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2 NATURAL HIERARCHICAL MATERIALS Many materials systems found in nature exhibit combinations of properties not found in synthetic systems. The unique performance of natural materials arises from precise hierarchical organization over a large range of length scales. The hierarchical architectures of cellulose aggregates in wood or collagen aggregates in cartilage or tendon provide excellent examples of natural composite materials designed for multifunctional applications. Even the ultrasoft membranes surrounding cells exhibit exceptional properties that emanate from structure on many length scales. These materials display unique properties that are affected by structure and generative processes at all levels of the biological structural hierarchy. Studies of materials of biological origin invariably yield surprises that demonstrate clearly that these properties have been refined by slow evolutionary engineering. This chapter focuses on the causal relationships between structure, at each level of the hierarchy and the resulting physical properties of the material or system in question. Some principles of biomaterials design and properties are discussed and illustrated in the context of several case studies on such materials as tendon, articular cartilage, wood, and nacre. In the course of its discussions, the committee considered these and many other biological materials systems. This process led to a series of recurring observations regarding the salient characteristics of this class of materials. The 17
18 Hierarchical Structures in Biology as a Guide for New Atatenals Technology committee suggests that hierarchical materials systems in biology can be characterized by: . . . . · recurrent use of molecular constituents (e.g., collagen), such that widely variable properties are attained from apparently similar elementary units; controlled orientation of structural elements; durable interfaces between hard and soft materials; sensitivity to and critical dependence on-the presence of water; properties that vary in response to performance requirements; . . . fatigue resistance and resiliency; controller! and often complex shapes; and capacity for self-repair. Each of these characteristics is discussed briefly herein, with reference to selected case studies and to other hierarchical biomaterial systems. RECURRENT USE OF MOLECULAR CONSTITUENTS Nature uses collagen in stunningly different ways: in the crimped fibers in tendon, which absorb, store, and transmit forces between muscle and bone; in the junctions between high and low modulus materials in articular cartilage; and as components of hard materials such as bone. At the molecular level, there are relatively minor differences among the collagens in these disparate biomaterials; all are similar in amino acid composition and all occur as collagen "molecules," coils of three interwound helical polypeptides about 300 nm in length (Figure 2-1~. Five collagen molecules align longitudinally with an overlap of approximately one quarter the molecular length to form a microfibril of 3.6-nm diameter. This so- called quarter stagger structure includes a gap between successive collagen molecules that gives the characteristic 64-nm banding pattern
Natural Hierarchical laterals ib°9~9v- <r - _ 19 Alpha chain ~ ~ o.1 am $.;::.: ~ Act: ~ it.... ~ :~ ~.,2,~,,~, ::.,c, ~ Triple helix Collagen molecule Collagen fibril with quarter stagger array Fibril with repeated banding pattern seen under electron microscope FIGURE 2-1 Building blocks of the collagen fibril. Source: Mow et al., 1992. By permission of the publishers, Butterworth-Heinemann, Ltd. Observed in the electron microscope and by x-ray diffraction (Wainwright et al., 1976~. The microfibrils are then assembled into collagen fibrils that may vary in diameter from 35 to 500 nm. These basic fibrils are combined and oriented to form more highly ordered structures with a particular morphology that determines the mechanical properties of the tissue. In the tendon, for example, the parallel alignment of crimped collagen fibers oriented longitudinally between muscle and bone provides nonlinear stress-strain behavior, with a gradual increase in stiffness upon elongation and a limiting elongation of a few percent (Kastelic and Baer, 1980~. In the body of the sea anemone, on the other hand, one finds the collagenous connective tissue called the mesoglea, which is a highly hydrated, low modulus (1 kPa) viscoelastic
