Interpreting electron-nuclear-magnetic field interactions from a hamiltonian expressed in tensorial notation.

The general experimental hamiltonian expressed in tensorial notation is assessed in a way to ensure that the outcomes from such a hamiltonian reflect correctly the electron-nuclear-magnetic field interactions and yields the appropriate parameters. Without such knowledge the use of hamiltonians in tensorial notation to analyse magnetic resonance spectra may lead to questionable or even meaningless results reflected in several publications over the years. Furthermore, the errors that may occur in handling mixed hamiltonians compound the problem.

A method for extracting muscle information from serum creatine kinase measurements--its potential value in the monitoring and management of inflammatory muscle disease.

A major problem in treating inflammatory myopathies is the very limited information available about the processes taking place. For instance serum creatine kinase levels are often dismissed as a means of gaining an understanding of what is happening or a means of monitoring a patient. This paper shall show how serum creatine kinase levels may be used to explore the processes taking place that create muscle inflammation. This is achieved by a detailed longitudinal study. Firstly, considerable laboratory data is gathered such as serum creatine kinase levels and blood pressure information. Secondly, the data is quantified using a scientific model. We shall illustrate the approach through an extensive nine-year study of a particular polymyositis patient. We identify three basic processes that may contribute to muscle inflammation and show how they may be interpreted from specific patient data. Furthermore, details are given for controlling and monitoring the disease to maximise the reduction in the muscle attack while reducing significantly the muscle inflammation and keeping the drug concentration at a minimum to ensure minimum side-effects and how to identify and handle drug-drug, drug-natural product and adverse drug interactions. Examples are given for a natural product, azathioprine and trandolapril.

Polymyositis--a further investigation.

In essence, this paper describes the model-based interpretation of measurements in order to gain insight into physiological processes. The paper extends the mathematical model developed previously to control and monitor a polymyositis patient. The extension considers two further yet different types of muscle attack. The model is applied to simulate, first, the total serum creatine kinase levels, which then are matched to the observed values. The outcomes of this approach yield considerable information about the reactions taking place including various concentration levels over time such as prednisolone. The changes in the muscle attack are estimated. Examples illustrate how the model may be used to assess, for a single patient, the maximum reduction of the muscle attack whilst keeping the prednisolone concentration as low as possible. The model has been successfully used to interpret variations in daily heart rate measurements of a polymyositis patient. Consequently, it is shown how daily heart rate measurements may now be used to complement the control and monitoring of the polymyositis patient. The model is used to explore multi-patient statistics. It shows the dangers of using such an approach. The model illustrates the need for longitudinal studies.

Controlling and monitoring polymyositis under steroid therapy.

This paper illustrates how considerable information may be extracted from the easily obtained serum creatine kinase levels as a function of prednisolone intake in controlling and monitoring polymyositis effectively. A simple process is developed to enable a clinician to determine readily the optimum prednisolone intake to give the minimum average steroid levels within the patient with an effective reduction in the muscle damage arising from the polymyositis. As part of the process it is demonstrated how the effect of other drugs or natural products may be ascertained and monitored. The effects of specific Mannatech products are detailed as an example.

The effect of surgery and severe injury on blood vessels.

This paper evolves from our previous work that developed a blood vessel model based on the way in which the total tension within the blood vessel wall varies with pressure due to the interaction of specific ions. We use the previous outcomes to examine the diameter of rat middle cerebral arteries (MCAs) as a function of pressure. The MCAs were isolated at 2 h, 1 and 5 days following sham injury and severe traumatic brain injury (TBI). First, we are able to quantify the diameter versus pressure curve in a way that yields three parameters. One of these parameters is the diameter at zero pressure that incorporates properties of the blood vessel walls and the vascular smooth muscle cells. The other two parameters are associated with the myogenic response and the myogenic tone. These parameters enable us to characterize, from the MCAs as a function of pressure in a calcium buffer, each blood vessel into one of three distinct distributions. One of these distributions reflects the optimum conditions. From our data with our blood vessel model, we demonstrate the effect of sham injury on the way in which blood vessels respond to pressure change that appears to recover over time with a half-life of about 40 h. In contrast, severe TBI greatly affects the blood vessel with no indication of recovery over the five-day monitoring period.

An insight into cortisol and polymyositis control with steroid therapy.

In the present report we have developed a mathematical model to describe the processes involved during high steroid therapy. We have shown that the model can predict clinical observations as well as determine the optimum steroid regimen without relying on trial and error methods. The model incorporates rate processes that simplify the physiological complexity as a few representative steps. In this way, it is possible to simulate clinical observations and then to predict clinical outcomes due to drug concentrations or additional reactions within the body. Specific examples are provided from patients with polymyositis and Becker's disease. For the first time, we provide an explanation into the control of cortisol production, and determine an optimum prednisolone concentration in order to minimize steroid side effects while maintaining adequate control of muscle degradation.

Mathematical modelling of responses of cerebral blood vessels to changing intraluminal pressure.

