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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.

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., (Copyright © 2012 Elsevier Ltd. All rights reserved.)

Bovine fertility is the subject of extensive research in animal sciences, especially because fertility of dairy cows has declined during the last decades. The regulation of estrus is controlled by the complex interplay of various organs and hormones. Mathematical modeling of the bovine estrous cycle could help in understanding the dynamics of this complex biological system. In this paper we present a mechanistic mathematical model of the bovine estrous cycle that includes the processes of follicle and corpus luteum development and the key hormones that interact to control these processes. The model generates successive estrous cycles of 21 days, with three waves of follicle growth per cycle. The model contains 12 differential equations and 54 parameters. Focus in this paper is on development of the model, but also some simulation results are presented, showing that a set of equations and parameters is obtained that describes the system consistent with empirical knowledge. Even though the majority of the mechanisms that are included in the model are based on relations that in the literature have only been described qualitatively (i.e. stimulation and inhibition), the output of the model is surprisingly well in line with empirical data. This model of the bovine estrous cycle could be used as a basis for more elaborate models with the ability to study effects of external manipulations and genetic differences., (Copyright © 2011 Elsevier Ltd. All rights reserved.)

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.

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.

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 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.

Objectives: In multiantenna applicators such as the SIGMA-60 or SIGMA-Eye, which consist of 4 or 12 pairs of antennas shunt to 4 or 12 amplifiers ("antenna couplets"), phases and amplitudes in the feed points of these antennas under certain conditions can significantly differ from the values selected at the multichannel amplifier (forward parameters), mainly due to coupling. In the SIGMA-Eye, this interaction is particularly affected by the transforming networks between the generators and the feed points, thus hampering the control of the feed point parameters. In this work, we perform measurements at existing applicators, present a formalism to describe the facts numerically, and investigate modifications of the transforming networks to improve the performance., Methods and Materials: We prepared an experimental setup for the SIGMA-Eye applicator that is fed by forward waves of a 12-channel amplifier system. In this setup, we made the water bolus, the interior of the tissue-equivalent phantom, and the entire transforming network accessible for measuring probes. Then, we constructed various alternative transforming networks such as Pawsey loops, LC matching networks, and power dividers and compared them with the original matching network of the SIGMA-Eye applicator. In particular, we utilized a high-resistive probe to determine the disturbances and influences caused by some channels with respect to some selected feed points of the SIGMA-Eye dipoles., Results: In the original SIGMA-Eye applicator, the influences of coupling channels on the phases and voltages in the feed point of a particular antenna are largest for adjacent longitudinal channels. Here, the +/- 10 degrees phase shift and +/- 30% voltage change were observed if the reference channel (i.e., the disturbed channel) and disturbing channel are equally powered. The changes eminently increased to -30 degrees to + 100 degrees phase shift and -80% to +50% voltage change if the reference channel is fed with much lower power (four to eight-fold) than the disturbing channel. The disturbance from distant channels is less but still significant, reaching shifts of -10 degrees to +50 degrees and -50% to +20%, respectively. Using Pawsey loops instead of the original ferrite rings in the SIGMA-Eye network, the efficacy of the baluns was improved by a more than a factor of 4. Using an LC matching network, dependencies on frequency and external arrangements can be reduced significantly. Applying a power divider circuit, the coupling between antennas combined to one channel is considerably diminished (down to <-25 dB)., Conclusion: Coupling between resonators (pairs of antennas including the matching network) reduces the control of the SIGMA-Eye applicator, i.e., it causes deviations between the selection of forward parameters at the amplifier and the total actual parameters in the feed points of the antennas. Modified transformation networks can improve the control, in particular by reducing sheath currents and asymmetries. There is a linear but variable relationship between selected (amplifiers) and actually given (feed points) parameters. This linear mapping (described by a matrix) and its characteristics need further investigation.

Background: A hyperthermia planning system has been developed for generating patient and applicator models as well as calculating and visualizing E-field and temperature distributions. Significant dependencies on models and algorithms have been found., Methods: Computerized tomography (CT) data sets are first transformed into so called 'labelled CT-volume'-data sets of equal resolution, which are used for segmentation. The first type of patient model obtained subsequently is based on regions with specified electrical properties representing tissues or organs (so called 'region-based model'). The second patient model renders a direct transformation of Hounsfield Units (HU) to electrical constants (so called 'HU-based model'). The FDTD-method (finite difference time domain) is then applied on a cubic lattice employing either an auxiliary 'sub-cubic lattice' (for HU-based segmentation) or a tetrahedron grid (for region-based segmentation) to assign the electrical properties, both representing the anatomy of the patient. E-field distributions are corrected by a post-processing procedure with respect to the geometry of interfaces defined by the tetrahedron grid. For comparison, the VSIE method (volume surface integral equation) is performed on the same tetrahedron grid. The applicator model assumes eight half-wavelength dipole antennas fed with constant voltages with water as background medium., Results: For both numerical methods (FDTD, VSIE) the resulting antenna input impedances as well as the current distributions along the antennas were quite similar and almost insensitive to the particular geometry model (region-based, HU-based). In contrast to that, the power deposition patterns in the interior of the patient depended strongly on those models. Major differences can be related to different labels of the tissue type bone in the HU-based model in comparison to the definition via regions. Conversely, comparable results were obtained using the VSIE method and the FDTD method on the region-based patient model with a posteriori correction at the tetrahedron grid points. SAR (specific absorption rate) elevations up to a factor of 10 were predicted when employing region-based models. Those peaks might correspond to specific toxicity of electromagnetic radiation clinically known as hot spot phenomena or musculo-skeletal syndromes. Conversely, HU-based models generated quite homogeneous power deposition patterns with fluctuations of at most factor 2., Conclusion: The methods employing region-based geometry models such as the VSIE method and FDTD method in conjunction with a posteriori correction at tissue interfaces result in comparable E-field distributions for regional hyperthermia. Due to its shorter calculation time, the FDTD method is currently used in the clinic. Predictions derived from HU-based models without prior corrections of tissue specifications are not always supported by clinical experience.

