(37a) Towards the Optimal Design of a Minimal Set of Clinical Tests for the Identification and Characterization of Von Willebrand Disease

            Von Willebrand disease
(VWD) is one of the most common bleeding disorders in humans, caused by qualitative
or quantitative deficiencies of von Willebrand factor (VWF), a multimeric
glycoprotein composed by a variable number of identical subunits, consisting of
2050 amino acid residues and up to 22 carbohydrate side chains [1]. VWF
mediates platelet adhesion, platelet aggregation, thrombus growth and binds,
transports and protects coagulation factor VIII. VWD occurs in a large variety
of forms and its symptoms range from sporadic nosebleeds and mild bleeding from
small lesions in skin, to acute thrombocytopenia or prolonged bleeding episodes
[2]. Diagnosis of VWD may be a complicated task, due to the various number of
VWD types (1, 2A, 2B, Vicenza etc.), therefore pharmacokinetic models [3] have
been recently proposed for the classification of the disease type, elucidating
the critical pathways involved in the disease characterization. However,
the complexity of the models requires long (at least 24 h) and invasive
non-routine tests like DDAVP to be carried out on the subjects to achieve a
statistically satisfactory estimation of the individual haemostatic parameters.
Therefore, the scientific community is pushing researchers to study a way to identify
the mechanistic model of VWD without the need of DDAVP test, exploiting only
basal clinical trials. The alternative basal tests which are considered in this
study are: (a) VWF propeptide (VWFpp) test [4] to quantify VWF elimination from
the blood stream; (b) VWF antigen (VWF:Ag) test to quantify VWF molecule in the
bloodstream; (c) VWF collagen binding (VWF:CB) test to assess the ability of
VWF to bind collagen and the presence of large VWF multimers. From these
clinical tests two other important physiological parameters are derived for
diagnostic purposes: i) VWFpp ratio expressed as the ratio between VWFpp
and VWF:Ag; ii) VWF:CB ratio defined as the ratio between VWF:CB and
VWF:Ag.

          
The overall objective of this project is to design a minimal set of basal
clinical assays for the identification of the PK model of VWD in order to
decrease the time and effort required for the diagnosis and characterization of
the disorder. For this purpose, a simplified version of the mechanistic model
of VWD by Galvanin et al. [3] is used. The model, illustrated
in Figure1a, assumes that high (HMW) and ultra-large (ULMW) molecular weight
multimers are released in the bloodstream from the endothelial cells. Then, HMW
and ULMW multimers are cleaved by the metalloproteinase ADAMTS13 into low
molecular weight multimers (LMW) and eliminated from the bloodstream. A
modified model is proposed in this work by including in the formulation a set
of explicit correlations linking the PK parameters (k₀, k₁,
k_e) to basal VWF:Ag, VWF:CB and VWFpp clinical tests and
readings. The new equations are obtained using response surface methodology
(RSM). RSM [6] is a design of experiment technique, used to develop “black-box”
regression models to establish a correlation between inputs and outputs in a
system. The approach is used to approximate the information coming from
experimental data with the aim of defining the profile of responses in the
experimental design space.

A two-stage model
identification procedure is applied based on RSM. In the first step, a model
discrimination based on Akaike index [7] is used to determine the best
structure of the response surface (linear, quadratic, with interactions, etc.).
In the second step a data mining procedure is carried out to estimate RSM
parameters in the most precise way. Following the procedure suggested in [8],
identifiability tests (sensitivity analysis and information content analysis)
are conducted to evaluate if PK model parameters can be uniquely estimated from
the experimental data. A linear response surface with interactions has been
successfully applied for each type of VWD and it represents the first step for
finding an explicit correlations between k_e and the two basal
quantities VWFpp ratio and VWF:CB. As an example, Figure 1b, which considers
healthy subjects with O blood group (HO), shows how the surface can be used to
represent the k_e data obtained from the simplified model.
Figure 1c illustrates the prediction of VWF:Ag and VWF:CB profile  following
DDAVP for a subject in HO category, once the new explicit relation for k_eis added to the simplified model. Results show a good agreement between the
simplified model and the modified model including RSM correlations. This work
represents a first step towards reaching model identification starting only
from basal clinical tests. This will allow an accurate diagnosis of the disease
without the invasive DDAVP test, resulting therefore into a better quality of
life for the patients.

References

[1] Zaverio M. Ruggeri (2007).
The role of von Willebrand factor in thrombus formation. Thrombosis Research,
120, S5-S9.

[2] D. Lillicrap (2007). Von Willebrand
disease-Phenotype versus genotype: Deficiency versus disease. Thrombosis
Research, 120, S9-S16.

[3] Galvanin, F.,
M. Barolo, R. Padrini, S. Casonato, F. Bezzo (2014). A model-based approach to
the automatic diagnosis of Von Willebrand disease. AIChE J., 60, 1718-1727.

[4] Casonato, A.,
Daidone, V., Padrini, R. (2011). Assessment of von Willebrand Factor Propeptide
Improves the Diagnosis of von Willebrand Disease. Semin Thromb Hemost, 37,
456-463.

[5] Sweeney, J.D.,
Hoerning, L.A. (1992). Intraplatelet von Willebrand factor and ABO blood
group.Thromb Res., 68(4-5), 393-398.

[6]
Box G., Benhken D., (1960). Some new 3 level designs for the study of
quantitative variables. Technometrics, 2, 455-475.

[7] Akaike, H., (1974). A new look at
the statistical model identification. IEEE transactions on automatic control,
19, 716-723.

[8] Asprey S.P,
Macchietto S. (2000). Statistical tools for optimal dynamic model building.
Computers and Chemical Engineering, 24, 1261-1267.