by George Marsh

What happens to a human head when it is hit in an

accident or by a weapon, or subjected to the violence

of an emergency ejection from a combat plane? This

question is something that interests QinetiQ, part of

the former UK Defence Evaluation and Research

Agency (DERA). Controlled experimentation on live

subjects is hardly an option, but computer modeling

of the head, with its constituent parts and materials,

is. George Marsh visited David Porter at QinetiQ’s

headquarters at Farnborough to investigate the

pragmatic approach that he and his colleagues take

to biomaterials and biostructures modeling.

Some fighter pilots alive today owe their survival to

tough, low-weight helmets whose qualities have been

refined as a result of biomechanical modeling. Porter

and his colleagues have modeled the human head as a

mechanical arrangement of a heavy ball on a rod

support, as a system of soft matter contained in a

hard case, as an arrangement of meso-scale sub-

systems, and as a combination of material systems

built up from the nano-molecular and atomic scales.

An extensive modeling hierarchy (Fig. 1) is held on

nothing more esoteric than a networked workstation

and server architecture. Nevertheless, thanks to a

process of focused simplification at each hierarchical

level, it is able to predict the mechanical behavior of

the human head and its constituents in reacting to

impacts with considerable accuracy.

HierarchyFundamental to the concept of hierarchy is that the causes

of any phenomenon observed at a particular scale must be

sought at a lower scale. Thus, for instance, quantum

mechanical calculations of binding energies, volume per atom

and vibrational frequencies within molecular chemistry

models can explain the way atoms and molecules come

together in an element or material. Subsequent consideration

at this next, physical, level of how defects form can help

engineers understand failure mechanisms at the ‘bulk’ level,

in major structures. An equivalent biological progression

would lead from atomistic to biostructural/material scales

via biomolecular and morphological levels. Each level in the

October 200232

A hard casefor modeling

ISSN:1369 7021 © Elsevier Science Ltd 2002

hierarchy represents a step up in both time and spatial

dimensions. Thus atomistic/molecular modeling at sub-

picosecond and angstrom scales is the base level, moving up

to millisecond and millimetric dimensions for mid-scale

physical/morphological models, and culminating in scales of

up to hours and meters for structural models.

Combinations of techniques from within the hierarchy

help QinetiQ scientists examine the material nature of

biological systems and create functional models using

simulations of synthetic polymers that are close analogues in

terms of their properties. Porter and his colleagues use

combinations of established models, often commercially

available, from within the hierarchy. This approach is made

more powerful by the use of tools which facilitate progress

through the levels. Notably these include quantitative

structure-property relations (QSPR), an empirical

simplification process that can help the user to move more

rapidly from atomic level to ideal properties, and the more

advanced group interaction modeling (GIM), which predicts

end properties from quantum considerations of the way

groups of atoms interact together. Essentially, these more

refined techniques can short circuit some of the steps

associated with working through the whole hierarchy.

Modeling processThe process starts with an exploration of existing data, in this

case for the human head – mechanical, anatomical, material,

medical, morphological etc. – involving every scale from

quantum/atomistic to bulk structural.

Porter and his coworkers search the available literature,

review existing models (predictive polymer models, for

instance, are well known in the pharmaceutical and chemical

industries), consult with other experts both internal and

external, and generally survey the knowledge base. Then

comes the crucial task of selecting from the amassed data

those elements most pertinent to the properties of interest,

for inclusion in the model. Simplification, important at each

level in the hierarchy, is a prolonged and carefully considered

process to ensure that everything of significance to a desired

property mix is secured, while anything which is not is

rigorously excluded. “We’re quite brutal in reducing

complexity,” explains Porter. “For instance, considering bone

at the molecular scale, we could get into the fine detail of

the 250 or so different compounds that make up the

chemistry, but most of this complexity is involved in the

growth and maintenance of the bone and, for the structural

properties we are interested in, we need only consider the

mineral and polymer phases in any detail. Essentially, we can

model bone as a mineral-plus polymer particulate-reinforced

nanocomposite, in which the hard mineral, hydroxyapatite, is

dispersed as tiny platelets throughout a collagen matrix.”

The power of the modeling hierarchy is formidable. At the

molecular scale, computer code sourced commercially makes

it possible to visualize the molecule of a particular form of

collagen, hydrated tropocollagen, and from it appreciate the

biopolymer’s physical properties qualitatively (Figs. 2 and 3).