Time-efficient and easy-to-use segmentation algorithms (contour generation) are a precondition for various applications in radiation oncology, especially for planning purposes in hyperthermia. We have developed the three following algorithms for contour generation and implemented them in an editor of the HyperPlan hyperthermia planning system. Firstly, a manual contour input with numerous correction and editing options. Secondly, a volume growing algorithm with adjustable threshold range and minimal region size. Thirdly, a watershed transformation in two and three dimensions. In addition, the region input function of the Helax commercial radiation therapy planning system was available for comparison. All four approaches were applied under routine conditions to two-dimensional computed tomographic slices of the superior thoracic aperture, mid-chest, upper abdomen, mid-abdomen, pelvis and thigh; they were also applied to a 3D CT sequence of 72 slices using the three-dimensional extension of the algorithms. Time to generate the contours and their quality with respect to a reference model were determined. Manual input for a complete patient model required approximately 5 to 6 h for 72 CT slices (4.5 min/slice). If slight irregularities at object boundaries are accepted, this time can be reduced to 3.5 min/slice using the volume growing algorithm. However, generating a tetrahedron mesh from such a contour sequence for hyperthermia planning (the basis for finite-element algorithms) requires a significant amount of postediting. With the watershed algorithm extended to three dimensions, processing time can be further reduced to 3 min/slice while achieving satisfactory contour quality. Therefore, this method is currently regarded as offering some potential for efficient automated model generation in hyperthermia. In summary, the 3D volume growing algorithm and watershed transformation are both suitable for segmentation of even low-contrast objects. However, they are not always superior to user-friendly manual programs for contour generation. When the volume growing algorithm is used, the contours have to be postprocessed with suitable filters. The watershed transformation has a large potential if appropriately developed to 3D sequences and 3D interaction features. After all, the practicality and feasibility of every segmentation method critically depend on various details of the user software as pointed out in this article.

A theoretical framework is presented for optimized heating of deep-seated tumours by phase and amplitude steering. The optimization problem for a specific tumour and perfusion case results in a functional dependency between power-level and maximum obtainable therapeutic efficiency. Different optimization criteria and strategies are outlined, which cause an increase of power or thermal dose in the tumour. Three tumour models (central pelvic tumour, eccentric abdominal tumour with or without necrosis) are analysed in detail. The simulation studies predict that appreciable parts of these tumours (50-100%) can be heated efficiently (42.5-43 degrees C) within the range of available and clinically tolerated power levels (1-5 kW/m), if tumour perfusion is less than 20-25 ml/100 g min. Some improvements are obtained by increasing the number of independent channels (from four to eight) and by the application of time-dependent (complementary) power-deposition patterns.

For indicator-dilution studies, complete thermal recovery after passage of heat through the pulmonary circulation would be desirable. However, the results in the literature obtained by extrapolation techniques are inconsistent. To overcome problems of the extrapolation approach, transport functions of the pulmonary circulation (including the left heart) were computed by deconvolution of pulmonary arterial and aortic pairs of thermodilution curves after central venous indicator injection (10 ml of an ice-cold blood indocyanine green dye mixture). Thermal recovery was determined as the finite integral of the transport function. Thirteen mongrel dogs under piritramid-N2O anesthesia were examined under base-line conditions, in orthostasis to alter the distribution of pulmonary blood flow (9 dogs), and in oleic acid edema (8 dogs). Using the deconvolution approach, thermal recovery was 0.97 +/- 0.04 under base-line conditions, 0.96 +/- 0.03 in orthostasis, and 0.96 +/- 0.05 in pulmonary edema. Thermal recovery determined from extrapolated dilution curves was greater than 100% in all groups, a physically impossible finding. It is concluded that thermal recovery is incomplete but insensitive with respect to the distribution of blood flow and to the size of the extravascular compartment. Monoexponential extrapolation is unsuited for the determination of thermal recovery.

This study evaluates the routine mathematic approach (monoexponential extrapolation) for analysis of transpulmonary thermal-dye dilution curves and estimates the effects of systemic-indicator recirculation by use of a deconvolution technique. Fifteen dogs anesthetized with N2O-piritramid were studied before and after induction of pulmonary edema by oleic acid. After introduction of central venous indicator (10 ml of a mixture of cold blood and indocyanine green dye), dilution data were recorded from the pulmonary artery and the ascending aorta. The conclusions were: (1) monoexponential extrapolation yields reasonably good estimates of the mean transit times of dye; (2) mean transit times of heat are usually overestimated by monoexponential extrapolation; (3) extravascular lung thermal volume assessed by monoexponential extrapolation is overestimated by 2.03 ml/kg of body mass under baseline conditions; and (4) the prepulmonary volume of distribution of heat exceeds that of dye by 1.4 ml/kg of body mass, thus increasing the overestimation of pulmonary extravascular heat-accessible space by the conventional technique.