20 Hierarchical Structures in Biology as a Guide for New Laterals Technology material that accommodates reversible extensions of more than 150 percent (see "Controlled Orientations. And in bone (surrey, 1979, 1984), oriented collagen fibrils increase the elastic modulus, the work of fracture, and the breaking strain of the associated hydroxyapatite mineral. Although it is clear that composition (e.g., the presence of water or minerals) is critical in determining the properties of these collagenous materials, the range of behavior achieved on the basis of this single versatile family of macromolecules, because of their architecture is astonishing. The lesson for materials design is that architecture and not composition alone must be considered in the creation and optimization of new materials systems for use in high- performance applications. Tendon provides an instructive example. CASE STUDY - TENDON Tendons connect muscle to bone around a joint, thereby transmitting the force and displacement of muscle into joint motion (Kastelic and Baer, 1980~. Tendons are subjected almost exclusively to uniaxial tensile loading directed along their length. Tendons must be elastic yet sufficiently stiff to transmit muscular force and capable of absorbing large amounts of energy without fracturing. For example, tendons absorb the shock to the knee joint in landing from a jump. This combination of mechanical properties is accomplished through the unique hierarchical structure of the tendon and the resulting incremental response to mechanical loads that provides initial elasticity, followed by high tensile stiffness and distributed plastic deformation to avoid catastrophic failure modes. In the tendon, collagen fibrils are organized into ultrastructural fibrils that interact to form microscopic fibers that are packaged into larger fibers that are aligned parallel to one another and oriented longitudinally between the muscle and bone (Figure 2-2~. The linkage among units at each level differs, giving an overall complex set of properties to the tendon. When these fibers are observed between crossed polarizers in the optical microscope, they have an undulating appearance. Further examination reveals the waveform to be a planar
Natural Hierarchical Alatenals zigzag or crimp rather than a helix (i.e., the microscopic structure does not reflect the helical conformation of the constituent collagen macromolecules). The crimp is ubiquitous in all mammalian tendons and other connective tissue types. i Ten~don Collagen molecule ~~ ~,~9 ~ Subfibril ~Fibril ~_% Microlibril ~ I lid /1,1~, ,~`,3 -~51 ~ ~] 3.5nm staining sites 1 1.5 nm 3.5 nm 1~20 nm ~1 64-nm periodicity~ Fibroblasts F~scicle Crimp structure \ l Fascicular membrane 1 50 500 nm 5~300 `~m 10~500 Em SCALE FIGURE 2-2 Hierarchical structure of the tendon. Source: Baer et al., 1992. The response of the various elements of the hierarchical structure of the tendon is reflected in the shape of the stress-strain curve (Figure 2-3~. At small tensile deformations, the curve is nonlinear, which is the case for all connective tissues. With further stretch, the curve becomes steeper and linear as a result of progressive straightening of the crimp. All normal physiological loads are confined to the nonlinear toe region of the curve. When all the fibers are straight, the modulus is high and constant. In the linear region, the fully straightened collagen fibers are further pulled elastically. If the load is released, the tendon will immediately and entirely recover its initial crimped morphology. At high strains, the tendon shows yielding and irreversible damage as the collagen fibers begin to disassociate into subfibers, fibrils, and microfibrils. Localized slippage and voiding between hierarchical levels account for the yielding observed at the macroscopic level. The hierarchical 21 - Reticular membrane
22 Hierarchical Structures in Biology as ~ Guide for New Aiatenals Technology 8 7 6 ~ 5 .E ~ 4 X - ~n to ~ 3 4 - ~n 1 o l /37 months / 24 months l 0 I // 12 months - ~!// °1 I a) 1 . o ._ cat a)1 a) -1 3 months I ~1.7 months _ to 17% 1 1 , , , - 0 2 4 6 8 10 12 Strain (%) FIGURE 2-S Strese-strain behavior of rat tail tendon as a function of age. Source: Kastelic and Baer, 1980. design distributes stresses throughout the levels of structure, thereby minimizing dangerous stress concentrations that could precipitate failure and fracture. The architecture of tendon provides important advantages in dynamic performance. For example, in the running human, the stresses used to launch the body off the ground at each step stretch the Achilles tendon elastically by about 4 percent. As the body leaves the ground, the leap is increased as much as 40 percent by the elastic recoil of the tendon. The total energy turnover for one foot-strike of a 70-kg man running at 4.5 m/s is about 100 I. Of this energy, about 17 ~ is stored as strain energy by the tendons in the arch of the foot, and 35 J is stored by the Achilles tendon. This energy storage amounts to a considerable savings in the cost of
