Chapter III.1.3
Correlation, Materials Properties, Statistics and Biomaterials Science
Introduction
In chapters prior to this one, this textbook has presented much on the characterization of biomaterials, assessment of biological reaction to biomaterials, and medical applications of biomaterials. What are the prospects for physical and chemical measurements for predicting the performance of new materials in complex medical applications? In other words, can we find relationships between the composition and structure of a biomaterial and its biological interactions, particularly in complex systems like living organisms? This chapter will address this question.
The reality is that physical or chemical measurements which can reliably predict in vivo biocompatibility are at this time unavailable for most biomaterials. It would be ideal, when considering a new material for medical applications, to use a spectroscopic technique to measure the properties and, from that physical measurement, predict how well the material will work in a particular application. Animal experiments are expensive, of questionable value for predicting performance in humans, and raise ethical issues (see Chapters II.3.7 and III.2.7). Human clinical trials are very expensive, and also raise ethical issues (Chapters III.2.7 and III.2.9). Can we predict or prescreen in vivo or in vitro performance from measurements of surface and other physical and chemical properties? This chapter, addressing correlation, will examine this question, and offer suggestions for future exploration.
Correlation implies dependence of one set of data on another. Correlations can take many forms. For biomaterials, some possibilities are:
1. Measure specific surface physicochemical properties (for example, contact angle), and correlate that with a biointeraction response such as a protein adsorption or blood cell interaction.
2. Measure protein adsorption or cell adhesion and predict in vivo performance.
3. Measure mechanical properties and predict the wear of an implanted hip prosthesis.
4. Measure an animal response to materials (for example, blood platelet consumption by the material), and predict clinical performance.
This chapter will primarily focus on those correlations that fit within number 1 above, but the comments made will have relevance to many correlations that can be envisioned for biomaterials.
Biocompatibility and Medical Device Performance
A re-examination of the definition of biocompatibility presented in the Introduction to this textbook and in Chapter II.3.2 is appropriate at this point.
Biocompatibility is the ability of a material to perform with an appropriate host response in a specific application (Williams, 1987).
The “biocompatibility” of a medical device can be defined in terms of the success of that device in fulfilling its intended function. Thus, the blood filtration module of a hemodialysis system might be defined by its ability to appropriately fractionate soluble blood components, its robustness over its intended lifetime, and its non-damaging interaction with the patient’s blood. Alternately, we can define a “blood compatibility” for the membrane, a “blood compatibility” for the silicone rubber header, a “blood compatibility” for the tubing, and a “blood and soft tissue compatibility” for the percutaneous connection between the apparatus and the patient’s bloodstream. Similarly, for a hip joint prosthesis, we can discuss the fatigue resistance of the device, the corrosion resistance of the device, the distribution of stresses transferred to the bone by the device, the solid angle of mobility provided, and the overall success of the device in restoring a patient to an ambulatory state. Again, the hip joint prosthesis performance might also be couched in terms of the tissue reaction to the bone cement, the tissue reaction to an uncemented titanium prosthesis stem, and the tissue reaction to the acetabular cup. In both of these examples, two cases are offered: in the first case, a whole system (device) performance is assessed, and in the second case, the biological reaction to specific components of the device (the biomaterials) is examined. The difference between the consideration of the whole device and the materials that comprise it is a critically important point. In certain contexts, only the performance of the complete device can be labeled as biocompatible. This distinction can be inferred from the US Food and Drug Administration (FDA) policy that only complete devices, and never materials, receive “approval.” Yet biomaterials scientists and engineers refer to the performance of the individual materials as “biocompatibility.” The materials performance can also be described as a “bioreaction” or “bioresponse.” This is a textbook on biomaterials, so it is appropriate to focus on the materials. “Bioreaction” is a much more straightforward descriptor than “biocompatible,” and this term will largely be used here and defined by example.
Toxicology assays, at times imprecisely referred to as biocompatibility assessment, were presented in Chapter II.3.3. These assays deal with measurement of substances that leach from materials, most of which will induce some cell or tissue reaction. Such assays will be discussed here, because the published correlations are clear, interpretable, and measurable. In contrast, if we concentrate on bioreactions to implanted materials that do not leach substances (i.e., most “biocompatible” biomaterials) the surface properties immediately assume a high profile as the prime candidate to control bioreaction. However, hardness, porosity, shape, movement, and specific implant site are also important. These issues will be addressed in working through important concepts in correlating material properties to bioreaction.
