( GUEST EDITORIAL J

What Is Stiffness?

Neil Watson, MA, MD, FRCSAdjunct Associate Professor,North Carolina State University,Raleigh, North CarolinaSenior Research Scientist,Triangle Research and DevelopmentCorporation,Research Triangle Park,North Carolina

M any of the difficulties that our patients faceafter hand injuries or surgery and much of

the time that they expend in rehabilitation are relatedto stiffness. Yet the word "stiff" can mean so manythings. To those disciplined in physics and engi­neering, the meaning is specific and can be definedmathematically. As clinicians, we must understandthe true scientific meaning of the word "stiffness"because with an increasing input of applied biome­chanicaI knowledge, stiffness, in its true scientificsense, is now being used as a measure of fracturehealing. It's no longer good enough simply to referto a joint or a limb as being stiff .

So what is the scientific definition of stiffness?Before defining stiffness in as simplistic a way aspossible, we must clarify the meanings of the wordswe are about to use. Otherwise, we will not knowwhat we are talking about and we will become con­fused by jargon.

A polymer is a substance made up of very bigmolecules. Large numbers of similar units are linkedtogether in a complex, twisted way and their rela­tionships may change constantly, predominantly inresponse to heat. Rubbers and plastics are polymers;metals are not. Many of the biologic substances, suchas proteins and polysaccharides, that make up nor­mal connective tissue as well as healing connectivetissue are polymers. Collagen, for example, is a pol­ymer. So we can look at the physical behavior pat­terns of some natural and manmade polymers andtranspose them into biologic settings . Of course, it's

A modified version of this editorial was presented at the Surgeryand Rehabilitation of the Hand- '90 Symposium and Workshop,March 11-14, 1990, Philadelphia, Pennsylvania.

Correspondence and reprint requests to Neil Watson, MA, MD,FRCS, 3409 White Oak Road , Raleigh, NC 27609.

Dr. Watson was formerly a consultant hand surgeon at the OxfordRegional Health Authority in England.

not quite as easy as that because in a living organism,whether healthy, diseased, or injured, there are manyfactors that govern the mechanical properties of tis­sues. But we can make a start with the basics.

We are all familiar with elasticity. We know thatrubber bands can be stretched a long way before theybreak, and that steel objects can't (unless your nameis Uri Geller, anyway) . But how can we define andquantify that difference in elasticity between rubberand steel, for instance, that we know so well fromexperience exists?

A modulus is defined as a constant, or coeffi­cient, that expresses numerically the degree to whicha property is possessed by a substance. That soundslike, and is, a mouthful. But read it again and re­member how we are about to use it-to define elas­ticity and stiffness, and to compare those propertiesin one substance or material with those in another.

In Figure I, a length of a substance (L) is fixedat one end and has a cross-sectional area (A). Apulling, or tensile, force (F) is applied to its free end.This force elongates the structure by a small amount(~L) and, at the same time, makes it thinner, so thatthe cross-sectional area (A) becomes less by ~A, where~A is the reduction in the cross-sectional area. Thenew length is L + ~L and the new area is A - ~A.

For practical purposes, we can assume that there isno change in volume.

The proportion of ~L to L, or relative increasein length, is defined as the tensile strain. Yes, wehave all heard of that term and perhaps we haveused it, but have we had its true meaning clearly inour heads? I hope we do now. And, at the sametime, we may understand that the force per unit areais the tensile stress.

Young's modulus of elasticity is expressed as :

tensile stresstensile strain.

It is commonly recorded as dynes per square centi-

July-September 1994 147

FIGURE 1. Tensile strain.

shear stressshear strain.

j.,------ ------1-----,III,

A I F~----+III,•

~------------~~--

FilL

Notice here that " stiffness in tension" is a preciselydefined scientific term. By contrast, the clinical ob­servation "stiff in extension" is just that, a clinicalobservation. It is not easily quantifiable, nor is itscause, or causes, stated.

If it were to behave properly as a polymer, whichit is, the collagen of Dupuytren's tissue or woundrepair would exhibit rubbery elasticity. If it did, wecould predict the responses to stretch and shear, butwe can't. Why not? It's too simplistic. You see, thereare also other factors (perhaps "stiff" muscles, "stiff"joints, or "stiff" skin), or some form of inhibition ofmovement, maybe in response to painful stimuli, thatcan be controlled either voluntarily or involuntarily.We must consider elastic moduli for neighboring tis­sues of the wound collagen, as well as other prop­erties of those tissues (e.g., viscosity of synovial fluidor viscosity of organizing hematoma) .

This leads to another concept-viscoelasticity.In other words, a material that has both elasticity,which we have considered, and viscosity, which wehave not considered. Are not hands viscoelastic? Theycontain tissues with elastic properties and tissues withviscous properties. Well , not really. Bouncing puttyis viscoelastic, but hands certainly don't behave likethat. And it's a good thing that they don't, otherwiseour hands would spread out into puddles every timewe put them down for a few minutes. Muscles areviscoelastic.

and in shear it is

examples and find that stiffness in tension isL~~--

meter and produces a figure that can be used forcomparisons. For example, Young's modulus is 1010

for collagen, 1011 for bone and for oak, 2 x 1012 forsteel, and 1.4 x 107 for rubber.

Hooke's law of elasticity states that ilL, th eamount of stretch, is proportional to force (F). How­ever, this law does not hold true for all materials.