The desk-top model can also be used to explore material

modifications. For example, injecting metal atoms at certain

key points in the structure, shifting hydrogen or oxygen

atoms, modifying the alanine, proline, and glycine groups, or

manipulating bonds changes the molecule’s properties.

Describing proteins as “polymer chicken wire”, and suggesting

that we should not be “over-awed” by them, Porter says that

of the vast number of chemicals involved, the trick is to

establish which it is necessary to consider for the given

purpose. In this case it turns out that a useful synthetic

analogue for collagen is branched Nylon 2, polyamide.

The pragmatic, structured simplification of this approach is

justified by its predictive power. For instance, it is possible to

predict the thermal and mechanical properties of collagen

from its simplified molecular representation by using QSPR

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October 2002 33

100

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Dim

ensi

ons

Anatomy Materials Modeling

Organismic

System

Organ

Tissue type(eg. muscle)

Cellular(eg. nerve cell)

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Atoms

Molecules

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Micro-scale

Object Continuummechanics

Defect/micromechanics

Mean field

Molecularmechanics

Quantummechanics

Fig. 1 The modeling hierarchy for biological tissue. Dimensions shown are in meters, but

the axis could equally represent time, ranging from fractions of picoseconds for quantum

considerations, to minutes or hours in structural modeling.

techniques, but Porter normally prefers the more powerful

GIM. This is, he believes, superior in its ability to derive visco-

elastic properties including the temperature at which

collagen ceases to be a solid (glass transition temperature in

composite terms), viscosity, and other rheologically

important factors (Fig. 4). Results derived from the integrated

model coincide well with those determined experimentally.

Moving to the mineral phase of bone, quantum-level

simulation of hydroxyapatite reveals the detail of a stiff,

brittle form of calcium phosphate having low heat capacity

and high bulk modulus (Fig. 5). Combining models for bone’s

two separate phases reproduces the anisotropic

nanocomposite structure of the compact form. Interface

dynamics are simulated at the nanoscale where the influence

of energetics – interchanges of thermal, configuration, and

cohesive (binding) energies taking place across the

boundaries – becomes crucial. Application of energetics

concepts is what enables GIM to bridge the vast range of

spatial dimensions involved in a way that is quantitatively

accurate and allows chemical and morphological structure to

be understood (Fig. 6). Energetics can also unify across the

time domain.

Simulating how bone reacts to impacts can involve models

ranging from simple mechanical to complex molecular, QSPR,

and GIM combinations. Researchers can visualize how

polymer molecules react to outside forces by altering shape,

form, and internal structure. QinetiQ found useful data by

studying how animals accomplish this. Through the use of ion

exchange mechanisms, for example, the normally soft and

jelly-like sea cucumber stiffens when it senses a threat.

Spiders use a similar mechanism to tailor the mechanical

properties of their webs.

Porter and colleagues have successfully simulated bone’s

tendency to soften on initial impact to enhance elasticity and

yield fractionally to the blow, then to stiffen as the applied

force increases to a tough, resistant form that maintains

rigidity to the point of fracture. Their model sheds light on

the redistribution of energy that takes place from the

polymer phase to the mineral. This change in elastic modulus

secures initial softening; then, when the mechanical stress is

high enough, the mineral plates begin to fracture, altering

their aspect ratio, so that the polymer’s ‘glassy’ component

increases at the expense of its rubber fraction – a form of

work hardening. Equations within the model express the

dynamics of this stress redistribution mechanism.

Illustrating GIM’s capability, QinetiQ scientists have used

the model to contrast the stress/strain relationships of a

cow’s femur and a deer antler. This example clearly illustrates

how bone adapts to these very different requirements, one

emphasizing elasticity and damage tolerance for combat

survival, and the other structural rigidity for load bearing.

Hard caseSoft brain tissue provides another example of how molecular

structure-property relations for synthetic materials can be

used to provide a picture of the complex nonlinear dynamic

properties of biological tissues. Similar polymer-based codes

to those used for bone can enable not only the brain’s

material properties to be modeled, but also its reactions to

impact and damage limitation mechanisms. Simulating its

material and structural characteristics again calls for a

APPLICATIONS FEATURE

October 200234

Fig. 2 Composite structure of bone, showing polymer and mineral phases.