Using words such as “correlation” and “dependence” requires some appreciation of data and statistics. This topic will be briefly addressed before the discussion of biomaterials and correlation.
Data, Information, and Statistics
Laboratory experiments generate data that comes from the measurement of the properties (biological and physical) of materials. Frequently we are given that data as a column of numbers (maybe a spreadsheet). Staring at these numbers is often unhelpful in understanding the system under study. What we really desire is not data, but information, about our system. This idea is illustrated in Figure III.1.3.1, proposing how clinical performance data and physicochemical measurement data might lead to the development of an improved implant device. Correlation is one way to process data so that it yields information.
FIGURE III.1.3.1 Clinical and physicochemical data are converted to useful information to optimize the performance of an implant device.
Correlation is a statistical tool useful for analyzing data so as to appreciate its variance, significance, and interrelationships. A general introduction to statistics is not presented here, but every biomaterials research and engineer should be versed in these mathematical tools. A few useful, general books on statistics as applied to scientific problems are Bevington and Robinson (2002), Mosteller and Tukey (1977), Anderson and Sclove (1986), and Urdan (2010). A book that can be useful in interpreting the meaning of statistics is Huck (2000). A search of Amazon.com found over 10,000 textbooks on statistics and probability.
Correlation
Correlation is a relationship (dependency) between two or more variables. Correlation does not necessarily mean cause and effect. For example, most people walking with open umbrellas in the rain will have wet feet. But, in this situation, it is obvious that umbrellas do not cause wet feet. We have a high correlation, but it misses the controlling factor (causative factor) in this example – the rain. Thus, we can propose that A (the umbrella) causes B (wet feet), B causes A, they cause each other or they are both caused by C (the rain). We cannot prove causation, but it can be strongly suggested. Often, where correlations are observed, the causative factor is obscured, and so we have data but little useful information. Where relationships are established between a dependent variable and an independent (or explanatory) variable, this is referred to as regression analysis.
It may be more productive to look at this problem in terms of calibration and prediction. Calibration in a practical (e.g., analytical) sense has been defined by Martens and Naes as the use of empirical data and prior knowledge for determining how to predict unknown quantitative information Y from available measurements X, via some mathematical transfer function (Martens and Naes, 1989). This could be as simple as plotting Y versus X and using a least squares fit to deal with modest levels of random noise or as complex as a multivariate calibration model to accommodate noisy data, interfering agents, multiple causes, non-linearities, and outliers. Multivariate methods will be elaborated upon toward the end of this chapter.
Aspects of the Bioreaction to Biomaterials
Bioreaction, a process related to, but more readily understood than “biocompatibility,” can have many manifestations. Some of these are listed in Table III.1.3.1. A bioreaction is most simply defined as an observed response upon interaction of a material with a biological system or system containing biomolecules. Can simple measured physical properties of materials be correlated with bioreactions? There are many examples where this is indeed the case. Table III.1.3.2 lists some of the surface physical measurements for materials that one might hypothesize as influencing bioreaction or biocompatibility.
TABLE III.1.3.1 Some Bioreactions
Note: These reactions are commonly observed with implant materials; however, their relationship to “biocompatibility” is not direct.
TABLE III.1.3.2 Physical Parameters of Biomaterial Surfaces that Might Correlate with Bioreactivity
The Case for Correlation: A Brief Review of the Literature
In the 1970s and 1980s there was widespread interest in using correlation to predict biomaterial performance. The lessons learned provided insights, but also tempered the enthusiasm for establishing such relationships. Still, papers continue to explore correlation and a few modern efforts will be described here.
An early and influential paper demonstrating that physical measurements might be correlated with observed reactions to biomaterials concerned extractables from biomaterials (Homsy, 1970). Many biomaterials were examined in this study. Each was extracted in a pseudoextracellular fluid. The extract was examined by infrared absorbance spectroscopy for hydrocarbon bands that are indicative of organic compounds. A positive correlation was observed between the strength of the IR absorbances and the reaction of the materials with a primary tissue culture of neonatal mouse heart cells (Figure III.1.3.2). This paper was important in scientifically justifying in vitro cell culture analysis for screening the toxicology of biomaterials, and for developing the principle that biomaterials should not unintentionally leach substances.