Natural Hierarchical Afatenals locomotion (Ker et al., 1987~. The fatigue resistance of the tendon is remarkable as well; an athlete who runs 10 miles a day can use each Achilles tendon 6 million times in a year without suffering permanent damage. CONTROLLED ORIENTATION 23 Even a cursory examination of tissues such as bone, mesoglea, or cartilage reveals the important role of orientation in defining the mechanical response of structural biomaterials. In bone, for example, the c-axes of the hydroxyapatite crystals are preferentially aligned not only with the axes of the associated collagen fibers but also with the directions of pull of the attached muscles. The hierarchical features of the tissue control the fracture properties of bone, particularly the toughness (surrey, 1984~. Fracture surfaces show considerable roughness, because the collagen fibers in neighboring lamellae of the bone are oriented at right angles to each other. The work of driving a crack across the interfaces made by the plates, sheets, and Haversian systems of bone is much greater than it would be if the material were homogeneous. All types of bone are anisotropic. For example, the tensile strength of compact bovine Haversian bone is 14S, 49, and 39 MPa in the longitudinal, tangential, and radial directions, respectively. These differences correlate directly with the orientation of the Haversian systems in the material. A second example of subtle orientational control may be found in the body of the large anemone Metridium (40 cm tall x 10 cm in diameter). The body is a hollow cylindrical wall consisting of two cell layers separated by a layer, 2 mm thick, of a collagenous connective tissue called mesoglea (Gosline, 1971 ). Mesoglea is a fibrous composite that consists of ~ percent microscopic collagen fibers (diameter of 1-5 ~m) embedded in I percent of a "rubbery" matrix of an amorphous polymer with high molecular weight in 91 percent seawater. The matrix surrounding the collagen fibers is probably a protein-polysaccharide complex that forms a dilute gel linked into a permanent network. The matrix accounts for both the extensibility and the elasticity of the mesoglea; the collagen acts as a reinforcing filler that provides rigidity to the soft matrix on short time scales. In the outer layer of mesoglea, collagen fibers lie in a crossed helical array and account for the ability of the animal to bend with tidal flows without kinking. But in the inner layer, the microscopic
24 Hierarchical Structures in Biology as a Guide for New Afatenals Technology collagen fibers are circumferentially oriented, reinforcing the body wall to the tenfold increases in body diameter (and one hundredfold increases in body volume) that the animal undergoes in its normal behavior. A third striking example of the role of orientation in controlling the mechanical performance of hierarchical biomaterials is provided by wood, in the second case study. CASE STUDY - WOOD Wood is a hydrated composite with a high specific strength and stiffness, especially in the direction of preferred reinforcement orientation (parallel to the trunk) (Vincent, 1990; Wainwright et al., 1982~. The fracture toughness of wood is outstanding, largely due to the hierarchical structural arrangement and the resulting failure-containment mechanisms. Wood is composed of the high-modulus, high- strength, crystalline polysaccharide, cellulose, in an amorphous matrix of hemicellulose, lignin, and other compounds. The architecture is that of an aggregate of microscopic cylindrical cell walls of the composite, with the cylinders lying parallel to the long axis of the stem, root, or leaf. The cellulose in the cell walls has a preferred orientation that varies according to its position along the radius of the cell and hence its age in the wall. The wood of many tree species occurs in concentric growth layers of cells that have large lumens (early wood) alternating with layers of cell walls that have small lumens (late wood). Figure 2-4 shows the hierarchical scale and complexity of wood. Wood is anisotropic and viscoelastic. Most studies on the physical properties of wood are done on oven dried timber (12 percent water saturation), but wood evolved to function in trees in its saturated (wet) state. The low density (600 kg me) of timber makes it an appropriate material for many manmade contrivances. Wood and mild steel show comparable stiffness per unit weight, but the specific strength of wood is four times that of mild steel.
