MECHANICS OF HEAD INJURIES

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438 For one intrathecal injection the penicillin was d3s= solved in the patient’s serum, to provide opsonic substances. Neither the intrathecal nor the intramuscular injec- tions caused any significant local or general reaction.. - The bacteriostatic powers of the blood and cerebro- spinal fluid were followed throughout penicillin treatment. My thanks are due to Professor Florey for the supply of penicillin, and for his advice as to administration and dosage, to Dr. T. A. Kemp and Dr. Duncan Gregg for-their assistance, and to Sister Downer whose unremitting care contributed materially to the satisfactory result. MECHANICS OF HEAD INJURIES A. H. S. HOLBOURN, MA EDIN, D PHIL OXFD RESEARCH PHYSICIST, UNIVERSITY LABORATORY OF PHYSIOLOGY AND DEPARTMENT OF SURGERY, OXFORD THE assumption that there is a mechanics of head injuries implies that, when the head receives a blow, the behaviour of the skull and brain during and immediately after the blow is determined by the physical properties of skull and brain and by Newton’s laws of motion. The most important physical properties of brain are :- (a) Its comparatively uniform density. Nerve tissue, blood, and cerebrospinal fluid all have about the same density as water. (b) Its extreme incompressibility. Brain substance does not appreciably change its size when subjected to a pressure which is uniform in all directions (a so-called hydrostatic pressure), and the incompressibility is about the same as that of water-it would take, for example, a force of about 10,000 tons to compress the brain to half its volume. (c) Its very small modulus of, rigidity. That is to say, brain offers a very small resistance to changes in shape com- pared with the resistance it offers to changes in size. For example, every surgeon knows that it takes only a small force on a retractor to produce quite a large deformation of the brain-nothing remotely comparable with 10,000 tons. (d) Compared with the feeble rigidity of the brain the rigidity of the skull is very great. For example, it takes about 1 ton to reduce the diameter of the skull by 1 em. (e) The shape of the skull and. brain are important in deciding the location of injuries. (f) It is reasonable to suppose that the brain behaves like the substances whose properties have so far been studied, and therefore that it is injured when its constituent particles are pulled so far apart that they do not join up again properly when the blow is over. In the case of a substance such as brain, whose modulus of incompressibility (bulk modulus) is large compared with its modulus of rigidity, the amount of pulling apart of the constituent particles is proportional to the shear-strain. (Shear-strain, or slide, is the type of’ deformation which occurs in a pack of cards, when it is deformed from a neat rectangular pile into an oblique-angled pile.) Hence the’ shear-strain present at any point in the brain should be at any rate a rough measure of the probability of injury at that point. In other words, shear-strains are the cause of injury, whereas compression and rarefaction strains are not. This is in conformity with the known results for peripheral nerve. Thus, Grundfest 1 found that nerves continued to conduct when subjected to a compression strain due to a pure hydrostatic pressure of 10,000 lb. per sq. in. Of course, this hydrostatic pressure is vastly greater than anything which can arise in a head injury. If, however, the pressure is not a purely hydrostatic one-if it is different in different directions-it must involve some shear, and a very small pressure of this type may be sufficient to injure a’nerve. The injuries to nerves produced by crushing with forceps or by stretching are examples of the effects of shear. Even when a nerve is squeezed with a pressure-cuff, the pressures are not equal at all places and in all directions, and therefore there are shear-stresses. It is undoubtedly these shear- stresses, and not the hydrostatic pressure, which produce the effects on the nerve. On the basis of the five properties (a-e) of the skull-brain system, one can predict the distribution of shear-strains, and therefore the locations of injuries, resulting from various types of blow. The mathematical theory falls naturally into two halves : (1) injury to the brain occurring as a result of distortion of the skull ; 1. Grundfest, H. Cold Harbor