FIGURE III.1.3.2 A hypothesis for a minimum biointereaction for surfaces with critical surface tensions around 22 dynes/cm.
In the late 1960s, Robert Baier and colleagues offered an intriguing hypothesis concerning surface properties and bioreaction that continues to stimulate new experiments (Baier, 1972). This hypothesis is based upon interfacial energetics of surfaces as approximated from contact angle measurements, and suggests that materials with critical surface tensions (see Chapter I.1.5) of approximately 22 dyne/cm would exhibit minimum bioreactivity (Figure III.1.3.3). Support for this hypothesis has been generated in a number of experiments spanning different types of biointeractions (Dexter, 1979; Baier et al., 1985). However, in a larger number of cases, this minimum has not been observed, raising questions about the generality of this concept (Lyman, 1970; Mohandas et al., 1974; Chang et al., 1977; Yasuda et al., 1978; Neumann, 1979).
FIGURE III.1.3.3 A correlation between baboon platelet consumption as measured in an ex vivo shunt system and hydrogel water content.
(From Hanson et al., 1980.)
Some of the clearest biointeraction correlations have been observed in simple, non-proteinaceous media. Linear trends of cell (mammalian and bacterial) adhesion versus various measures of surface energy have been noted (Mohandas et al., 1974; Chang et al., 1977; Yasuda et al., 1978; Neumann et al., 1979). For example, Chang and co-workers (1977) found that the adhesion of washed pig platelets to solid substrates increased with increasing water contact angle, a parameter that generally correlates well with solid surface tension. It is interesting that these simple linear trends often vanish or diminish if protein is present in the attachment medium (Chang et al., 1977; Neumann et al., 1979; van der Valk et al., 1983). More complex surface energetic parameters have also been explored to correlate bioreaction to surface properties (Kaelble and Moacanin, 1977).
Correlations between material properties and long-term events upon implantation are less frequently seen in the literature. However, some important examples have been published. The baboon A–V shunt model of arterial thrombosis has yielded a number of intriguing correlations (Harker and Hanson, 1979). Using an ex vivo femoral–femoral shunt, this model measures a first order rate constant of platelet destruction induced by the shunt material (the units are platelets destroyed/cm2/day). The values for this surface reactivity parameter are independent of flow rate (after the flow rate is sufficiently high to ensure kinetically limited reaction), length of time that the reaction is observed, blood platelet count, and surface area of the material in contact with the blood. In one experiment, a series of hydrogels grafted to the luminal surfaces of 0.25 cm i.d. tubes was studied (Hanson et al., 1980). The platelet consumption (see Chapter II.3.5) was found to increase in a simple, linear fashion with the equilibrium water content of the hydrogels. This correlation, illustrated in Figure III.1.3.4, is particularly intriguing because the hydrogel materials studies were amide-, carboxylic acid-, and hydroxyl-based. The only clear, correlating parameter was equilibrium water content. In another study, the platelet consumption of a series of polyurethanes was observed to decrease in a linear fashion as the fraction of the polyurethane C1s ESCA surface spectrum that was indicative of hydrocarbon moieties increased (Hanson et al., 1982).
FIGURE III.1.3.4 Four very different surfaces with similar average roughness (Ra).
There have been many attempts to correlate specific protein adsorption with biological reaction. A 1975 study showed that the number of platelets adsorbed to polyurethanes correlated inversely with the amount of albumin adsorbed in competition with fibrinogen and IgG (Lyman et al., 1975). For a series of polyurethanes, platelet attachment was shown to correlate with the amount of fibrinogen adsorbed (Chinn et al., 1991). However, two surprising outlier points could not be explained – two materials that adsorbed high fibrinogen levels adhered low levels of platelets. Bailly et al. (1996) used a direct ELISA method to measure adsorbed fibrinogen on catheters, and found that in vitro platelet adhesion and in vivo catheter thrombogenicty correlated with the amount of adsorbed fibrinogen. Hu et al. (2001) have isolated specific domains within fibrinogen that help to explain their observation that the level of adsorbed fibrinogen correlates with the magnitude of the foreign-body reaction at short (~3 day) implantation times. These studies all implicate levels of adsorbed fibrinogen with complex biological reactions.
