmental model is performed by means of a regularized Gauss-Newton algorithm for numerical optimization. This analysis shows that the proposed three-compartment model equals the performance of a standard Sokoloff’s two-compartment system in fitting the data. However, it provides estimates of some of the parameters, such as the phosphorylation rate of FDG, more consistent with prior biochemical information. These results are made more solid from a computational viewpoint by proving the identifiability and by performing a sensitivity analysis of the proposed compartment model.

A novel method for hemodynamic analysis of penile erection

Measurement of blood flow velocity through the cavernosal arteries via penile color Doppler ultrasound (PDUS) is the most common objective method for the assessment of erectile function. However, in some clinical cases, this method needs to be augmented via the invasive intracavernosal pressure (ICP) measurement, which is arguably a more direct index for erectile function. The aim of this study is to develop a lumped parameter model (LPM) of the penile circulation mechanism integrated to a pulsatile, patient-specific, bi-ventricular circulation system to estimate ICP values non-invasively. PDUS data obtained from four random patients with erectile dysfunction are used to develop patient-specific LPMs. Cardiac output is estimated from the body surface area. Systemic pressure is obtained by a sphygmomanometer. Through the appropriate parameter set determined by optimization, patient-specific ICP values are predicted with only using PDUS data and validated by pre- and post-papaverine injection cavernosometry measurements. The developed model predicts the ICP with an average error value of 3 mmHg for both phases. Penile size change during erection is predicted with a ~15% error, according to the clinical size measurements. The developed mathematical model has the potential to be used as an effective non-invasive tool in erectile function evaluation, expanding the existing clinical decision parameters significantly.

Computerized evaluation of mean residence times in multicompartmental linear system and pharmacokinetics

Deriving mean residence times (MRTs) is an important task both in pharmacokinetics and in multicompartmental linear systems. Taking as starting point the analysis of MRTs in open or closed (Garcia-Meseguer et al., Bull Math Biol 2003, 65, 279) multicompartmental linear systems, we implement a versatile software, using the Visual Basic 6.0 language for MS-Windows, that is easy to use and with a user-friendly format for the input of data and the output of results. For any multicompartmental linear system of up to 512 compartments, whether closed or open, with traps or without traps and with zero input in one or more of the compartments, this software allows the user to obtain the symbolic expressions, in the most simplified form, and/or the numerical values of the MRTs in any of its compartments, in the entire system or in a part of the system. As far as we known from the literature, such a software has not been implemented before. The advantage of the present software is that it reduces on the work time needed and minimizes the human errors that are frequent in compartmental systems even those that are relatively staightforward. The software bioCelTer, along with instructions, can be downloaded from http://oretano.iele-ab.uclm.es/~fgarcia/bioCelTer/.