Symposia on Quantitative Biology, 1936, vol. iv, p. 179. and (2) injury to the brain occurring whether or not the skull is distorted. LOCALISED INJURY DUE TO SKULL DISTORTION As one would expect, distortion of the skull is most severe near the point of application of the blow. It consists mainly of an indentation of the skull. If fracture of the skull does not occur, the shear-strains in the brain are mainly confined to a superficial region close to the dent ; hence the injury to the brain consists mainly of a superficial bruising near the point of applica- tion of the blow. Waves of compression and rare- faction (sound waves) emanate from this region and travel back and forth through the brain, but since, as explained in (f), it is only shears which are injurious, these sound waves do not cause any damage. If the skull fractures, then shear-strains are produced in the brain in the immediate neighbourhood of the fracture, so that the injury is comparatively superficial in this case also. A fracture in the skull is the most probable cause of tearing of the dura, particularly where it is strongly adherent, as in the very young and very old. When haemorrhage from a large vessel does take place, its most probable location is where a fracture line crosses the vessel, because the shears are largest near the fracture. In this way, extradural, subdural and subarachnoid haemorrhages can occur. The shears which arise as a result of skull distortion without fracture are much smaller and therefore probably hardly ever cause haemorrhages from large vessels. Subdural and subarachnoid haemorrhages from large vessels may also result from the second mechanism of injury, which will now be considered. INJURY DUE TO ROTATION As well as the strains which arise in the brain as a consequence of cranial bending there are others which could arise even if the skull were absolutely undeform- able. These are called into play by the change in the velocity of the head caused by the blow. The most general type of change in velocity which a blow can produce can be analysed into a change in the straight- line, or linear, velocity together with a change in the rotational velocity about some axis. Hence the forces which the most general type of change in velocity can produce can be analysed into the linear acceleration forces due to the change in linear velocity, and centri- fugal forces, coriolis forces and rotational acceleration forces, due to the change in rotational velocity. The linear acceleration forces tend to produce compressional or rarefactional strains which, from (f), have no injurious effect. The shear-strains, which are also produced by the linear acceleration, are small. They are produced mainly in the neighbourhood of foramina where tissue has a tendency to be extruded or sucked in, and in the neighbourhood of ventricles owing to the slight difference in density between CSF and brain tissue. These shear- strains produced by the linear acceleration forces are small compared with those accompanying the change in rotational velocity, and may therefore be neglected, at any rate as a first approximation. Blood as well as tissue can be sucked in or pressed out through foramina as, a result of either the linear accel- eration or the skull bending, but owing to the viscosity and inertia of the blood the amount involved is small. In addition the effect only lasts during the blow. Hence, it can be neglected, at any rate as a first approximation. In any case it can never be the cause of, say, small capillary haemorrhages in regions remote from foramina. That no appreciable relative movement takes place between the constituent parts of the brain as a result of the linear acceleration may readily be verified by anyone who cares to fill a narrow-necked flask with water, and to add a little shredded cotton-wool in order to render visible any movement of the water. A purely linear change in the velocity of the flask produces no visible effect in the water-it moves bodily with the flask. Water has no rigidity, so that very small forces tending to produce deformations in the water would readily be detected if they existed. The idea that the brain is loose inside the skull, and that when the head is struck it rattles about like a die in a box, thereby causing coup and contrecoup injuries, is erroneous. The centrifugal and coriolis forces called into play by the -rotation can also be neglected, because they are