The authors have designed a mathematical model to investigate the influences of the physical and chemical properties of the cerebral blood vessel resistance on vessel diameter. The model is based on the way the total tension within the blood vessel walls varies due to specific ions interacting and affecting the vascular smooth muscle cells and the vascular walls. In particular, we shall model a series of calcium sites and derive a generalized equation of the diameter as a function of pressure. The model includes the action of the vascular smooth muscle cells and the elasticity of the vascular walls, the pressure exerted on the walls by the blood and the effect of alterations to their properties within the blood vessel. They are formulated in terms of three parameters: the diameter at zero pressure, the myogenic response as the pressure tends to zero and a term associated with the myogenic tone. All three parameters may be reliably extracted from diameter-pressure measurements. The model was successfully used in quantifying diameter oscillations and dynamic myogenic responses that are frequently observed both in vivo and in vitro. Finally, we tested the model on experimental data obtained from the resistance of cerebral vessels that have been isolated from rats. In particular, we have first shown that the blood vessel characteristics are such that the diameter change due to calcium ion variations is at a maximum value. Second, we have shown that blood flow affects the myogenic response and third, we can explain the affect of ATP on the vessel diameter.

A mathematical assessment of the precision of parameters in measuring resonance spectra.

The accurate interpretation of in vivo magnetic resonance spectroscopy (MRS) spectra requires a complete understanding of the associated noise-induced errors. In this paper, we address the effect of complex correlated noise patterns on the measurement of a set of peak parameters. This is examined initially at the level of a single spectral analysis followed by addressing the noise-induced errors associated with determining the signal parameters from the peak parameters. We describe a relatively simple method for calculating these errors for any correlated noise pattern in terms of the noise standard deviation and correlation length. The results are presented in such a way that an estimate of the errors may be made from a single MRS spectrum. We also explore how, under certain circumstances, the lineshape of the signal may be determined. We then apply these results to reexamine a set of in vivo 31P MRS spectra obtained from rat brain prior to and following moderate fluid percussion injury. The approach outlined in this paper will demonstrate how meaningful results may be obtained from spectra where the signal-to-noise ratio (SNR) is quite small and where knowledge of the precise shape of the signal and the detail of the noise pattern is unknown. In essence, we show how to determine the expected errors in the spectral parameters from an estimate of the SNR from a single spectrum, thereby allowing a more discriminative interpretation of the data.

A critical assessment of noise-induced errors in 31P MRS: application to the measurement of free intracellular magnesium in vivo.

Phosphorus magnetic resonance spectroscopy (31P MRS) is a noninvasive technique that has been used to estimate free intracellular magnesium concentration (free [Mg2+]). Free [Mg2+] is computed from the chemical shift separation between the alpha- and beta-phosphate resonances of ATP. The current study was undertaken to critically assess the influence of noise effects in estimating free [Mg2+] in rat brain subjected to moderate parasagittal fluid percussion-induced injury. We show that contrary to published data, free [Mg2+] does not significantly change for up to 4 h after moderate trauma in different rat strains and using different surface coils. Before injury, free [Mg2+] = 0.56 +/- 0.11 (mean +/- SD, n = 36) and 4 h post-trauma, free [Mg2+] = 0.56 +/- 0.28. Our results suggest that explanations for this discrepancy comprise errors of chemical shift assignments accompanying low signal-to-noise ratios and the method of analysis employed. Indeed, the authors propose that spectra of beta-ATP signal-to-noise ratio less than 5:1 will produce significant noise-induced errors. We conclude that without knowledge of the inherent errors in 31P MRS spectroscopy and appropriate statistical analysis, caution should be exercised in calculating free [Mg2+] and using these changes as a basis for proposing pharmacotherapeutic interventions.

Interpretation of 31P MRS spectra in determining intracellular free magnesium and potassium ion concentrations.

The current paper develops a simple mathematical model for the determination of the concentration of ionic species using the chemical shifts of ATP from phosphorus magnetic resonance spectroscopy (31P MRS) spectra. An iterative method is used to evaluate the equilibrium constants for a range of Mg/ATP equilibria. Initially, an expression for free magnesium concentration is determined by consideration of four equilibria. We then demonstrate how any number of equilibria may be included using this simplified analysis, by incorporation of pseudo equilibrium constants. This approach may be applied to the interpretation of both ex vivo and, more importantly, in vivo MRS spectra. Furthermore, the authors suggest that the commonly used equation for determining free intracellular magnesium concentration as presented by Gupta and colleagues is an oversimplification, particularly under conditions of fluctuating pH.

Early gastric cancer. Clinicopathologic study.

The incidence and clinicopathologic features of early gastric cancer encountered among surgical specimens from gastric resections for carcinoma in a recent three-year period, 1977 to 1979, at the Mallory Institute of Pathology were studied and compared with those of a pre-endoscopic period 10 years earlier, 1967 to 1969. It was found that early gastric cancer now comprises a greatly increased proportion of lesions leading to gastric resection, mainly as a result of endoscopy and biopsy of gastric ulcers of benign appearance. In the recent period, there were six early gastric cancers in a total of 22 gastric resection specimens compared with one in 27 gastric resections performed for carcinoma in the pre-endoscopy period. Five of the six patients in the recent period are alive without evidence of disease four to five years following surgical resection. The single patient in the earlier period died postoperatively. Applying the classification of the Japanese Endoscopic Society, there were three depressed or ulcerated lesions (type IIc or III), three elevated or polypoid lesions (type I or IIa), and a single flat lesion (type IIb). All three ulcerated lesions were interpreted as benign peptic ulcers on conventional upper gastrointestinal studies. Findings on endoscopic biopsy were positive in all cases (six of six). Although not encountered frequently in the United States, early gastric cancer, nonetheless, appears to be indistinguishable from the disease as it is described in Japan in terms of its pathologic morphology, growth patterns, coexistent or related lesions of the stomach, and curability by surgical resection. If early gastric cancer is to be recognized more frequently, knowledge of the disease and a high index of suspicion on the part of physicians are essential.