Michael J. Chappell

Efficient Removal of Immunoglobulin Free Light Chains by Hemodialysis for Multiple Myeloma: In Vitro and In Vivo Studies

Of patients with newly diagnosed multiple myeloma, approximately 10% have dialysis-dependent acute renal failure, with cast nephropathy, caused by monoclonal free light chains (FLC). Of these, 80 to 90% require long-term renal replacement therapy. Early treatment by plasma exchange reduces serum FLC concentrations, but randomized, controlled trials have shown no evidence of renal recovery. This outcome can be explained by the low efficiency of the procedure. A model of FLC production, distribution, and metabolism in patients with myeloma indicated that plasma exchange might remove only 25% of the total amount during a 3-wk period. For increasing FLC removal, extended hemodialysis with a protein-leaking dialyzer was used. In vitro studies indicated that the Gambro HCO 1100 dialyzer was the most efficient of seven tested. Model calculations suggested that it might remove 90% of FLC during 3 wk. This dialyzer then was evaluated in eight patients with myeloma and renal failure. Serum FLC reduced by 35 to 70% within 2 hr, but reduction rates slowed as extravascular re-equilibration occurred. FLC concentrations rebounded on successive days unless chemotherapy was effective. Five additional patients with acute renal failure that was caused by cast nephropathy then were treated aggressively, and three became dialysis independent. A total of 1.7 kg of FLC was removed from one patient during 6 wk. Extended hemodialysis with the Gambro HCO 1100 dialyzer allowed continuous, safe removal of FLC in large amounts. Proof of clinical value now will require larger studies.

Evaluation of frequency and time-frequency spectral analysis of heart rate variability as a diagnostic marker of the sleep apnoea syndrome

The sleep apnoea/hypopnoea syndrome (SAHS) elicits a unique heart rate rhythm that may provide the basis for an effective screening tool. The study uses the receiver operator characteristic (ROC) to assess the diagnostic potential of spectral analysis of heart rate variability (HRV) using two methods, the discrete Fourier transform (DFT) and the discrete harmonic wavelet transform (DHWT). These two methods are compared over different sleep stages and spectral frequency bands. The HRV results are subsequently compared with those of the current screening method of oximetry. For both the DFT and the DHWT, the most diagnostically accurate frequency range for HRV spectral power calculations is found to be 0.019–0.036 Hz (denoted by AB2). Using AB2, 15 min sections of non-REM sleep data in 40 subjects produce ROC areas, for the DFT, DHWT and oximetry, of 0.94, 0.97 and 0.67, respectively. In REM sleep, ROC areas are 0.78, 0.79 and 0.71, respectively. In non-REM sleep, spectral analysis of HRV appears to be a significantly better indicator of the SAHS than the current screening method of oximetry, and, in REM sleep, it is comparable with oximetry. The advantage of the DHWT over the DFT is that it produces a greater time resolution and is computationally more efficient. The DHWT does not require the precondition of stationarity or interpolation of raw HRV data.

Global identifiability of the parameters of nonlinear systems with specified inputs: A comparison of methods

The two methods available for analyzing the global structural identifiability of the parameters of a nonlinear system with a specified input function, the Taylor series approach and the similarity transformation approach, are compared and contrasted through application to three examples. It is shown that, as for linear systems, it is very difficult to predict which of the available methods will result in the least effort for a particular example. The role of modern symbolic manipulation packages in the analysis is assessed. The third example proves intractable using the similarity transformation approach as originally formulated, but the analysis is completed using a reformulation that exploits the polynominal form of the system equations in the example.

Differential algebra methods for the study of the structural identifiability of rational function state-space models in the biosciences.

In this paper methods from differential algebra are used to study the structural identifiability of biological and pharmacokinetics models expressed in state-space form and with a structure given by rational functions. The focus is on the examples presented and on the application of efficient, automatic methods to test for structural identifiability for various input-output experiments. Differential algebra methods are coupled with Gröbner bases, Lie derivatives and the Taylor series expansion in order to obtain efficient algorithms. In particular, an upper bound on the number of derivatives needed for the Taylor series approach for a structural identifiability analysis of rational function models is given.

Structural identifiability of the parameters of a nonlinear batch reactor model

The similarity transformation approach is used to analyze the structural identifiability of the parameters of a nonlinear model of microbial growth in a batch reactor in which only the concentration of microorganisms is measured. It is found that some of the model parameters are unidentifiable from this experiment, thus providing the first example of a real-life nonlinear model that turns out not to be globally identifiable. If it is possible to measure the initial concentration of growth-limiting substrate as well, all model parameters are globally identifiable.

Identifiability of uncontrolled nonlinear rational systems

In this paper an approach for the identifiability analysis of uncontrolled rational systems is provided. The method is based on the use of a local smooth state space transformation. In particular it is shown that, provided the model satisfies an observability rank condition, the state trajectories of an uncontrolled system corresponding to parameter vectors with outputs that are identical locally in time, are connected via a smooth transformation.

A Comparison of Six Deconvolution Techniques

We present results for the comparison of six deconvolution techniques. The methods we consider are based on Fourier transforms, system identification, constrained optimization, the use of cubic spline basis functions, maximum entropy, and a genetic algorithm. We compare the performance of these techniques by applying them to simulated noisy data, in order to extract an input function when the unit impulse response is known. The simulated data are generated by convolving the known impulse response with each of five different input functions, and then adding noise of constant coefficient of variation. Each algorithm was tested on 500 data sets, and we define error measures in order to compare the performance of the different methods.

Extensions to a procedure for generating locally identifiable reparameterisations of unidentifiable systems

In this paper extensions to an existing procedure for generating locally identifiable reparameterisations of unidentifiable systems are presented. These extensions further formalise the constructive nature of the methodology and lend themselves to application within symbolic manipulation packages. The extended reparameterisation procedure is described in detail and is illustrated with application to two known non-trivial examples of unidentifiable systems of practical relevance.

Structural identifiability for a class of non-linear compartmental systems using linear/non-linear splitting and symbolic computation

Under certain controllability and observability restrictions, two different parameterisations for a non-linear compartmental model can only have the same input-output behaviour if they differ by a locally diffeomorphic change of basis for the state space. With further restrictions, it is possible to gain valuable information with respect to identifiability via a linear analysis. Examples are presented where non-linear identifiability analyses are substantially simplified by means of an initial linear analysis. For complex models, with four or more compartments, this linear analysis can prove lengthy to perform by hand and so symbolic computation has been employed to aid this procedure.

A procedure for generating locally identifiable reparameterisations of unidentifiable non-linear systems by the similarity transformation approach

A method is presented for the generation of locally identifiable reparameterisations of non-linear systems which have been shown to be unidentifiable via application of the similarity transformation approach. The existence of the reparameterised system in terms of the maximum permissible number of locally identifiable parameters is provided and is crucially dependent upon the ability to find the rank deficiency of an appropriate (and possibly infinite) jacobian matrix. The reparameterisation procedure is described in detail, and is illustrated with application to two known non-trivial examples of unidentifiable non-linear systems.