Fig. 3 Structure of hydrated tropocollagen, the matrix phase of bone nanocomposite.

hierarchical approach in which, at one level, the brain is

merely a soft ‘blob’ inside a hard case, at another a collection

of lipid polymers, and at yet another a combination of white

and gray matter. The modeling is completed by inclusion of

cartilage and connective tissue. Soft flesh, however, does not

lend itself to this pragmatic treatment since it has no

adequate simple analogues.

Moving to the level of bulk properties, descriptions of the

dynamic mechanical behavior of biological tissues developed

at nano- and molecular-scales can be fed into familiar

engineering models, notably finite element analysis (FEA), to

simulate structural behavior. Again, apparently ruthless but

carefully conceived simplification pares down the high

number of starting parameters to just a few. While FEA and

other rigid body models best represent the hard shell-plus-

softer core and anatomical load-bearing aspects of compact

bone, various cellular models are used to reproduce the

characteristics of porous bone. Codes describing full

composite analogues for bone are brought together with

those for brain and other tissues to achieve a more

comprehensive model. This can then be fed into modeled

scenarios to simulate the effects of

accelerations/decelerations plus impacts in crashes and other

events (Fig. 7).

ApplicationsHelmets that help pilots survive extreme situations have

benefited from this pragmatic approach. Their fibrous

composite, particulate composite, foam, and other material

combinations provide high protection against impact with

exceptionally low weight. This last factor helps prevent injury

by adding as little as possible to the naturally high moment

of inertia possessed by the human head.

Consideration of why nature contrives to combine in bone

two materials with unremarkable physical properties into a

mineral/polymer combination, which is structurally

outstanding, has itself proved productive. It has stimulated a

biomimetic approach to the synthesis of nanocomposites

exhibiting similar property prioritization – that is survivability

and sustainability first, and mechanical optimization second.

“Adapting nature’s approach to engineering composites could

yield improved characteristics,” says Porter. “If we consider

that the synergy between the hydroxyapatite mineral and the

collagen polymer accounts for many of the features of

interest to us in bone, then maybe we should be looking for

similar synergies ourselves rather than relying on a single

really tough phase like carbonfiber.”

The scope of further applications is potentially

tremendous. For example, police authorities could be

October 2002 35

APPLICATIONS FEATURE

Fig. 4 Within a group interactive model (GIM), primary engineering and rheological

parameters are simulated using established mathematical relationships.

Fig. 5 Molecular models of bone’s mineral phase, hydroxyapatite, predict its stiff but

brittle characteristics.

Fig. 6 Crucial energetics modeling has to take place at the nanoscale since most energy

interchange takes place within a few nanometers of the interface between material

phases.

interested in the effects of rubber bullets or batons on bone,

or defense forces might wish to explore the effects of

frequent marching or other repetitive physical activity.

Health benefits could also result from investigations of the

reaction of bone to external stimuli. For example,

understanding how movement can counter osteoporosis

could benefit not only space agencies, but also the general

population. An important aim of on-going work is to model

the reaction of bone and tissue to accumulated stress and the

mechanisms of stress fracture. A better understanding could

lead to improved designs for protective clothing.

Still more ambitious is the biomimetic thrust to reproduce

the favorable characteristics of bone – in particular its

balance of toughness, stiffness, and damping – in synthesized

composites for prosthetics. Collagen-mimicking polymers

could find application in ‘soft’ actuators or shape-changing

materials forming the basis for artificial muscle. This is the

holy grail, but outcomes to date seem to indicate that it is

deliverable. The use of GIM highlights the importance of

events at the nanometer scale in determining the properties

of such materials, and should facilitate their design. MT

APPLICATIONS FEATURE

October 200236

Fig. 7 Group interaction modeling (GIM) can shed light on the effects of forces at work on

a human head when subjected to an impact.

FURTHER READING

1. Allington, R., et al., J. Defence Science (2001) 6 (1)

2. Porter, D., and Cherry, M., (2001) in: Computer Methods in Biomechanics

and Biomechanical Engineering – 3, Middleton, J., (ed.) Gordon and Breach,

Amsterdam, p. 483-488

3. Porter, D., (1995) Group Interaction Modeling of Polymer Properties, Marcel

Dekker, New York