Natural Hierarchical Afatenals . - Tree m 25 -S3 Secondary Cell Wall ~ ~ S2 -S1 Primary Cell Wall 7= A' /~ Macrofibrils in amorphous matnx glycopro~eins Bundles of \~¢ it/ ~In amorphous / hemicelluloseJ - | mains Plant Cell Walls Macrolibril Mlcrotibril 1 ~1- - 1 -- 1 -- -- amorpl70us domain | crystalline domain parallel polymer chains i1~4 1inked glucose cm/mm ~ m rim SCALED FIGURE 2-4 Structural hierarchy of cellulose in wood. (Courtesy of D. Kaplan, U.S. Army Natick Research, Development, and Engineering Center) The most remarkable property of wood is fracture toughness that is 10 times greater than would be predicted considering volume fractions of fibers and matrix in fibrous composites. These predictions assume that the creation of new surface area by fiber pu11-out is the major mechanism responsible for fracture toughness. The mechanism accounting for the high fracture toughness for wood is helical column buckling of the cellulose fiber- wound cell wall (leronimidis, 1976~. Interfibrillar cracks due to shearing will open and propagate longitudinally while the cylindrical wall collapses inward, which allows each cell wall to be pulled apart without being broken in two.
26 Ilierarch~cal Structures in Biology as a Guide for New Laterals Technology DURABLE INTERFACES BETWEEN HARD AND SOFT MATERIALS The performance of hierarchical materials systems depends critically on the formation of appropriate interfaces between structural elements of disparate scale and composition. Particularly intriguing and challenging from the point of view of system design are interfaces between materials of widely different stiffness (i.e., between hard and soft materials). Nature uses a variety of strategies to make such interfaces. In bone, for example, it has been proposed that the interface between collagen and the hundredfold stiffer hydroxyapatite is formed via epitaxial crystallization of the mineral on a phosphorylated collagen template (Glimcher, 1984~. In articular cartilage, collagen orientation changes from parallel to the surface in the outer zone, to a perpendicular orientation at the interface, with fibers extending into the bone (see Case Study-Articular Cartilage). And in mollusk shell nacre, the next case study, a protein-chitin "sandwich" serves to interconnect much stiffer inorganic crystals, absorbing much of the work of fracture via ductile deformation and the formation of new surface. CASE STUDY - MOLLUSK SHELL NACRE (MOTHER OF PEARL) The inner nacreous layer of mollusk shells is a layered composite that has outstanding strength and hardness white maintaining remarkable fracture toughness (Jackson et al., 1988; Sarikaya et al., 1990~. The high volume fraction of the reinforcing (hard) phase, compared with processible synthetic composites, allows strength and hardness to approach that of the monolithic material. The reinforcing phase is bound with a very thin layer of soft but tenacious matrix that imparts fracture toughness to the composite. The structure of nacre is shown in Figure 2-5. Aragonite "bricks" make up layers 150-500 nm thick that are interspersed with layers of organic polymeric material 20-250 nm thick. The aragonite bricks are plate-like
Natural Hierarchical Materials single crystals with specific orientation relationships among crystals of the same layer, as well as among crystals of successive layers. The organic matrix phase is continuous throughout the material and is composed of the aminopolysaccharide, chitin, coated with a protein that promotes adhesion to the aragonite plates. The mechanical properties of nacre are better than those of most monolithic ceramics, with fracture strength of 185 ~ 20 MPa and fracture toughness, K,c = ~ +3 MPa m-% (Sarikaya et al., 1990~. The work of fracture across layers is 1 kJ me, and between layers is 0.1 kJ ~ ma. Toughening mechanisms revealed by fractographic analysis of fracture surfaces and indentation cracks include (1) crack blunting and branching; (2) microcrack formation; (3) sliding and pull-out of aragonite plates; (4) polymeric ligament formation, akin to crazing, which bridges cracks; and (5) possible strain hardening and shearing of the organic material. THE ROLE OF WATER 27 Water is ubiquitous in biological materials, in amounts varying from a few percent in fibrous proteins to more than 90 percent in mesoglea. Water forms strong hydrogen bonds with biological macromolecules and facilitates motion on all length scales, from molecular to macroscopic. The elasticity and toughness of many biological materials depend critically on hydration. In nacre, for example, toughness and ductility double upon hydration without significant loss of stiffness (Vincent, 1990~. Swelling pressures resulting from the presence of water in biological structures help to oppose compressive loads. In articular cartilage, for example, water constitutes 65-80 percent of the tissue and is confined in a swollen network of collagen fibers and proteoglycan aggregates. As described in the fourth ease study, the resulting hydrostatic pressure accounts for most of the apparent compressive modulus of the material and provides a source of lubricating fluid, which maintains the low coefficient of friction in the joint.