Transcript of MECHANICS OF HEAD INJURIES

438

For one intrathecal injection the penicillin was d3s=solved in the patient’s serum, to provide opsonicsubstances.

Neither the intrathecal nor the intramuscular injec-tions caused any significant local or general reaction..- The bacteriostatic powers of the blood and cerebro-spinal fluid were followed throughout penicillin treatment.My thanks are due to Professor Florey for the supply of

penicillin, and for his advice as to administration and dosage,to Dr. T. A. Kemp and Dr. Duncan Gregg for-their assistance,and to Sister Downer whose unremitting care contributedmaterially to the satisfactory result.

MECHANICS OF HEAD INJURIES

A. H. S. HOLBOURN, MA EDIN, D PHIL OXFDRESEARCH PHYSICIST, UNIVERSITY LABORATORY OF PHYSIOLOGY AND

DEPARTMENT OF SURGERY, OXFORD

THE assumption that there is a mechanics of headinjuries implies that, when the head receives a blow, thebehaviour of the skull and brain during and immediatelyafter the blow is determined by the physical propertiesof skull and brain and by Newton’s laws of motion.The most important physical properties of brain are :-

(a) Its comparatively uniform density. Nerve tissue, blood,and cerebrospinal fluid all have about the same density aswater.

(b) Its extreme incompressibility. Brain substance doesnot appreciably change its size when subjected to a pressurewhich is uniform in all directions (a so-called hydrostaticpressure), and the incompressibility is about the same as thatof water-it would take, for example, a force of about 10,000tons to compress the brain to half its volume.

(c) Its very small modulus of, rigidity. That is to say,brain offers a very small resistance to changes in shape com-pared with the resistance it offers to changes in size. For

example, every surgeon knows that it takes only a small forceon a retractor to produce quite a large deformation of thebrain-nothing remotely comparable with 10,000 tons.

(d) Compared with the feeble rigidity of the brain therigidity of the skull is very great. For example, it takesabout 1 ton to reduce the diameter of the skull by 1 em.

(e) The shape of the skull and. brain are important indeciding the location of injuries.

(f) It is reasonable to suppose that the brain behaves likethe substances whose properties have so far been studied, andtherefore that it is injured when its constituent particles arepulled so far apart that they do not join up again properlywhen the blow is over. In the case of a substance such asbrain, whose modulus of incompressibility (bulk modulus) islarge compared with its modulus of rigidity, the amount ofpulling apart of the constituent particles is proportional tothe shear-strain. (Shear-strain, or slide, is the type of’deformation which occurs in a pack of cards, when it isdeformed from a neat rectangular pile into an oblique-angledpile.) Hence the’ shear-strain present at any point in thebrain should be at any rate a rough measure of the probabilityof injury at that point. In other words, shear-strains are thecause of injury, whereas compression and rarefaction strainsare not. This is in conformity with the known results forperipheral nerve. Thus, Grundfest 1 found that nerves

continued to conduct when subjected to a compression straindue to a pure hydrostatic pressure of 10,000 lb. per sq. in.Of course, this hydrostatic pressure is vastly greater thananything which can arise in a head injury. If, however, thepressure is not a purely hydrostatic one-if it is different indifferent directions-it must involve some shear, and a verysmall pressure of this type may be sufficient to injure a’nerve.The injuries to nerves produced by crushing with forceps orby stretching are examples of the effects of shear. Evenwhen a nerve is squeezed with a pressure-cuff, the pressuresare not equal at all places and in all directions, and thereforethere are shear-stresses. It is undoubtedly these shear-stresses, and not the hydrostatic pressure, which produce theeffects on the nerve.

On the basis of the five properties (a-e) of theskull-brain system, one can predict the distribution ofshear-strains, and therefore the locations of injuries,resulting from various types of blow. The mathematicaltheory falls naturally into two halves : (1) injury to thebrain occurring as a result of distortion of the skull ;1. Grundfest, H. Cold Harbor Symposia on Quantitative Biology, 1936,

vol. iv, p. 179.

and (2) injury to the brain occurring whether or not theskull is distorted.

LOCALISED INJURY DUE TO SKULL DISTORTION,

As one would expect, distortion of the skull is mostsevere near the point of application of the blow. Itconsists mainly of an indentation of the skull. Iffracture of the skull does not occur, the shear-strains inthe brain are mainly confined to a superficial region closeto the dent ; hence the injury to the brain consistsmainly of a superficial bruising near the point of applica-tion of the blow. Waves of compression and rare-

faction (sound waves) emanate from this region andtravel back and forth through the brain, but since, asexplained in (f), it is only shears which are injurious,these sound waves do not cause any damage.

If the skull fractures, then shear-strains are producedin the brain in the immediate neighbourhood of thefracture, so that the injury is comparatively superficialin this case also. A fracture in the skull is the mostprobable cause of tearing of the dura, particularly whereit is strongly adherent, as in the very young and veryold. When haemorrhage from a large vessel does takeplace, its most probable location is where a fracture linecrosses the vessel, because the shears are largest nearthe fracture. In this way, extradural, subdural andsubarachnoid haemorrhages can occur. The shearswhich arise as a result of skull distortion without fracture ‘

are much smaller and therefore probably hardly evercause haemorrhages from large vessels. Subdural andsubarachnoid haemorrhages from large vessels may alsoresult from the second mechanism of injury, which willnow be considered.