In Figure 2, instead of pulling on the piece ofmaterial or applying a tensile force (as was done inFig. 1), a different force is applied at right angles tothe tensile force . This force changes the shape in adifferent way (the new shape is shown by the dottedlines) . The angle p' is known as the shear strain. Thelinear amount of deformation is s. The shear stressis F divided by A. Now we have another modulus,the shear modulus. It is expressed as:

We could derive another modulus for volume or bulkin a similar way.

Now, to produce the deformations we have con­sidered, work has to be done. When an elastic ma­terial is stretched, some of the work of stretching itis stored within the material and then produces theenergy for the elastic to recoil when the stretching isover. The work that is " recovered" and used in therecoil may be expressed as a percentage of the workdone in th e stretching. This value is known as re­silience (i.e. , by how much something cat:' return toits original shape after deformation). Some of theenergy will always be lost as heat. This differencebetween energy to stretch and energy to recoil canbe plotted, and values can be calculated. The curvesproduced are known as hysteresis curves or loops.The Greek word "hysteresis" means a shortcoming.In the context of elasticity, hysteresis means the dif­ference between energy to deform and energy torecoil.

Only now can we define stiffness (S). When anelastic recoiling force is expressed as SilD and thematerial has been lengthened by distance ilD,thenthe stiffness is S. We may apply this to our original

148 JOURNAL OF HAND THERAPY

L

----- p' ....-_ S-- ..L.-- -.....

A

'--...... p'---- .-- .--~•

F •I..FIGURE 2. Shear modulus.

Now let's discuss fibers. These are a subdivisionof polymers, and it is into this subdivision that col­lagen fits . Therefore, we should look particularlycarefully at their properties and specifically at colla­gen, which interests us so much. Collagen exhibitsa fringed fibril structure. According to Hearle, in someplaces molecules run together and are joined, as ina crystalloid structure. This area is called a fibril. Inother areas there is no such form and molecules sim­ply run in a random fashion. Interestingly, one enor­mous molecule may run through the structure suchthat in some places it is part of a fibril and in otherplaces it simply wanders about in the middle of noth­ing in particular. The fibrils themselves are long, but,paradoxically, their constituent parts are relativelyshort.

This characteristic of a fiber, its arrangement intofibrils, confers upon it mechanical properties that dif­fer from those of randomly arranged structures . Forour interest this means differences in elasticity. Arandom structure has the same Young's modulus forany direction of deforming force. This is not so witha fiber: the more it is organized, the greater thisdifference becomes.

What do we know about the mechanical prop­erties of collagen fibers? These fiber s can be stretchedfor 10% to 20% of their lengths before they break.Some of the stretching is due to structural rearrange­ment rather than actual fiber lengthening. But, bio­logically , collagen has a high modulus of elasticity(as we've seen already), making it a well-adaptedprotein for tendons and ligaments, tissues that arerequired to resist tensile forces. In some situations,particularly pregnancy, collagen becomes more ex­tensible.

"Stiffness" of collagen is more difficult to define.Muscle is viscoelastic and, more excitingly, contrac­tile. The mechanisms by which those contractionsoccur within the muscle are beyond the scope of thisdiscussion. Briefly, as a result of complex physico­chemical properties, muscles may contract and shorten(isotonic contraction), or they may contract but re­main the same length (isometric contraction). Thesecontractions are controlled by both voluntary andinvoluntary components of the nervous system. Forexample, we do not consciously control the heartmuscle; it is on "automatic," just as the muscles 'ofthe gut are. The resting length of the muscle is afunction of complex electrical circuits. These are"feedback" circuits, which fire in response to length-

•

ening and shortening. The information is picked upin the muscle spindles. (Incidentally, stretch recep­tors also exist within ligaments.)

We must be especially wary about the restinglengths of muscles, particularly the lumbrical mus­cles. Rested too short or too long, these circuits ma ybecome set at new levels that are not within a goodfunctional range. And if the fibers contract or becomefibrotic, whether due to injury or neural malfunction,they may "stiffen."

I now want to discuss joints and how they stiffen .Basically, they stiffen in one of two wa ys: either theopposing articular surfaces may, as a result of diseaseor damage, become rough or perhaps even "dry,"so that they are no longer free to move easily, oneagainst the other, as in osteoarthritis; or adhesionsmay develop in such a way that they prevent jointmovement by "sticking" structures together that arenormally free to move with respect to each other.Such adhesive stiffness, which can and does presentsuch a problem with the gliding of tissues, not onlyaround joints but also, and especially, with respectto the flexor tendon mechanism, therefore cannot beseen as a function of the elasticity of the componenttissues that we considered earlier.

So, what is an "adhesion," and why should itcause so much trouble and stiffness? In a biologicsense, it is a description of a state in which tissuesbecome adherent to each other. The biological "glue"is fibrous tissue, and the fibrous tissue is usually theconsequence of injury or disease . Why do some peo­ple form more of this glue, and therefore get morestiffness, than do others? We simply don't know.

I hope that by considering some of those defi­nitions that in physics determine the definition andquantification of stiffness, your own thoughts as towhy inflexibility, or "clinical" stiffness, might haveoccurred and how best to lessen it have been re­awakened. But, as in so many branches of medicine,prevention is better than cure. As physicians, wemust control disease before it leads to unwanted fi­brotic side effects. As surgeons we must minimizethose situations in which the fibrocyte loves to growand multiply (e.g., damaged tissues, hematomas, andinfection) . As hand therapists, by splinting, stretch­ing, molding, and reeducating the tissues, we canminimize or prevent clinical stiffness, or inflexibility.Although we may not be able to cure stiffness, wewill almost certainly be able to alleviate it by edu­cating ourselves and our patients.

july-September 1994 149