Parameter identification in a tuberculosis model for Cameroon.

A deterministic model of tuberculosis in Cameroon is designed and analyzed with respect to its transmission dynamics. The model includes lack of access to treatment and weak diagnosis capacity as well as both frequency- and density-dependent transmissions. It is shown that the model is mathematically well-posed and epidemiologically reasonable. Solutions are non-negative and bounded whenever the initial values are non-negative. A sensitivity analysis of model parameters is performed and the most sensitive ones are identified by means of a state-of-the-art Gauss-Newton method. In particular, parameters representing the proportion of individuals having access to medical facilities are seen to have a large impact on the dynamics of the disease. The model predicts that a gradual increase of these parameters could significantly reduce the disease burden on the population within the next 15 years.

A mathematical model of the human menstrual cycle for the administration of GnRH analogues.

The paper presents a differential equation model for the feedback mechanisms between gonadotropin-releasing hormone (GnRH), follicle-stimulating hormone (FSH), luteinizing hormone (LH), development of follicles and corpus luteum, and the production of estradiol (E2), progesterone (P4), inhibin A (IhA), and inhibin B (IhB) during the female menstrual cycle. Compared to earlier human cycle models, there are three important differences: The model presented here (a) does not involve any delay equations, (b) is based on a deterministic modeling of the GnRH pulse pattern, and (c) contains less differential equations and less parameters. These differences allow for a faster simulation and parameter identification. The focus is on modeling GnRH-receptor binding, in particular, by inclusion of a pharmacokinetic/pharmacodynamic (PK/PD) model for a GnRH agonist, Nafarelin, and a GnRH antagonist, Cetrorelix, into the menstrual cycle model. The final mathematical model describes the hormone profiles (LH, FSH, P4, E2) throughout the menstrual cycle of 12 healthy women. It correctly predicts hormonal changes following single and multiple dose administration of Nafarelin or Cetrorelix at different stages in the cycle.

A complex mathematical model of the human menstrual cycle.

Despite the fact that more than 100 million women worldwide use birth control pills and that half of the world's population is concerned, the menstrual cycle has so far received comparatively little attention in the field of mathematical modeling. The term menstrual cycle comprises the processes of the control system in the female body that, under healthy circumstances, lead to ovulation at regular intervals, thus making reproduction possible. If this is not the case or ovulation is not desired, the question arises how this control system can be influenced, for example, by hormonal treatments. In order to be able to cover a vast range of external manipulations, the mathematical model must comprise the main components where the processes belonging to the menstrual cycle occur, as well as their interrelations. A system of differential equations serves as the mathematical model, describing the dynamics of hormones, enzymes, receptors, and follicular phases. Since the processes take place in different parts of the body and influence each other with a certain delay, passing over to delay differential equations is deemed a reasonable step. The pulsatile release of the gonadotropin-releasing hormone (GnRH) is controlled by a complex neural network. We choose to model the pulse time points of this GnRH pulse generator by a stochastic process. Focus in this paper is on the model development. This rather elaborate mathematical model is the basis for a detailed analysis and could be helpful for possible drug design.

Visualization of the variability of 3D statistical shape models by animation.

Models of the 3D shape of anatomical objects and the knowledge about their statistical variability are of great benefit in many computer assisted medical applications like images analysis, therapy or surgery planning. Statistical model of shapes have successfully been applied to automate the task of image segmentation. The generation of 3D statistical shape models requires the identification of corresponding points on two shapes. This remains a difficult problem, especially for shapes of complicated topology. In order to interpret and validate variations encoded in a statistical shape model, visual inspection is of great importance. This work describes the generation and interpretation of statistical shape models of the liver and the pelvic bone.

Clinical use of the hyperthermia treatment planning system HyperPlan to predict effectiveness and toxicity.

PURPOSE: The main aim is to prove the clinical practicability of the hyperthermia treatment planning system HyperPlan on a beta-test level. Data and observations obtained from clinical hyperthermia are compared with the numeric methods FE (finite element) and FDTD (finite difference time domain), respectively. METHODS AND MATERIALS: The planning system HyperPlan is built on top of the modular, object-oriented platform for visualization and model generation AMIRA. This system already contains powerful algorithms for image processing, geometric modeling, and three-dimensional graphics display. A number of hyperthermia-specific modules are provided, enabling the creation of three-dimensional tetrahedral patient models suitable for treatment planning. Two numeric methods, FE and FDTD, are implemented in HyperPlan for solving Maxwell's equations. Both methods base their calculations on segmented (contour based) CT or MR image data. A tetrahedral grid is generated from the segmented tissue boundaries, consisting of approximately 80,000 tetrahedrons per patient. The FE method necessitates, primarily, this tetrahedral grid for the calculation of the E-field. The FDTD method, on the other hand, calculates the E-field on a cubical grid, but also requires a tetrahedral grid for correction at electrical interfaces. In both methods, temperature distributions are calculated on the tetrahedral grid by solving the bioheat transfer equation with the FE method. Segmentation, grid generation, E-field, and temperature calculation can be carried out in clinical practice at an acceptable time expenditure of about 1-2 days. RESULTS: All 30 patients we analyzed with cervical, rectal, and prostate carcinoma exhibit a good correlation between the model calculations and the attained clinical data regarding acute toxicity (hot spots), prediction of easy-to-heat or difficult-to-heat patients, and the dependency on various other individual parameters. We could show sufficient agreement between the calculations and measurements for power density (specific absorption rate) within the range of assessed precision. Tumor temperatures can only be estimated, because of the rather variable perfusion conditions. The results of the FE and FDTD methods are comparable, although slight differences exist resulting from the differences in the underlying models. There are also statistically provable differences among the tumor entities regarding the attained specific absorption rate, temperatures, and volume loads in normal tissue. However, gross fluctuations exist from patient to patient. CONCLUSION: The hyperthermia planning system HyperPlan could be validated for a number of the 30 patients. Further improvements in the implemented models, FE and FDTD, are required. Even at its present state of development, hyperthermia planning for regional hyperthermia delivers valuable information, not only for clinical practice, but also for further technologic improvements.

Experimental and numerical investigation of feed-point parameters in a 3-D hyperthermia applicator using different FDTD models of feed networks.

Experimental and numerical methods were used to determine the coupling of energy in a multichannel three-dimensional hyperthermia applicator (SIGMA-Eye), consisting of 12 short dipole antenna pairs with stubs for impedance matching. The relationship between the amplitudes and phases of the forward waves from the amplifiers, to the resulting amplitudes and phases at the antenna feed-points was determined in terms of interaction matrices. Three measuring methods were used: 1) a differential probe soldered directly at the antenna feed-points; 2) an E-field sensor placed near the feed-points; and 3) measurements were made at the outputs of the amplifier. The measured data were compared with finite-difference time-domain (FDTD) calculations made with three different models. The first model assumes that single antennas are fed independently. The second model simulates antenna pairs connected to the transmission lines. The measured data correlate best with the latter FDTD model, resulting in an improvement of more than 20% and 20 degrees (average difference in amplitudes and phases) when compared with the two simpler FDTD models.