Sparse sampling

Typically, a series of several 2D spectra are recorded with various relaxation delays, ranging from very short to the longest delays, which usually correspond to 1.5-2 relaxation times. The delay values are usually selected so that they are uniformly distributed over this time interval or so that the signal values are uniformly spread. Another sparse sampling strategy proposed in [12] is based on an optimal sampling scheme for a monoexponential decay function a five-point variant of this strategy uses one measurement at a very short relaxation delay and four measurements at 1.3 T2 (or 7 i). 

Fig. 13.1 An ideal activity landscape. In such landscapes, which are conceptually similar to the gently rolling Flint Hills of Kansas depicted in the figure, it is generally assumed that similar molecules have similar biological activities [3]. It is clear from the figure that even relatively sparse sampling of chemistry space may be sufficient to construct a reasonable estimate of the activity landscape.

Yao, M., Swaminathan, A., and Srinivas, N. (2007). Assessment of dose proportionality of muraglitazar after repeated oral dosing in rats via a sparse sampling methodology. Biopharm. Drug Dispos. 28 35-42. 

Baker Rushton continued to show that erythrolabe was present in both normals and deutranopes174. They also showed the results of differential adaptation but without any calibration of the bleach parameter and a sparse sampling of the spectrum. The figures do not provide unequivocal separation of the spectra. 

An alternate approach is the population pharmacokinetic approach, or study. This approach relies on infrequent (sparse) sampling of blood from a larger population than would be used in a standard pharmacokinetic study to determine pharmacokinetic measures and/or parameters. 

Application of Sparse Sampling and Population Kinetic Methods... 

There have been attempts to study the pharmacokinetics of macromolecules by applying the sparse sampling strategy and population kinetic methods described in Chapter 10 (36, 77). In one study, erythropoietin was administered SC to 48 healthy adult male... 

EIGURE 32.13 Correlation betwreen observed and predicted erythropoietin concentration values analyzing sparse sampling data Auth a population pharmacokinetic model (no r value given). (Reproduced wnth permission from Hayashi W et al. Br J Clin Pharmacol 1998 46 11-9.)... 

Altogether, tectonically emplaced and abyssal mantle rocks provide insights into upper mantle compositions and processes that are complementary to the information conveyed by mantle xenoliths (See Chapter 2.05). They provide coverage to vast regions of the Earth s upper mantle that are sparsely sampled by mantle xenoliths, particularly in the ocean basins and beneath passive continental margins, back-arc basins, and oceanic island arcs. 

Figure 10 An interpolated map of DMS concentrations. The map is based upon 15,617 DMS measurements from 150 cruises. Concentrations are in nM. Sampling points are represented by white circles indicating that many areas are sparsely sampled (Kettle et al., 1999) (reproduced by permission of American Geophysical Union from Glob.

The sparse sampling approach for characterizing PPK yields better estimates of intersubject variability than the traditional approaches (discussed later) that yield positively biased estimates of this measure of dis-persion.f A combination of robust (accurate and precise) estimates of intersubject variability and the mean parameter value for a drug is useful for selecting a starting dose for drug therapy in a patient, and allows Bayesian feedback analysis to be performed for dosage individualization. 

Hu, C. Moore, K.H. Kim, Y.H. Sale, M.E. Statistical issues in a modeling approach to assessing bioequivalence or PK similarity with presence of sparsely sampled subjects. J. Pharmacokinet Pharmacodyn 2004, 31 (4), 321-339. 

In all cases, the variability for the PDQC charges in Table 2 is highest for the central carbon atom. As Woods et al. note, the exposure of the van der Waals surface of the methanol carbon atom is quite limited. As a result, the electrostatic potential will be more sparsely sampled in this region and perhaps therefore will not be as well described by the final parameters. Classical electrostatics is likely playing a role here as well. Classically, all the charge on a charged object is found on the surface of the object. Because class III charge... 

Contrary to popular wisdom, more is not necessarily better. It is interesting to note (Table 4) that increasing the sampling density does not always result in an increase in the rank of the LLS problem. When the density of points is increased from a sparse sample (100 points), the rank may increase slightly, but further increases do not lead to increases in the rank. In fact, in many instances the rank actually decreases as the sample size gets much beyond 1000 points. 

Mahalati K, Belitsky P, Sketris I, West K, PanekR. Neoral monitoring by simplified sparse sampling area under the concentrationtime curve its relationship to acute rejection and cyclosporine nephrotoxicity early after kidney transplantation.Transplantation 1999 68 55-62. 

Distributed Processing models of not even suggested that there is "responsible" for consciousness, become even more mysterious, to philosophers at least. But if our unitary conscious experience is not the experience or awareness of the totality of sensory input (and mental reflection) itself, but rather the after-the-fact experience of our own habit routines activated by the sensory data, and overlaid with only a sparse sampling of the sensory data relevant to the habit routine complex called into play, the binding problem disappears. 

PK and PD have been linked by many models, sometimes mechanistic and at other times empirical. These models are especially useful in better understanding the dose strategy and response, especially when applied by stochastic simulation. The population approach can be applied to multiple types of data—for example, both intensely and sparsely sampled data and preclinical to Phase 4 clinical data— and therefore has found great utility when applied to PK/PD modeling. 

The PPK approach can allow one to combine heterogeneous types of data from varying sources. For example, one could pool data from several different studies, study centers, variable biomatrices (plasma plus serum), intensely plus sparsely sampled data, or experimental plus observational data. The combining of differing data sets often increases the power to identify multicompartment or nonhnear models, to incorporate additional covariates, or to gain precision in the estimation of the model. 

We first discuss BE assessment in the presence of sparsely sampled subjects and then discuss pharmacodynamic endpoint bioequivalence. 

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