A mathematical model of optimized radioiodine-131 therapy of Graves' hyperthyroidism

Background

The current status of radioiodine-131 (RaI) dosimetry for Graves' hyperthyroidism is not clear. Recurrent hyperthyroidism and iatrogenic hypothyroidism are two problems which interact such that trying to solve one leads to exacerbation of the other. Optimized RaI therapy has therefore begun to be defined just in terms of early hypothyroidism (ablative therapy) as physicians have given up on reducing hypothyroidism.

Methods

Optimized therapy is evaluated both in terms of the greatest separation of cure rate from hypothyroidism rate (non-ablative therapy) or in terms of early hypothyroidism (ablative therapy) by mathematical modeling of outcome after radioiodine and critically discussing the three common methods of RaI dosing for Graves' disease.

Results

Cure follows a logarithmic relationship to activity administered or absorbed dose, while hypothyroidism follows a linear relationship. The effect of including or omitting factors in the calculation of the administered I–131 activity such as the measured thyroid uptake and effective half-life of RaI or giving extra compensation for gland size is discussed.

Conclusions

Very little benefit can be gained by employing complicated methods of RaI dose selection for non-ablative therapy since the standard activity model shows the best potential for cure and prolonged euthyroidism. For ablative therapy, a standard MBq/g dosing provides the best outcome in terms of cure and early hypothyroidism.     

A mathematical model of insulin secretion

Diabetes mellitus is a chronic state of excessive blood glucoselevels (hyperglycaemia), which may result from many environmentaland genetic factors, often acting jointly. The major regulatorof glucose concentration in the blood is insulin. It is knownthat about 50% of the insulin is taken up by the liver on passingthrough it after secretion from the pancreas. The precise valueof this fractional uptake is not known, so the prehepatic insulinsecretion rates cannot be readily estimated from the plasmainsulin concentration levels. By utilizing the equimolar secretionof insulin and connecting peptide (C-peptide) from the pancreas,a noninvasive method has been formulated. This was based ona compartmental model which involved the pancreas, liver, andplasma. The resulting differential equation yielded a gammavariate solution which could be readily linearized. The modelwas then tested on 56 normal (51 nonobese and 5 obese) subjects,and three groups of subjects with diabetes who could be labelledas mild, moderate, and severe (based on the fasting plasma glucoseconcentration) with 83, 88, and 64 subjects respectively. Wehave focused on the human patient environment of the clinicianto produce a distinct model which gave a consistent patternwithin all four groups with good fits between observed and theoreticalvalues of the plasma insulin levels. The consequent rates forinsulin secretion were consistent across the groups and wereclinically meaningful.     

A mathematical model of left-ventricular function

A model of the left ventricle is developed which characterises ventricular elastance as a function of end-diastolic volume and time. The heart model is terminated in a modifiedWindkessel load, and accurately simulates the mechanical response of the heart to various various pre- and after-load conditions.     

A mathematical model of post-canalization thrombolysis

During the initial phase of lysis of an occlusive thrombus using lytic agents such as tissue plasminogen activator, blood flow through the centre of the clot is established (the process of recanalization). Following canalization, the clot remains on the vessel wall and further lysis is required. This paper develops a multi-species mathematical model to describe the bulk chemical reactions in the bloodstream and the convective and diffusive transport of chemical species to and from the clot surface in conditions following canalization. For the steady state case, the model indicates that the process of clot lysis following initial recanalization is dominated by surface chemical reactions and the bulk reactions play little role in the lytic process. Lytic rate is dependent on the clot geometry and flow conditions. The rate of clot dissolution is greatest at the upstream end of the clot and decreases steadily downstream due to lytic agent being removed from the flowing blood as it binds to the clot surface. This model may be further developed and used to simulate and compare different lytic regimes.     

A new method for photodynamic therapy of melanotic melanoma -- effects of depigmentation with violet light photodynamic therapy

Melanotic melanomas have a poor response to photodynamic therapy (PDT). The reason for this is that melanin absorbs light over the entire wavelength region used for PDT (400-750 nm). Photobleaching of melanin is an approach to overcome this obstacle. In the present work, reflectance spectroscopy was applied to study depigmentation of human and murine skin with different melanin contents, and effects induced by PDT with topical application of methyl 5-aminolevulinate (MAL) on B16F10 melanotic melanomas transplanted to nude mice. Depigmentation and inhibition of tumor growth after violet light (420 nm) exposure, red light (634 nm) exposure, and combinations of both were studied. Reflectance spectroscopy was suitable for evaluation of the pigmentation of both human and murine skin. Skin depigmentation leads to increase in reflectance. PDT with violet light bleached some of the melanin in the skin above the B16F10 melanomas, and possibly also in the upper part of the melanomas. This resulted in a larger growth inhibition of tumors first given PDT with violet light and then with red light compared to treatments using the reverse order of illumination, namely, red light before violet light. It is concluded that violet light PDT can bleach melanin in melanotic tumors and therefore increase their sensitivity to red light PDT. This finding indicates a new PDT modality that can be further developed for treatment of superficial melanotic melanomas and possibly other diseases where pigmentation is a problem.     