A material parameter that lends itself to correlation is roughness or surface texture. Roughness is readily measured using a scanning electron microscope, a profilometer or an atomic force microscope (see Chapter I.1.5). Relationships between roughness and blood hemolysis (Wielogorski et al., 1976) or thrombogenicity (Hecker and Scandrett, 1985) were reported. Textures and roughness are also extremely important to the fixation of materials into hard tissue, and to the nature of the foreign-body response observed (Thomas and Cook, 1985; Schmidt and von Recum, 1991; Brauker et al., 1992) (see Chapter I.2.15). A complication in the use of the roughness parameters is differentiation between porosity and roughness, and also an appreciation of the difference between the average feature amplitude (often call Ra) and the nature of the roughness (e.g., are rolling hills and jagged rocks of the same height also of the same roughness; see Figure III.1.3.5)? Specific porosities, which might be measured as rougher or smoother surfaces, profoundly impact biological reactions (Brauker et al., 1992; Bryers et al., 2012).
FIGURE III.1.3.5 Cross-sectional views of four surfaces with similar average roughness (Ra).
Clinical results correlated with material properties are infrequent, in part because materials used in clinical studies are generally not characterized to measure the parameters appropriate to make such correlations, and also because of the complexity of interpreting data from humans. However, a few such studies have been published. In the 1970s, a contact angle measurement criterion was established as a quality control paramater for qualifying the clinical success of processed umbilical cord vascular grafts (Shapiro et al., 1978). In another example, rigid gas permeable contact lens wettability was correlated with subject discomfort, and a predictive trend was noted (Bourassa and Benjamin, 1989). Catheters that are used in humans were evaluated in a test system closely simulating clinical application (Wilner et al., 1978). Catheters were classified into three groups related to their probable success, but clear relationships to surface properties were not discerned. Studies by Bailly et al. (1996) were more successful at establishing relationships between catheter properties and in vivo thrombogenicity. The complications in performing control studies, the difficulties in assembling a sufficiently large experimental population, the complexity of the materials (devices), and the human biology make clinical correlation challenging.
Issues Complicating Simple Correlation
Correlations should allow us to take readily measured physical properties and use that information in the design of improved biomaterials. Although many studies suggesting intriguing possibilities are cited here, this textbook does not present these correlations as rules that can be used in biomaterials design. It should be clear by now that, although many correlations have been noted, there is often contradictory evidence about what the correlating factors are, and the nature of the correlations. Also, in many systems, no obvious correlations have been noted.
The most widely-used correlating factor has been surface energetics, possibly because contact angles can be readily measured in any laboratory (Chapter I.1.5). Surface energetic parameters relate back to the second law of thermodynamics, and it is well-established that the interactions of simple colloid particles can be modeled using thermodynamic and electrostatic arguments. If living cells are treated as simple colloid particles with fixed mass, charge density, polar forces, and hydrophobic interactions, thermodynamic (energetic) modeling may be appropriate (Gerson and Scheer, 1980; Fletcher and Pringle, 1985). However, living cells most often cannot be viewed as “hard, charged spheres.” Living cells can change their surface characteristics in response to surfaces and other stimuli. Also, specific (e.g., receptor) interactions do not lend themselves to this simple thermodynamic modeling. For example, two surfaces with similar (but not the same) immobilized oligopeptides, and hence essentially the same surface energy, may interact very differently with cells, if one of the oligopeptides represents a minimal recognized sequence for the cell surface receptor. This was observed with fibroblast cell attachment where an immobilized peptide containing an RGD unit (arginine-glycine-aspartic acid) and a closely related immobilized peptide containing an RGE segment (where the E indicates glutamic acid) were compared (Massia and Hubbell, 1990). The RGD peptide was highly active in inducing cell spreading, while the RGE peptide was not (see Chapter I.2.17 for details on this experiment). Finally, the nature of the correlations may be multivariate rather than univariate. This concept will now be discussed.