INJURY DUE TO ROTATION

As well as the strains which arise in the brain as aconsequence of cranial bending there are others whichcould arise even if the skull were absolutely undeform-able. These are called into play by the change in thevelocity of the head caused by the blow. The mostgeneral type of change in velocity which a blow canproduce can be analysed into a change in the straight-line, or linear, velocity together with a change in therotational velocity about some axis. Hence the forceswhich the most general type of change in velocity canproduce can be analysed into the linear accelerationforces due to the change in linear velocity, and centri-fugal forces, coriolis forces and rotational accelerationforces, due to the change in rotational velocity. Thelinear acceleration forces tend to produce compressionalor rarefactional strains which, from (f), have no injurious

effect. The shear-strains, which are also produced bythe linear acceleration, are small. They are producedmainly in the neighbourhood of foramina where tissuehas a tendency to be extruded or sucked in, and in theneighbourhood of ventricles owing to the slight differencein density between CSF and brain tissue. These shear-strains produced by the linear acceleration forces aresmall compared with those accompanying the change inrotational velocity, and may therefore be neglected, atany rate as a first approximation.Blood as well as tissue can be sucked in or pressed out

through foramina as, a result of either the linear accel-eration or the skull bending, but owing to the viscosityand inertia of the blood the amount involved is small.In addition the effect only lasts during the blow. Hence,it can be neglected, at any rate as a first approximation.In any case it can never be the cause of, say, smallcapillary haemorrhages in regions remote from foramina.That no appreciable relative movement takes place

between the constituent parts of the brain as a result ofthe linear acceleration may readily be verified by anyonewho cares to fill a narrow-necked flask with water, andto add a little shredded cotton-wool in order to rendervisible any movement of the water. A purely linearchange in the velocity of the flask produces no visibleeffect in the water-it moves bodily with the flask.Water has no rigidity, so that very small forces tendingto produce deformations in the water would readily bedetected if they existed. The idea that the brain isloose inside the skull, and that when the head is struckit rattles about like a die in a box, thereby causingcoup and contrecoup injuries, is erroneous.The centrifugal and coriolis forces called into play by

the -rotation can also be neglected, because they are

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Fig. t—intensity of the shear-strains resulting from a forwards rotation caused by a blow on the occiput.Fig. 2-lntensity of the shear-strains due to a rotation in the horizontal plane caused by a btow near the upper jaw or temp!es.Fig. 3-intensity of the shear-strains due to a rotation inethe coronal plane caused by a blow above the ear.

Key-Scale of maximum shear-strain (= distortion) in arbitrary units of shear. The units differ in the three diagrams.

small, and not of a type very liable to cause injury.Usually the rotational acceleration forces are the maincause of brain injury. That the change in the rotationalvelocity of the head is likely to cause injury may easilybe seen by giving a sudden rotation to the flask full ofwater mentioned previously. The water tends to staybehind, and only’the flask rotates. Hence, as a resultof the rotation a particle of water attached to the insidesurface of the flask becomes separated from a neighbour-ing particle not thus attached. Large shear-strains areproduced. Water is, of course, less rigid than thebrain, so that this model exaggerates the effect ofshearing stresses.

Fig. 1 is a parasagittal section of the brain passingthrough the tip of the temporal lobe. The shear-strainsshown in it are those which are produced by a rotationsuch as might be caused by a blow on the occiput. Thefigure was obtained by making a model of this cross-section of the brain out of 5 % gelatin, with % formalinadded as a preservative. The gelatin was cast into theparaffin-wax " skull," and then cut free with a taut wire.After this, the model was allowed to stand until slightadhesions grew across the water-filled gap between" brain " and " skull." By this means there was

obtained a shear-strain distribution which was inter-mediate between that for the " brain " completely freefrom the " skull " and that for the " brain " firmlyattached to the " skull." The gelatin adhesions had arough mathematical correspondence with the attach-ments between the pia and the somewhat less extehsiblearachnoid. When the model, placed in a circularpolariscope, was given a sudden forwards rotation, theshear-strains in the gelatin became visible owing to thecolours they produced in the field of view (Coker andFilon).2 -