A mathematical model of exoprotein production in bacteria

We present a simple mathematical model for the synthesis of extracellular proteins by a class of bacteria which secrete significant quantities of this exoprotein in late-exponential and stationary phases. This model is the simplest generalization of Michaelis-Menten kinetics (the Monod model) and agrees well with laboratory experiments in batch culture. The model may serve as a simple prototype for the analysis of certain virulent bacterial infections in vivo, particularly that of Pseudomonas aeruginosa in burn wounds.     

Characterization of Photofrin photobleaching for singlet oxygen dose estimation during photodynamic therapy of MLL cells in vitro

A singlet oxygen dose model is developed for PDT with Photofrin. The model is based on photosensitizer photobleaching kinetics, and incorporates both singlet oxygen and non-singlet oxygen mediated bleaching mechanisms. To test our model, in vitro experiments were performed in which MatLyLu (MLL) cells were incubated in Photofrin and then irradiated with 532 nm light. Photofrin fluorescence was monitored during treatment and, at selected fluence levels, cell viability was determined using a colony formation assay. Cell survival correlated well to calculated singlet oxygen dose, independent of initial Photofrin concentration or oxygenation. About 2 x 10(8) molecules of singlet oxygen per cell were required to reduce the surviving fraction by 1/e. Analysis of the photobleaching kinetics suggests that the lifetime of singlet oxygen in cells is 0.048 +/- 0.005 micros. The generation of fluorescent photoproducts was not a result of singlet oxygen reactions exclusively, and therefore did not yield additional information to aid in quantifying singlet oxygen dose.     

A Monte Carlo model for out-of-field dose calculation from high-energy photon therapy

As cancer therapy becomes more efficacious and patients survive longer, the potential for late effects increases, including effects induced by radiation dose delivered away from the treatment site. This out-of-field radiation is of particular concern with high-energy radiotherapy, as neutrons are produced in the accelerator head. We recently developed an accurate Monte Carlo model of a Varian 2100 accelerator using MCNPX for calculating the dose away from the treatment field resulting from low-energy therapy. In this study, we expanded and validated our Monte Carlo model for high-energy (18 MV) photon therapy, including both photons and neutrons. Simulated out-of-field photon doses were compared with measurements made with thermoluminescent dosimeters in an acrylic phantom up to 55 cm from the central axis. Simulated neutron fluences and energy spectra were compared with measurements using moderated gold foil activation in moderators and data from the literature. The average local difference between the calculated and measured photon dose was 17%, including doses as low as 0.01% of the central axis dose. The out-of-field photon dose varied substantially with field size and distance from the edge of the field but varied little with depth in the phantom, except at depths shallower than 3 cm, where the dose sharply increased. On average, the difference between the simulated and measured neutron fluences was 19% and good agreement was observed with the neutron spectra. The neutron dose equivalent varied little with field size or distance from the central axis but decreased with depth in the phantom. Neutrons were the dominant component of the out-of-field dose equivalent for shallow depths and large distances from the edge of the treatment field. This Monte Carlo model is useful to both physicists and clinicians when evaluating out-of-field doses and associated potential risks.     

A mathematical model for quantifying training

A systems modelling approach has been used to quantify the dose-response nature of training. Considerable attention has been focused on the modelling process with little work on the determination of the training impulse (TRIMP) scores. Currently, the methods employed to calculate TRIMPs are subject to various limitations including the use of generic ordinal category or exponential weighting factors for higher exercise intensities. These weightings are necessary to prevent excessively high scores from long duration, low intensity bouts of exercise. We propose a new method to calculate TRIMP scores based upon a whole body bioenergetic model. Our method is individual specific, removing many of the previous limitations. Furthermore, this model could enable a greater comparison of continuous and interval training methods. This model takes into account the length of repetition(s), concentration of the interval session and mode of recovery. This approach, while requiring further research, offers a potential improvement in the accuracy of training load calculations.     