Multivariate Correlation
Cause and effect observations are widely used by scientists and engineers to develop generalizations valuable for predicting and modeling phenomena. For example, if the temperature of a solution is increased (the cause), the reaction rate between two chemicals in the solution will increase in a well-defined manner (the effect). There is a simple univariate correlation between temperature and reaction rate. However, many systems, particularly multicomponent systems that are so often important to biomaterials science, have competing reactions that are dependent upon each other (e.g., the product of one reaction may influence the rate of another reaction). Thus, we do not see a simple relationship, but rather many changes occurring simultaneously. Our eye cannot discriminate the key trend(s) in this “stew” of changing numeric values. Multivariate statistics is a class of statistical methods that looks for trends, patterns, and relationships among many variables. Also, where contemporary analytical instrumentation produces large amounts of complex (e.g., spectral) data, multivariate statistics can assist in examining the data for similarities, differences, and trends. Where large data sets overload our ability to discern relationships, multivariate methods thrive on large amounts of data and, in fact, become more accurate and useful. This class of statistical methods has come into its own only with the introduction of powerful computers, since the methods are computation-intensive. Many general introductions to multivariate statistics are available (Sharaf et al., 1986; Massart et al., 1988; Martens and Naes, 1989; Wickens, 1995; Brereton, 2003; Manly, 2004). Multivariate statistics applied to problems involving chemistry are often referred to as “chemometrics.”
An important general principle in multivariate analysis is dimensionality reduction. A plot of x versus y requires us to think in two dimensions. A “three-dimensional” plot of x, y, and z can still be easily visualized. Where we have w, x, y, and z as the axes, we lose the ability to absorb the information in graphical form and visualize trends to the data. However, if we take our three-dimensional example, we can visualize a projection (shadow) of the three-dimensional data cluster in two dimensions. We have reduced the dimensionality from 3 to 2. Similarly, our four-dimensional data set can be projected (by a computer) into a three-dimensional space. Thus, we have a data representation we can visualize in order to look for trends. This dimensionality reduction is readily performed by computers using linear algebra methods. The projection of a five-dimensional data set is a four-dimensional shadow, a structure in space our minds cannot visualize. But a computer has no such limitations in looking for relationships in complex multidimensional data sets. The number of dimensions that the computer can work with is, for all practical purposes, unlimited.
There are many multivariate statistical algorithms useful for analyzing data. They are sometimes divided into classification methods (also called cluster analysis methods) and factor analysis methods (Mellinger, 1987). Classification methods find similarities in groups of data points, and arrange them accordingly. Factor analysis methods take data and transform them into new “factors” which are linear combinations of the original data. In this way the dimensionality of the problem is reduced. Factor analysis methods useful for multivariate correlation with data sets such as are acquired in biomaterials research include principal component analysis (PCA) (Wold et al., 1987) and partial least squares (PLS) regression (Geladi and Kowalski, 1986). Review articles oriented to the issues in biomaterials science are Wagner et al. (2006) and Park et al. (2009). Two important points about these methods are that they do not require a hard model (rarely do we have such a quantitative model), and that they make use of all the data (i.e., we do not have choose which data we want to put into the correlation model). There are numerous examples of the application of these methods to biomaterials research (Wojciechowski and Brash, 1993; Perez-Luna and Ratner, 1994; Kempson et al., 2010; Barnes et al., 2012). The power of these statistical methods is being recognized, and they will become standard data analysis tools. This is because they make efficient use of all data, thrive on large amounts of data produced by modern instruments, are objective in that we do not have choose which data to use, are congruent with biomaterials studies that typically have many interrelated variables, and reduce the influence of noise and irrelevant variables, thereby effectively increasing the signal-to-noise ratio.
Multivariate statistical methods can be a great boon to data analysis, but they will not solve all problems in biomaterials science. They should be considered as powerful hypothesis generators. The correlations and trends noted using such analysis represent a new view of the significance of data that we cannot appreciate by staring at spectra or tables. New hypotheses about the importance of materials variables can be formulated, and then they must be tested. Multivariate statistical methods also provide powerful tools for experimental design, but these will not be discussed here.
Conclusions
Perhaps the reader expected this chapter to provide instruction on the importance of wettability, or roughness or carboxyl group concentration on biological reaction? Unfortunately, biomaterials science is not yet at the state where we can assemble a handbook of design data about the relationships between surface structures and biological reactions. We do not fully-understand the controlling variables from the biology or the materials science sufficiently well to generalize many of our observations. What this chapter does do is to suggest that such relationships probably exist, and to point out that there are powerful mathematical methods that have the potential to help us generalize our data into correlations and trends useful in biomaterials and medical device design.
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