28 Hierarchical Structures in Biology as a Guide for New Materials Technology . ~ . .. FIGURE 2-5 The structure of nacre. Source: Sarikaya et al., 1990. ,,.~
Natural Hierarchical Afatenals CASE STUDY - ARTICULAR CARTILAGE Articular cartilage (Mow et al., 1990; 1992) is a natural hierarchical material exhibiting high strength and stiffness; functionally gradient microstructure; and outstanding friction, lubrication, and wear characteristics. Compositional and organizational characteristics provide the appropriate Reformational behavior required for cartilage to function as the low-friction, wear-resistant bearing materials at the ends of long bones (hip, knee, shoulder, etc.) and sides of sesamoid or carpus bones (patella, wrist bones, etc.) in highly loaded conditions. Articular cartilage is a porous-permeable, fiber- reinforced composite filled with fluid. The fibrous component is primarily type II collagen, and the gel matrix is made of aggregating proteoglycans. Collagen and proteoglycan form interpenetrating networks that create a strong solid matrix. Water, is by far the largest component (70 to 90 percent) of the tissue by wet weight as it is with most biologic tissues. Water contains a physiologic concentration of electrolytes that is required for osmotic equilibrium. The collagen network is cohesive, strong, and permanent, and it provides the required tensile stiffness and strength for cartilage. These properties derive from the intrinsic properties of the collagen molecule and the hydroxypyridinium cross-links that exist between collagen fibers. The proteoglycan aggregates form a labile network that provides the compressive stiffness that results from their bulk compressive stiffness and from the swelling pressure. The swelling pressure has two components --Donnan osmotic pressure and charge-to- charge repulsion amongst fixed negative charges (COO and SO3-) on the glycosaminoglycan groups of proteoglycans. Figure 2-6 illustrates the collagen microstructural organization of articular cartilage. Collagen content and collagen fiber orientation vary with depth from the articular surface. In the tissue, collagen content decreases and proteoglycan content increases from the surface zone to the inner zone next to the bone. Collagen fiber 29
30 Hierarchical Structures in Biology as a Guide for New Afatenals Technology orientation can be characterized in three zones: the outer surface zone has a preferred orientation parallel to the surface; the middle zone has orientation at nearly 45° to the surface; the deep zone has orientation perpendicular to the bony interface, with the fibers extending into the bone for effective anchorage. This is an excellent example of a junction between materials of high and low modulus. Normal articular surface is textured with ripples and dimples, with characteristic dimensions ranging from 0.1 to 10.0 ,um. These features function to trap pockets of synovial fluid that enhances fluid-film lubrication between the two bearing surfaces of the joint. In addition, the formation of the fluid lubricant film in joints is augmented by a circulation of water from cartilage. The high water content in the surface zone is particularly important for this self-lubrication process to develop. Zones Superficial tangential (10-20%) Middle (40-60%) ~ I, Deep (30%) _ Articular surface Calcified cartilage / ',~V'~.@c8~7~=,~~cV~ e~t5~_-,~O_ -"v~.v''"~' "v''= ~ A._ ~ Cancellous bone FIGURE 2-6 Ultrastructural organization of collagen fibers throughout the depth of articular cartilage. Source: Mow et al., 1992. By permission of the publishers, Butterworth-Heinemann, Ltd. The hierarchical architecture of diarthroclial joints and articular cartilage is illustrated in Figure 2-7. The charged nature of proteoglycans and electrolytes at the nanometer scale is responsible for tissue swelling, hydration, and pre-stress in the collagen network. The molecular and ultrastructural organizations of the
Natural Hierarchical Afawnals collagen-proteoglycan solid matrix are responsible for the fiber-reinforced composite nature of the tissue. The pre- stress (or residual stress) in the collagen network that results from proteoglycan swelling is believed to have an important physiologic function similar to pre-stressed reinforcement bars in concrete beams. The degree of hydration in the cartilage depends on the balance of swelling pressure and the elastic pre-stress developed in the solid matrix and is the most important factor governing cartilage mechanical properties and function. The cells in each zone of the tissue are structural features at the microlevel, and they are responsible for the phenotypic expression of the protein and carbohydrate products that are required to make collagen and proteoglycan