A model to estimate the outcome of prostate cancer photodynamic therapy with TOOKAD Soluble WST11

Interstitial photodynamic therapy is becoming an interesting modality to treat some early stage prostate cancers. A light-sensitive drug is injected to the patient and activated by light using optical fibres inserted inside the prostate. In this work, we were interested in the characterization of the light action model for the WST11 (Tookad? Soluble) drug. A retrospective analysis was performed on results from 28 patients enrolled in phase I and II trials with the WST11 drug. A drug dose of 4 mg/kg patient, dose light of 200 J cm(-1) and wavelength of 753 nm were used. Correlation between the illuminated volume and the obtained necrosis, measured at day 7 MR images, was clearly established. This result suggests that photodynamic therapy planning is possible based on this model.     

Electron microscopic study of monkey retina after photodynamic treatment

The purpose of this histological study was to determine the effects of photodynamic treatment, using a hematoporphyrin derivative and argon laser, on normal retinas of monkeys. Ten cynomolgus monkeys were treated with a hematoporphyrin derivative, given intravenously at a dose of 2.5 mg/kg. Forty minutes or 1 or 3 days after the injection, argon laser photoradiation was given over a 2.0-mm-diameter with a 10-min exposure and at an intensity of 40, 100, or 200 mW. The eyes were enucleated 1, 3, 4, 15, 18, 21, 35, or 38 days after the photoradiation and tissue samples were observed under a transmission electron microscope. The most fragile regions in the retina were the retinal nerve fibers, the outer segments of the visual cells, and the retinal pigment epithelium. Vascular endothelial cells were also fragile. The retinal capillary was easily obstructed, and the choriocapillaris was also occluded in an animal with severe retinal damage. The Mueller cells had the highest tolerance to the photodynamic treatment. Thus, exposing the normal part of the retina to light during photodynamic therapy should be avoided.     

Utility of the F98 rat glioma model for photodynamic therapy.

A syngeneic rat brain tumor model consisting of F98 glioma cells in Fischer rats was investigated for its utility in PDT studies. Results of in vitro studies demonstrated that the F98 cell line was sensitive to ALA-PDT, especially at low light irradiances. Histological examination revealed that F98 tumors share many fundamental characteristics with human GBMs, including rapid growth and infiltrative behavior. ALA-PDT in normal brain showed that high light fluences (26 J) delivered at relatively low powers (10 mW) are capable of causing significant edema. These findings suggest that light irradiation parameters should be chosen carefully when treating tumor-bearing animals. Rats inoculated with F98 cells preincubated in ALA showed a significant survival advantage following light exposure. Taken together, the results suggest that the F98 rat glioma model is appropriate for PDT studies of malignant gliomas.     

A mathematical model of the electrocardiographicQT-RR relationship

A mathematical model of the electrocardiographicQT-RR relationship is presented. Numerical estimates produced a curve that fits reasonably well the empirical approximation made with Bazett's formula. The model is general and would agree in principle with previous membrane theories; this fact should encourage experiments in the mammalian heart and in single cells. The ‘activation’ constant A was found to be 3·88×10^?2 1/s. The critical periodT _k =x ₀ estimated from the experimental data was 0·5 s with a corresponding critical frequencyf _k of 120 beats/min. These values are valid for the whole ventricle of the snakeConstrictor constrictor; beyondf _k fibrillation would be expected to occur.     

Avastin enhances photodynamic therapy treatment of Kaposi's sarcoma in a mouse tumor model.

The goal of the current study was to determine if the antiangiogenic drug Avastin would improve the effectiveness of Photodynamic Therapy (PDT) in a xenograft model of Kaposi's sarcoma (KS). Human KS-Imm tumors transplanted in nude mice were treated with Photofrin-mediated PDT. Expression parameters of proangiogenic molecules were documented and the tumoricidal effectiveness of PDT combined with the VEGF inhibitor Avastin was determined. PDT induced increased expression of HIF-1alpha, VEGF, PGE2, TNF-alpha, and IL-1beta within treated KS tumor tissue. Significant overexpression of KS cell derived human VEGF and to a lesser extent overexpression of host cell derived mouse VEGF were detected within treated tumors. Combining PDT with Avastin resulted in a significant increase in the long-term responsiveness of treated KS tumors when compared to individual treatments. These results demonstrate for the first time that Avastin can improve PDT treatment effectiveness and suggest that VEGF inhibitors may ameliorate the clinical efficacy of PDT.