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 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.

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.

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.

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.