and to maintain the specific structural organization in each zone of cartilage throughout life. This self-repair process is essential for maintaining the structural integrity of the tissue. When the biologic maintenance and repair processes fail, the cohesive collagen-proteoglycan solid matrix weakens, cartilage gains excessive hydration, and it fails to function as a bearing material in the joint. In this case, diseases such as arthritis develop. Normal cartilage has a coefficient of friction ranging from 0.005 to 0.02. Diseased cartilage has higher coefficients of friction. To put these figures in perspective, the value of ice on ice is 0.01~.1, and for graphite on steel, about 0.1. The complex architecture of articular cartilage results in a joint that can endure millions of cycles, under heavy loads (up to 18 MPa), without failure. The tensile modulus varies from zone to zone, from 41 MPa near the surface to 1.0 MPa near the bone. The equilibrium compressive modulus (1.5 MPa) does not appear to vary with zone and is provided equally by the bulk compressive stiffness and the swelling pressure. Under dynamic loading, very high compressive moduli have been reported (50 MPa). This apparent stiffness is provided largely by the pressure developed in the incompressible water component of the tissue. Thus, water has a major role in the ability of normal cartilage to oppose compressive loads in physiologic conditions. 31
32 Hierarchical Structures in Biology as a Guide for New Afatenals Technology Oculars Carobs ~ ~ 5\ Led || HICK (0.5cn~15cm) 67 nm Collagen Triple Helix Jolnt Cavig'' Subchondral Cortex Cancelhus id and Marrow Collagen Proteoglycans 1 1 ~ ~1 Nano (10 tin-10~m) Jesus (10~10~m) 1 ChondrocyI. Arikular Cartable ~'o'm.O 'm ~ . 15llm~ Ultra (10~10~m) Ulkro (10 7m-10~m) FIGURE 2-7 Hierarchical architecture of diarthrodial joints and the constituent articular cartilage. Source: Mow et al., 1992. By permission of the publishers, Butterworth-Heinemann, Ltd. Finally, the collagen-proteoglycan solid matrix is viscoelastic, with a shear modulus that increases monotonically with frequency from 0.2 MPa at 0.01 Hz to 2.5 MPa at 20 Hz. Thus the shear stiffness of cartilage is provided by collagen within the collagen-protoglycan solid matrix. PROPERTY VARIATION IN RESPONSE TO CHANGING PERFORMANCE REQUIREMENTS Perhaps the most fascinating characteristic of many natural materials is their capacity to respond-via changing properties to changes in performance requirements. For example, while the spines of the sea urchin are moving, the attacher! ligaments are soft and extensible, but when the animal is stimulated,the ligaments become
Natural Hierarchical Materials 33 viscous, causing the joints to stiffen (Motokawa, 1984; Trotter and Koob, 1989~. The effect is so dramatic that the calcite spines will fracture before the stiffened joints will give way to a sudden blow. The catch connective tissue of the urchin contains collagen alders In a tendon-like parallel array. Extending into the array are axons of nerve cells whose bodies lie in a ganglion outside the tissue. These ligaments lie parallel to muscles that bend the joint at the base of the spines, allowing the animal to point its spines at aggressors or to use its spines as stiff legs for walking. Isolated ligaments deprived of calcium ions are soft, while those exposed to natural concentrations of calcium are extremely viscous. Neurotransmitters (to which the isolated ligaments are sensitive) may be produced by the attendant nerve cells to control the ionic environment and thus the mechanical properties of the ligaments. . . . - CASE STUDY - SHARK SKIN The skin of sharks and other fishes operates mechanically as a two-dimensional membrane that is 2-4 mm thick and formed into a pressurized cylinder (Wainwright et al., 1978~. Shark skin is more than 80 percent collagen by volume. Its thick inner layer is made up of collagen fibers in 30 to 90 layers that are each 10 Am thick. Fibers in each layer are parallel, and fibers in alternating layers wrap around the animal's body in right- and left-handed helices. This makes the body a fiber- wound, pressurized cylinder. The fibers lie closely spaced in a viscous matrix of cells and other extracellular materials as yet unknown. When the fish swims, it bends its body in left and right directions, stretching the skin 10-15 percent on the outside and compressing it 1-15 percent on the inside of the bends. Thus the skin normally functions by stretching 10 percent, even though collagen's breaking strain is about 4 percent. The crossed-helical array of fibers and the hierarchical structure of the skin permit this range of motion. The shark's body is mostly muscle, which is a cellular viscoelastic solid of constant volume. When muscle contracts, shortening one side of the fish, it bulges
