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32 Overview of Cell Sources The cells used thus far to engineer cartilage have varied with respect to donor age (embryonic, neonatal, immature, or adult), differentiation state (precursor or phenotypically mature), and method of preparation (selection, expansion, gene transfer) The sources of chondrogenic cells have included bovine chondrocytes [See, eg, Buschmann et al, 1992; Freed et al, 1998; Pei et al, 2002b], rabbit chondrocytes [See, eg, Fedewa et al, 1998], equine chondrocytes [See, eg, Heath, 2000; Litzke et al, 2004], embryonic chick limb bud cells [See, eg, Elder et al, 2000], human chondrocytes [See, eg, Sittinger et al, 1994] and mesenchymal stem cells derived from bone marrow [Meinel et al, 2004a] The choice of cell type can affect in vitro culture requirements (eg.

In this approach, the classic nonlinear exponential model (Equation 18.21) is now in the form of a latent growth curve with structured loadings (as in Browne & duToit, 1991; McArdle & Hamagami, 1996). Individual trajectories start at different initial levels, but then rise or fall in exponential fashion towards some asymptotic values. In this approach, the group curve is based on the latent means and is not based on an averaging of exponential functions (cf. Keats, 1983; Tucker, 1966). This common factor approach allows us to use current computing techniques to examine the empirical t of this nonlinear model. A related approach has been used with a form of the von Bertalanffy model, dyn /dt = (

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these two models, see the special issue of Multivariate Behavioral Research, 1990, Volume 25, Issue 1 (also see 1996, Volume 31, Issue 4 for discussion of indeterminacy per se) In understanding this debate, it is important to note that all procedures for CA and ECFA are the same except for one: CA starts with 10 in the main diagonal of the correlation matrix and CFA starts with a communality estimate (thus taking into account the existence of variance unique to the single variable) This is the only mathematical difference between the two Everything else is the same (which is why they are both special cases of the general factor analytic model) The Case for Common Factor Analysis The rationale for CFA comes from Equation 61 and assumptions about data Including the uniqueness term in the equation makes it a CFA.

, medium supplements, structure, and degradation rate of scaffold) and in vivo function (eg, potential for integration) of engineered cartilage constructs Articular chondrocytes are phenotypically stable if cultured under appropriate conditions (eg, up to 7 8 months in vitro [Hauselmann et al, 1994; Freed et al, 1997]) and can be used to engineer mechanically functional cartilaginous constructs [Buschmann et al, 1995; Freed et al, 1997; Vunjak-Novakovic et al, 1999; Obradovic et al, 2001; Schaefer et al, 2002] However, adult chondrocytes are not easily harvested; cells from younger donors tend to be more responsive to environmental stimuli [(See, eg, Heath, 2000]), and cell expansion responds to growth factors [Martin et al, 1999, 2001b; Pei et al, 2002a].

The uniqueness term includes all of the variable s variance not associated with the factors, part of which is random error So, the CFA rationale goes, CFA should be used whenever at least some reliabilities are less than 10 that is, whenever some variables contain any random error Of course, this argument runs, who can show, or assume, that all their variables are without random error Where is the evidence for such variables in the social sciences And if we know the variables have error, is it not rational to build that into our mathematical models Dropping the uniqueness term also means that the factors and only the factors underlie the scores for each variable Hence in the population, the communality is to be 10 This is the justi cation for using 10 in the main diagonal of the correlation matrix.

This means that the multiple correlation of the factors with each of the variables is also 10 Unfortunately, the derivative is that the variables, being sets of linear combinations of a fewer number of factors, will form a nonGramian correlation matrix Such a matrix has an in nite number of solutions and so cannot be factored at all Therefore, CA is a self-contradictory model (The only reason that CA works is that the model is wrong for the data no two of the variables being analyzed have a multiple correlation of 10 with the same factors, so none truly t the model) Although component advocates raise the problem of estimating communalities and factor scores, such estimates are consistent and easily made The variations on factor scores are variations among scores that generally correlate 9 or better in simulation and plasmode studies.

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