The strains could be calculated mathematically by themethod of relaxations. Hence the jelly is to be regardedmerely as an elegant and rapid calculator of the strainsinz a system with the properties (a-e). Gelatin is usedmerely for convenience. Exactly the same shear-strainswould arise, for example, in glass or metal. Even inthe case of an alloy consisting of an aggregate of’crystalsof different sizes, shapes, densities and elasticities, theshear-strains, averaged over regions large compared withthe size of the crystals, are exactly the same as ingelatin. But the average shear-strain in a particularregion of an alloy gives no clue as to what exactlyhappens to the crystals there. For example, the crystalsmay themselves be uniformly strained, or they’may bestrained only in parts, or they may merely move relativeto one another. In the same way, though the shear-strains obtained from the jelly model indicate the regionsof brain liable to damage, they give no indication ofwhat this damage consists. It may consist of tearingof blood-vessels, tearing of axons, disrupting of cellbodies, tearing apart of synapses, or injuring of someparts of the nerves by amounts insufficient to cause actualbreakage.2. Coker, E. G. and Filon, L. N. G. Treatise on Photoelasticity, Cambridge,

1931.

The most prominent features of fig. 1 are the largeamount of shear-strain in the anterior part of thetemporal lobe, and the comparative absence of shear-strain in the cerebellum. The main reason for thelarge amount of shear-strain at the tip of the temporallobe is that the skull gets a good grip on the brain in thisregion owing to the inwardly projecting ridge of thelesser wing of the sphenoid bone, so that the skull rotatesthe brain mainly by means of the force it exerts on thisportion of the brain. Hence this is where most of thestrains appear. Elsewhere the brain tends to slipsomewhat relative to the skull, so that smaller strainsare produced. The relative slip between brain andskull is greatest near the vertex, which is far removedfrom any place where the skull can get a grip on thebrain to turn it round. Hence the brain tends to getleft behind in this region and it therefore rubs againstthe skull more than in other places. The superficialregion of strain in the vertex is due to the effect offriction and connexions between skull and’brain. Thisallows the skull to get a small amount of grip on thebrain. In. the case we are considering, of a blow on theocciput, this region of superficial shear-strain due torubbing would extend to the falx, against which thebrain would rub in the same way as against the vertexof the skull. The comparative absence of strain in thelateral cerebellar lobe is due mainly to its small size-itdoes not require such large forces to make it rotate asare required to make the cerebrum rotate. It should benoted that there is hardly any part -of the brain whichis completely free from strain.What evidence there is from autopsies in the case of

blows on the occiput confirms a distribution of haeJllor-rhages corresponding roughly to the areas of higheststrain shown in g. 1 (see, for example, Courville).It is, of course, possible that the brain is also damaged inregions where the strain is insufficient to cause

haemorrhage. -

That shear-strains correspond to damage in the caseof a jelly is shown by fig. 4, which is a photograph-of themodel taken after it had been subjected to a moreviolent rotational jerking. Note that besides the regionof extreme fragmentation in the temporal and frontallobes.there is a superficial layer near the vertex. Theslight damage in the lateral sinus and occipital pole is anartefact. The appearance of the jelly is remarkablysimilar to the post-mortem appearance of a brain afteran extremely severe occipital injury.

Figs. 2 and 3 are shear-strain diagrams for typicalhorizontal and coronal sections rotated in their ownplanes. Fig. 2 shows the effect of a rotation whichwould be most easily produced in real life by a sidewaysblow in the neighbourhood of the upper jaw. It wouldalso be produced to some extent by a sideways blow onthe temples. The rotation in fig. 3 corresponds to thatwhich is most easily produced by a blow above the ear.Both these sections are somewhat more unsatisfactorythan the previous one because the effect, on the sectionconsidered, of strains in neighbouring sections is more