: 34 Hierarchical Structures in Biology as a Guide for Mew Afatenals Technology and causes an increase in pressure against the skin on that side. High modulus fibers wound helically around flexible cylinders reinforce against aneurysms that can be caused by internal pressure and allow the cylindrical body to bend without kinking. Stress in the skin of any thin-walled cylinder equals the pressure multiplied by the ratio of the body radius to the skin thickness. Skin stress in a fast swimming shark rises with pressure by as much as 200 percent. Since the skin is only stretching by 15 percent at most, to bear the increased stress the apparent stiffness of the skin increases amazingly, by a factor of 13. Thus, during normal function, stiffness, a material property normally thought to be static, is changing according to the demands of muscle action. The increase in stiffness apparently allows the skin to act in transmission of force from muscle in the anterior parts of the fish to manipulate the tail. It is likely that the study of biological materials capable of this kind of environmental response will reveal a rich variety of mechanisms for coupling of sensory information and the physical and mechanical properties of materials. Such studies should provide concepts useful in the design of new classes of advanced ("smart") materials with the capacity to adapt rapidly and productively to changing environments. FATIGUE RESISTANCE AND SELF-REPAIR Organisms are remarkably durable, especially in view of the fragility of their molecular constituents. The mechanisms by which organisms and tissues withstand damage without catastrophic failure are of interest with respect to the design of damage-tolerant materials and structures. In some tissues (e.g., in bone), durability results from a complex process of remodeling and reconstruction (surrey, 1984~. In others (e.g., in cellular membranes and associated soft tissues), resistance to wear and fracture emerges from the architectural features of the structure itself.
Natural Hierarchical Alatenals CASE STUDY - CELL MEMBRANES AND SOFT TISSUES The structure of cell membranes and their assembly into soft tissue can provide remarkable durability and wear resistance to biological organisms (Bloom et al., 1991; Evans, 1985; Evans and Skalak, 1980; Lipowsky, 1991~. The core layer of the membranes of animal and plant cells is a bilayer in which lipids, surfactants with short alkyl polymer chains, are organized into a hydrophobic film sandwiched between hydrophilic surfaces in which other cosurfactants (e.g., cholesterol, integrin proteins, ion channels, etc.) are embedded. Adjacent to the lipid core is a scaffolding of cytoskeletal proteins (e.g., actin), which supports the bilayer through specific sites of attachment along the inner surface of the membrane. Embedded inside the cell and often within a cytoskeletal mesh, other nonstructural organelles form a visceral slurry in which many biochemical functions are carried out, such as protein and lipid fabrication and chemical energy storage and generation. The membrane is hyperdeformable and ultrasoft with low extension modulus, for example, 0.1 to 1 kPa for the red blood cell (the modulus of soft rubber is 0.1 to 1 MPa). The lipid bilayer chemically isolates and regulates the cell interior; the cytoskeletal network provides mechanical support and controls the ability of the cell to change shape and, in some cells, to move. Large deformations are made possible by wrinkles and folds in the membrane. Cholesterol augments the cohesive and anchoring strength of the bilayer tenfold. Thus, in the red blood cell, a rigid polymer scaffolding has been interfaced with a fluid membrane to form a compatible composite that is two orders of magnitude softer than existing synthetic elastomers. At the next higher level of the structural hierarchy, a soft tissue, such as skin or liver, can be described as an aggregate of fluid membrane capsules which is supported by internal networks that are connected to form a compatible composite that is resistant to wear and fracture. Cells are bonded together by specific molecular "welds" between integral proteins in adjacent membrane 35
