Neil D. Evans

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.

Treatment of Acute Renal Failure Secondary to Multiple Myeloma with Chemotherapy and Extended High Cut-Off Hemodialysis

BACKGROUND AND OBJECTIVES Extended hemodialysis using a high cut-off dialyzer (HCO-HD) removes large quantities of free light chains in patients with multiple myeloma. However, the clinical utility of this method is uncertain. This study assessed the combination of chemotherapy and HCO-HD on serum free light chain concentrations and renal recovery in patients with myeloma kidney (cast nephropathy) and dialysis-dependent acute renal failure. DESIGN, SETTING, PARTICIPANTS, & MEASUREMENTS An open-label study of the relationship between free light chain levels and clinical outcomes in 19 patients treated with standard chemotherapy regimens and HCO-HD. RESULTS There were sustained early reductions in serum free light chain concentrations (median 85% [range 50 to 97]) in 13 patients. These 13 patients became dialysis independent at a median of 27 d (range 13 to 120). Six patients had chemotherapy interrupted because of early infections and did not achieve sustained early free light chain reductions; one of these patients recovered renal function (at 105 d) the remaining 5 patients did not recover renal function. Patients who recovered renal function had a significantly improved survival (P < 0.012). CONCLUSION In dialysis-dependent acute renal failure secondary to myeloma kidney, patients who received uninterrupted chemotherapy and extended HCO-HD had sustained reductions in serum free light chain concentrations and recovered independent renal function.

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.

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.

An identifiability analysis of a parent-metabolite pharmacokinetic model for ivabradine.

The paper considers the structural identifiability of a parent–metabolite pharmacokinetic model for ivabradine and one of its metabolites. The model, which is linear, is considered initially for intravenous administration of ivabradine, and then for a combined intravenous and oral administration. In both cases, the model is shown to be unidentifiable. Simplification of the model (for both forms of administration) to that proposed by Duffull et al. (1) results in a globally structurally identifiable model. The analysis could be applied to the modeling of any drug undergoing first-pass metabolism, with plasma concentrations available from drug and metabolite.

Structural indistinguishability between uncontrolled (autonomous) nonlinear analytic systems

In this paper, an approach for analysing the structural indistinguishability between two uncontrolled (or autonomous) analytic systems is presented. The approach involves constructing, if possible, a smooth mapping between the trajectories of two candidate models. If either of the models satisfies an observability criterion, then such a transformation always exists when the models are indistinguishable from their outputs. The approach is illustrated by examples from epidemiology and chemical reaction kinetics. One important outcome is that the susceptible, infectious, recovered (SIR) and SIR with temporary immunity (SIRS) models are shown to be indistinguishable when a proportion of the number of infectives is measured.

The structural identifiability and parameter estimation of a multispecies model for the transmission of mastitis in dairy cows.

A structural identifiability analysis is performed on a mathematical model for the coupled transmission of two classes of pathogen. The pathogens, classified as major and minor, are aetiological agents of mastitis in dairy cows that interact directly and via the immunological reaction in their hosts. Parameter estimates are available from experimental data for all but four of the parameters in the model. Data from a longitudinal study of infection are used to estimate these unknown parameters. A novel approach and application of structural identifiability analysis is combined in this paper with the estimation of cross-protection parameters using epidemiological data.

Exploration of the intercellular heterogeneity of topotecan uptake into human breast cancer cells through compartmental modelling.

A mathematical multi-cell model for the in vitro kinetics of the anti-cancer agent topotecan (TPT) following administration into a culture medium containing a population of human breast cancer cells (MCF-7 cell line) is described. This non-linear compartmental model is an extension of an earlier single-cell type model and has been validated using experimental data obtained using two-photon laser scanning microscopy (TPLSM). A structural identifiability analysis is performed prior to parameter estimation to test whether the unknown parameters within the model are uniquely determined by the model outputs. The full model has 43 compartments, with 107 unknown parameters, and it was found that the structural identifiability result could not be established even when using the latest version of the symbolic computation software Mathematica. However, by assuming that a priori knowledge is available for certain parameters, it was possible to reduce the number of parameters to 81, and it was found that this (Stage Two) model was globally (uniquely) structurally identifiable. The identifiability analysis demonstrated how valuable symbolic computation is in this context, as the analysis is far too lengthy and difficult to be performed by hand.

Systems Pharmacology Approach for Prediction of Pulmonary and Systemic Pharmacokinetics and Receptor Occupancy of Inhaled Drugs

Pulmonary drug disposition after inhalation is complex involving mechanisms, such as regional drug deposition, dissolution, and mucociliary clearance. This study aimed to develop a systems pharmacology approach to mechanistically describe lung disposition in rats and thereby provide an integrated understanding of the system. When drug‐ and formulation‐specific properties for the poorly soluble drug fluticasone propionate were fed into the model, it proved predictive of the pharmacokinetics and receptor occupancy after intravenous administration and nose‐only inhalation. As the model clearly distinguishes among drug‐specific, formulation‐specific, and system‐specific properties, it was possible to identify key determinants of pulmonary selectivity of receptor occupancy of inhaled drugs: slow particle dissolution and slow drug‐receptor dissociation. Hence, it enables assessment of factors for lung targeting, including molecular properties, formulation, as well as the physiology of the animal species, thereby providing a general framework for rational drug design and facilitated translation of lung targeting from animal to man.