Evaluation of cerebrospinal fluid alpha-synuclein seed amplification assay in PSP and CBS.

Background: Seed amplification assay (SAA) testing has become an important biomarker in the diagnosis of alpha-synuclein related neurodegenerative disorders. Objectives: To assess the rate of alpha-synuclein SAA positivity in progressive supranuclear palsy (PSP) and corticobasal syndrome (CBS), and analyse the clinical and pathological features of SAA positive and negative cases. Methods: 106 CSF samples from clinically diagnosed PSP (n=59), CBS (n=37) and indeterminate parkinsonism cases (n=10) were analysed using alpha-synuclein SAA. Results: Three cases (1 PSP, 2 CBS) were Multiple System Atrophy (MSA)-type SAA positive. 5/59 (8.5%) PSP cases were Parkinson's disease (PD)-type SAA positive, and these cases were older and had a shorter disease duration compared with SAA negative cases. In contrast, 9/35 (25.7%) CBS cases were PD-type SAA positive. Conclusions: Our results suggest that PD-type seeds can be detected in PSP and CBS using a CSF alpha-synuclein SAA, and in PSP this may impact on clinical course.

On the transformation of compartmental systems and the indeterminacy of the volume of distribution.

A general compartmental system with multiple-point elimination is transformable to a single-point elimination system. Transformation is achieved by a similarity transformation of the rate constant matrix, A, with a diagonal matrix, D. The elements of D (1, d1, d2,...) are equivalent to the "first-pass" effect between compartments and compartment 1. Application of the derived transformation demonstrates that the volume of distribution as defined by the normalized first-moment function is a minimal volume of distribution when there is no "first-pass" effect between the drug input compartment and the observation compartment. In all other cases, the volume of distribution is a meaningless metric since it may be a minimal or maximal metric and the exact status is indeterminate. Theorems on the non-negativity of the elements of (-A)-1 are derived.

Theorem on the apparent volume of distribution and the amount of drug in the body at steady state.

For an N-compartmental system, with irreversible drug loss from the sampled compartment, the equilibrium concentration, C (infinity), obtained with a zero-order drug input is related to the total amount of drug in the system, T, by C (infinity) V = T. The scalar V is the volume of distribution of the corresponding closed system. The moment functions of the open system define V, and hence T is directly calculable. The derivation is general in the sense that the topology of the system is not specified and no functional form for C (t) is required.

Mathematical basis and generalization of the Loo-Riegelman method for the determination of in vivo drug absorption.

A general numerical deconvolution method is derived for the determination of in vivo drug input functions. The derivation is based on linear interpolation of observed drug concentrations and deconvolution of the resulting trapezoidal function. Derived in vivo input functions are discontinuous. A general expression for the cumulative drug input is also derived. The latter expression is a generalization of the Loo-Riegelman equations. This deconvolution method give similar results to the "point-area" deconvolution method when deriving in vivo drug input functions.

Number of exponential terms describing the solution of an N-compartmental mammillary model: vanishing exponentials.

The solution for a linear mammillary model is always described by a summation of m + 1 negative exponential terms with constant coefficients. m + 1 less than or equal to N, where N is the number of compartments in the model. m is equal to the number of distinct values for the peripheral Ej values. Use is made of matrix notation and the theorems of Browne concerning the eigenvalues of a matrix. The consequences of vanishing exponentials are derived, and in particular the apparent volume of distribution frequently calculated from experimental data is shown not to be unique.

Applications of a recirculatory stochastic pharmacokinetic model: limitations of compartmental models.

General equations for the time integral on [0, infinity) of the venous drug concentration-time function after intravenous and oral drug administration are derived. A physiologically realistic stochastic recirculating model is applied in the derivations. The quotient of the intravenous drug dose and the integral on [0, infinity) of the resulting venous blood drug concentration function is equivalent to a summation of organ clearances only provided that drug elimination does not occur in the pulmonary system, and in general it is not equivalent to "total body clearance." In general, mammillary compartmental models are not isomorphic with recirculating models. A necessary condition for isomorphism is that the pulmonary system be conservative toward the drug. Equations for the pulmonary "first-pass" effect derived via the compartmental analysis are invalid. A valid expression for the pulmonary "first-pass" effect is derived. General equations derived via compartmental analysis for the extent of hepatic metabolism and the hepatic first-pass" effect are shown to be valid. A generally applicable expression for the advantage of close intraarterial drug administration is derived. The limitations of compartmental models for representing drug distribution and elimination are discussed, and the advantages of recirculating models are emphasized.

Mathematical basis of point-area deconvolution method for determining in vivo input functions.

The point-area method for deconvolution derives a "staircase" input function which, when convolved onto the characteristic function, gives an output function coincidental with the given output data points. The area--area method for deconvolution is shown to be erroneous.

A model independent method for estimating the in vivo release rate constant of a drug from its oral formulations.

A simple equation by which the first-order release rate constant of a drug from its oral formulation can be calculated is derived. The derivation is independent of any hypothetical concepts of drug distribution or elimination.

The influence of smoking on the intersubject variation in pentazocine elimination.

The cumulative urinary excretion over 24 h of pentazocine, under conditions of acidic urinary pH, has been measured in smokers and non-smokers using both male and female subjects (seventy subjects in total). A restricted urban population was studied. An overall three-fold inter-subject variation in elimination was observed. The cumulative urinary excretion of pentazocine was normally distributed in both smokers and non-smokers. Smokers metabolize 40% more pentazocine than non-smokers. It is concluded that induction is principally responsible for the observed subject variability.

Simple transformation method for predicting plasma drug profiles from dissolution rates.

A transformation factor is described which related in vitro drug dissolution from a preparation to the corresponding in vivo plasma drug concentrations. This factor, derived from the dissolution profile and the corresponding in vivo plasma concentration of a single formulation, was used to predict plasma concentration profiles of similar formulations simply from dissolution data.

General derivation of the ideal intravenous drug input required to achieve and maintain a constant plasma drug concentration. Theoretical application to lignocaine therapy.

A constant plasma drug concentration can be achieved and maintained by the intravenous administration of an initial bolus loading dose in conjunction with a constant rate and an exponential intravenous drug infusion. The drug input required to achieve a constant plasma drug concentration is derived without making any assumptions about the nature of drug distribution within the body or elimination from the body.

General theory for rapidly establishing steady state drug concentrations using two consecutive constant rate intravenous infusions.

Steady state plasma drug concentrations can be achieved rapidly and safely by a drug input mode consisting of two consecutive constant rate intravenous infusions. A general method for calculating the relative rates of the two infusions is presented. The derivation is independent of the concepts of compartmental distribution and elimination of drugs within the body.

A general equation for the ratio of the areas below the blood or plasma concentration time-curves following intravenous and oral drug administration and its application to inter-subject variations in drug elimination.

1 When a drug is metabolized in the liver the total area under the plasma or blood concentration-time curve following oral drug administration is less than the area obtained after intravenous drug administration. This difference has been termed the 'first-pass effect'. 2 General equations for the areas below the blood or plasma concentration-time curve of a drug following intravenous and oral drug administration are derived. 3 An explicit expression for the ratio of areas below the blood or plasma concentration-time curves following intravenous and oral drug administration is derived. 4 By the application of the derived equations it is shown that the relative contribution of hepatic drug metabolism and urinary excretion to inter-subject variation in drug elimination can be easily ascertained.