3. Courville, C. B. Arch. Surg, 1942, 45, 19.

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marked than before. In addition, both these sectionsshould really have sections of ventricle included inthem. This would disturb the strain system somewhat ;and there would be a tendency for the strains to con-gregate near the ventricular walls. An unsatisfactoryfeature of fig. 3 is that the cavernous sinus is reallymore yielding than bone, whereas in the model it isjust as, unyielding. In spite of these defects, however,figs. 2 and 3 do correspond reasonably well to the injuriescaused by temporal and high parietal blows respectively.The main discrepancy between these figures and thepost-mortem findings is that, by all accounts, the super-ficial injury at the sides of the temporal lobes shown infig. 2 appears to be found at one side only-usually,though not invariably, the opposite side to the side ofthe blow (Courville 8). It must be remembered, how-ever, that these two figures refer only to those unusualcases in which the rotations are exactly in the planes ofthe sections. It will be just as unusual therefore tofind exactly symmetrical damage of this type as it is tofind exactly symmetrical damage due to a blow on theocciput. There are other less obvious factors makingfor asymmetry.As the brain is so incompressible, it will be impossible

for any empty spaces to be formed anywhere as a resultof the blow. Hence, since no spaces can be formedbetween the skull and brain, the surface of the brain cannever move away from the interior skull surface : it cantherefore only slide along it. Since the dura is com-paratively firmly attached to the skull, the motion ofthe dura relative to the skull will usually be negligible.Hence the main motion must be the sliding of the piarelative to the arachnoid and of the arachnoid relativeto the dura-the latter being presumably greater. Inthis process the vessels which drain the cortical veins

Fig. 4-Effect on a jelly of a violent rotational jerking In its own plane.

into the venous sinuses will be stretched, and may breakanywhere along their length, causing subdural or

subarachnoid haemorrhages. For a rotation in the planeof fig. 1, the relative sliding motion is greatest near thevertex, since it is furthest removed from any. placewhere the skull or dural processes are so shaped as to geta good grip on the brain. Hence this is the most probable

region for haemorrhages of this type. For rotations inthe planes of figs. 2 and 3 the sliding is greatest at thesides of the convexities, but there are no communicatingveins in this position. For all directions of rotation thesliding is minimal in the neighbourhood of the base, sothat the cranial nerves, arteries and veins of the baseusually escape rotational damage. When the pia movesrelative to the arachnoid, the tethering trabeculae andperforating vessels may be torn. This type of injuryis most likely to occur near the vertex for rotations inthe plane of fig. 1, and at the sides for rotations in theplanes of either figs. 2 or 3.

If the gelatin model were given a purely linear changein velocity, no shear-strains would be visible, because,

as previously mentioned, a change in linear velocity,tends to produce compression and rarefaction only.Hence, for a system with the properties (cc--e) the theoryof contrecoup is without physical foundation. The so-called contrecoup injuries are really rotational injuries.The distribution of shear-strain in a real brain depends

to some extent on factors which are not accuratelyknown. Hence there may be considerable deviationsfrom the distribution shown in figs. 1, 2 and 3. Thesefigures do, however, give good grounds for believingthat head injury is primarily a problem in pure physics,and consequently that rotations are of paramountimportance. The results which follow, being dependentonly on the neglect of all the effects of the blow exceptthe rotation, are more certain.

If there is no rotation or only a very small or slow one,there is no rotational injury. Thus, if the head is so wellfixed that it cannot rotate at all when it receives a blow,there will be no rotational injury. Denny-Brown andRitchie Russell 4 found that it was very difficult toproduce concussion in cats when the head was fixed, buteasy when it was free to move.’ This points to the factthat concussion is a rotational injury. One wouldcertainly expect it to be so because skull-distortioninjury is localised, and because much greater local injuryto the cerebral hemispheres can be produced at operationwithout loss of consciousness. As is shown in figs. 1; 2and 3, rotational shear-strains are present throughoutthe whole brain in greater or lesser degree, and aretherefore much more likely to be the cause of a pheno-menon such as unconsciousness. Up to the present,technical difficulties have prevented any estimation ofthe shear-strains in the brain stem. When a person:shead is crushed between the slowly moving buffers oftwo railway trucks in a shunting accident, only a slowrotation can be produced ; and in such accidents there isusually no concussion.The momentum of a rifle bullet is surprisingly small,