36 Hierarchical Structures in Biology as a Guide for New laterals Technology bilayers, which provide transmission of cytoskeletal stress from one cell to the next. The lipid bilayer envelopes are thus "transparent" to stress, and the mechanical properties of the tissue arise from the network of cytoskeletons that penetrate the bilayer capsules. Intercellular connections easily translate along the fluid bilayer, and the membranous envelope readily flows to accommodate network deformation. Friction between cells is minimized by highly hydrated glycoprotein spacers. SHAPE CONTROL The beautiful and intricate shapes of biological structures are apparent to even the most naive observer (Figure 2-~. But perhaps even more remarkable are the mechanisms by which structural shapes are controlled in biology. The shapes of a few simple biological structures (e.g., simple viruses), are entirely determined by the interactive properties and shapes of their macromolecular components, as these govern the self-assembly of the structures. However, complex shapes emerge from small scales to large, through intricate processes of molecular and supra-molecular assembly. Molecular information in biology is translated into structural features that are orders of magnitude larger in scale, and into performance properties that serve the survival needs of the organism. An understanding of these processes offers the prospect of significant new approaches to the fabrication of complex synthetic structures. Large biological structures consist of cells and matrices. The overall shape of such a structure is governed by the disposition of the component cells and of the matrices that some of them manufacture. The matrix-producing cells are closely apposed to existing matrix and may eventually become enveloped in matrix that they form. At any time during manufacture, the evolving shape of a biological structure is the product of multiple, successive hen-and-egg events: the cells that are currently making matrix are at specific sites because of earlier events in the development of the organism, and they, in turn, influence the sites where future cells will produce additional matrix. The number of synthetically active cells at a given site depends on earlier replication of cells by cell division; on migration of cells over preexisting structures; and on numerous genetic programs that control cell division, specialization of cells, and synthetic acitivity. In
Natural Hierarchical Aiatenals 37 addition, there are a variety of control feedback loops, many of which are poorly understood. Cells can mutually influence each other through diffusible factors, such as hormones and cytokines; cells repond to signals from adjacent matrix; and the biosynthetic activity of matrix-producing cells may even respond to local, repeated mechanical stress. From the above, it follows that the intimate relationships between the local manufacturer of matrix components, for example, a fibroblast cell, and the matrix to which it adheres, which may be part of a tendon or bone, influence both the local composition and the orientation of new matrix and, eventually, the shape of the completed tendon or bone. The local composition readily acquires a layered, or even interwoven, structure due to repeated cycles of deposition by sets of cells. Shape is not only influenced by geographically different rates of formation but also by selective removal of existing matrix or of complex combinations of cells and matrix. Tadpoles initially make a tail but then lose it when they turn into frogs. The whole head of a newborn infant could fit into the skull cavity of the adult head that it later develops into. This is partly because of selective removal of bone from the inner surface of the skull even while more bone is added to the outer surface during growth. The removal of existing matrix cluring growth can be highly selective not only at the macroscale of sculpting a previous shape but also at the microstructural level. For example, the walls and ends of a tubular long bone are not continuously solid but consist of trabeculae of bone that run along lines of mechanical stress during average, common use. These trabeculae are not permanently fixed but can change during abnormal use of limbs, as with a lopsided gait after injury to the one leg. Thus normal and pathological bone removal change the shape and structure of an earlier biological form. In summary, biological shape is the outcome of repeated deposition and selective removal. A critical feature during biological manufacture is that the microfactory, the cell, is intimately and locally associated with the evolving matrix. Importantly, many cells function at any one time, and the successive actions of cells are influenced by the history of manufacture. In general, shape and size are not fixed but change with the development and age of the organism.
Hierarchical Structures in Biology as a Guide for New Afatenals Technology FIGURE 2-8 Scanning electron micrographe of the rasping tongue of the mollusk Urosalpir~x cinereaSol~yensis. The mineralized structure contains crystalline magnetite in an ordered matrix of organic fibrile. Magnification: (a) 200x, (b) 575x, (c) 980x, (d) 980x. Source: Carriker et al., 1974.