and therefore the rotational velocity it can produce issmall. If a 10 g. bullet travelling at 400 metres per sec.is completely stopped by the head, the rotational velocityproduced is about the same as that produced when onewalks into a wall at 2 miles per hour. It is well knownthat wounds from low-velocity bullets often do notproduce concussion. A bullet, owing to its small mass,is an example of an object having a large kinetic energyand at the same time a small momentum. It is owingto this that in low-velocity gunshot wounds the plainlyvisible injury to scalp, skull and brain in the path of thebullet (which depends mainly on the kinetic energy) ismuch larger than the invisible damage due to rotation(which depends mainly on the momentum). On theother hand, when the head hits a wall or a pavement, themasses involved are large so that the kinetic energiesare small and the momenta large. Hence the plainlyvisible injury is in this case small compared with theinvisible damage due to rotation. Now objects whichare generally found in motion-bullets, balls, bricks, &c.- are usually less massive than the stationary objectswhich, one’s head is likely to hit. Hence collisions withstationary objects will usually produce more rotationaldamage than one would expect from the external injury.This is no doubt why it is often said that it makes adifference whether the head or the object causing theinjury is in motion-a statement which, taken at its facevalue, is clearly absurd. For certain directions of blowat certain points of the head-notably points on themidline-a blow, however hard, produces no_ rotation.In association football, the direction of the ba<anc .s apoint of the head at which it is " headed " are related insuch a way that little rotation is produced by the impact.As an example of the opposite effect, one of the easiestways of producing a rapid rotation of the head is tostrike the chin sideways and upwards. This is- thefavourite knock-out blow in boxing.For blows of long duration, the shear-strains in the

brain are proportional to the force (assuming that thedirection and point of application remain constant).That is to say, the injury is independent of the time forwhich the force acts. Hence one might say, fromNewton’s second law, that the injury is proportional tothe acceleration, or rate of change of velocity of the head.On the other hand, for very short blows the injury is

4. Denny-Brown, D., and Russell, W. R. Brain, 1941, 64, 93.

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Fig. 5&mdash;.Section showing large-scale symmetry combined with positive-negativesymmetry in the details.

proportional to the force multiplied by the time forwhich it acts. Hence, from Newton’s second law, theinjury is proportional to the change of velocity of thehead and not to the rate of change-i.e., acceleration.For this reason, the term

" acceleration concussion "

may well prove misleading. The change-over from onelaw of injury to the other occurs gradually somewhere inthe region between 1/5 and 1/500 sec. Experiments arein progress to find a more accurate value for the criticalduration of the blow. The change-over from one lawof injury to the other is accompanied by a change in thedistribution of the shear-strains. Figs. 1, 2 and 3 referto forces of long duration.Using the fact that the change in linear velocity

produces no effect, and using the theorem in kinematicsthat any rotation about any axis is equivalent to anequal rotation about any other axis together with atranslation, we have the result that equal rotations aboutall parallel axes produce exactly the same injury. ’ Forexample, it makes no difference whether the rotationtakes place about an axis through the centre of thebrain or about a parallel one through a point in theneck.

Figs. 2 and 3 show sections of the brain in which theright-hand side is the mirror-image of the left-hand side.The strains on the right-hand side are also the mirror-image of the strains on the left-hand side. This sym-metrical distribution holds for rotations about any axislying in the median plane. But this result only holdsaccurately in the case of simple substances such asgelatin. For substances such as brain, in which theYoung’s modulus of elasticity for stretches parallel tothe fibre directions may be different from the modulusfor stretches perpendicular to the fibre directions, and inwhich the relationship between stress and strain isnon-linear, this symmetry is not perfect. A moreaccurate statement of the facts in the case of rotationsabout any axis in the median plane is as follows : thelarge-scale injury on one side of a symmetrical sectionof the brain is approximately the mirror-image of thelarge-scale injury on the other side, but the minordetails need not be mirror-images&mdash;for example, theymay in exceptional circumstances be as it were negativeson one side and positives on the other. Fig. 5 showsthe predicted effect. The injured gyri on one sidecorrespond to the injured gyri on the other, but in

each individual gyrus an injured portion on one

side- is the mirror-image of an uninjured portion ontile! &the... -

_

In the case of symmetrical sections, we can at once seethat whether the rotation consists of a bending to theright or a bending in the opposite direction, the large-scale injury, being symmetrical; will be approximatelythe same in either case. But it can be shown that thisresult is not confined to symmetrical sections. Forexample, theory shows that the large-scale injuryproduced by the rotation which occurs when the head isstruck centrally on the occiput is approximately thesame as that produced by the opposite rotation whichoccurs when the head is struck centrally on the forehead(fig. 1 refers in fact to either blow). The details may,however, be different. In this connexion a remark byCourville is interesting: " Essentially identical lesionsof the subfrontal and anterior temporal regions result

from contact of either the frontal region or the occipitalregion of the moving head."

. SUMMARY

The theory of head injury is developed on the assump-tion that, during and immediately after the blow, allfactors other than the purely physical can be neglected.On this assumption there are two main causes of

injury: (1) deformation of the skull with or withoutfracture ; and (2) sudden rotation of the head which isresponsible for the so-called contrecoup injuries, forsome intracranial haemorrhages and probably for con-cussion.The agreement between the theoretical predictions

and the observed facts is good, considering, the numberof data which are only imperfectly known. Hence onecan be reasonably confident that only minor modificationsto the theory will be necessary to explain quantitativelythe usual type of accident.

It is impossible to thank all those who have been helpful.This research would not have succeeded without the help of,among others, Prof. Hugh Cairns, Major W. Ritchie Russell,Dr. Dorothy S. Russell, Mr. G. F. Rowbotham, Dr. A. H. T.Robb-Smith and Dr. David Whitteridge, together with thefacilities of the Oxford University Laboratory of Physiologyplaced at my disposal by Prof. E. G. T. Liddell.

EFFECTS OF DRINKINGSMALL QUANTITIES OF SEA-WATER

AN EXPERIMENTAL STUDY

W. S. S. LADELL, M R C S *

(From the Research Unit, National Hospital, Queen Square)DURING the last year work has been carried out in this

laboratory, for the Medical Research Council’s committeeon the care of shipwrecked personnel (MRC War Memo-randum No. 8), on the physiology of subjects receivingthe same food and water as shipwrecked men in lifeboats.! tA full report of all the work has been prepared and willbe published elsewhere ; in the meantime results andconclusions which have to do with the consumption ofsea-water are presented here. In particular the effectsof drinking sea-water upon the chloride balance, the ureaexcretion, the urinary output, and the body-weightlosses of the shipwrecked man-called for short, the" man on the raft "-are considered in some detail.Some references to experiments in which salt water wasnot drunk are also made.An extensive series of experiments has shown that a

man requires between 800 c.cm. and 1000 c.cm. of.waterper day to satisfy all his requirements, the actual amountvarying with the previous metabolic history of thesubject, his activity and his diet during the experiment.With an intake less than this he contracts a " waterdebt " to his own tissues. It was found that a man inwater debt continues to produce 350-450 c.cm. of urineper day. The same low output was found whether thewater debt was large or small and it was maintainedthroughout the longest experiments, which were for nowater intake 4 days, and for limited water intake 10 days(1 day no water ; 5 days 540 c.cm. ; 4 days 60 c.cm. perday). During the period of low urinary output the ureaconcentration in the urine rose to as much as 6% but thetotal urea output was inadequate, and there was nitrogen-retention with a rise in blood-urea. At the same timesalt losses in the urine were high on the first day, but theyfell in a day or two to a low level. In all experiments thediet provided not more than 1 gramme- of sodiumchloride daily, but the excretion was greater than this,so there was always a slight negative salt-balance in thoseexperiments where no sea-water or saline was drunk.

In addition to the physiological effects which aredescribed later there was, under these experimentalconditions, a definite psychological value in having theextra volume of fluid available for drinking, even thoughit was salt to’ taste. This was not only my personal* Receiving a research grant from the Medical Research Council.t The secretary, Dr. B. S. Platt, asks us to point out that the com-

mittee, in Memorandum No. 8, do not recommend the drinkingof sea-water. In reaching this decision they took account ofother relevant factors besides the evidence recorded in thepresent paper.-ED. L.