without a stethoscope , we do not normally hear our own heart beat , although there are some pathological conditions when it can be heard ( e.g. , high blood pressure , pulsatile tinnitus , and superior semicircular canal dehiscence ) . in these cases ,
the perceived heart sound is usually the result of signals from arteries external to the cochlea rather than pressure changes generated within cochlear vessels .
the energy requirements of the cochlea are high , in particular the for na / k ion exchange pumps that generate the endolymphatic potential .
the cochlea appears to have a unique blood supply vasculature that ensures a dampening of cardiovascular pressure changes , essentially converting a pulsatile flow to a more linear stream .
the requirement for this damping mechanism is obvious given the sensitivity of cochlear hair cells to detect mechanical signals .
the most direct blood supply to the organ of corti is sparse , typically a small arteriole running adjacent to the basilar membrane .
on the other hand , the dense capillary network of the stria vascularis is richly supplied , and it is these feeding vessels that are described and modeled in the present study . in many peripheral capillary beds ( e.g. , skin , lips , and
blood pressures changes of up to 12  mmhg have been measured in the skin of healthy human adults .
this degree of pulsation in vessels of the stria vascularis would be highly disruptive to cochlear sensory mechanisms .
at best , there would be a constant percept of heartbeat that might mask other auditory signals .
more importantly , direct low - frequency pressure changes to the organ of corti complex could amplitude modulating the whole system .
mechanical events could be of a magnitude to cause damage ( an internal acoustic trauma ) .
the present study explores the physical properties of vascular supply to stria vascularis and the adaptation of this system to attenuate cardiac pulse transmission .  
corrosion  of soft tissue , yields a cast of the interior lumen of the blood vessels .
cochlear vasculature of the pig and the chinchilla are described . in particular , we examine the structure and function of tortuous arterioles that feed the capillary beds of stria vascularis .
we have characterized some of the important properties of these vessels and we suggest that these convoluted vessels are adaptations to dampen the cardiovascular pressure changes that could disturb cochlear mechanics .
we also present a mathematical model to illustrate the role of these vessels in attenuating cardiovascular pulsations within the cochlea .
young adult pigs ( sus scrofa ; n = 5 ) and adult chinchillas ( chinchilla laniger ; n = 6 ) were used . in the anesthetized animal , a transcardial [ 5 , 6 ] or aortic perfusion   of the head and upper body was carried out , clamping off lower body vessels . the right atrium was incised to allow venous return of perfusate .
perfusions were carried out using a peristaltic pump ( masterflex l / s precision variable - drive peristaltic pump ; cole - parmer canada inc . ,
this pressure is in the normal physiological range so as to avoid possible distortion of the vessel architecture [ 813 ] .
u / l )   0.9% nacl ( saline ) to wash out all the blood and help to prevent blood clots forming in smaller capillaries .
the saline was replaced by either mercox ii resin ( ladd research , williston , vt , usa ) or batsons ' resin ( polysciences ' inc . , warrington , pennsylvania , usa ) for 13 minutes .
once the resin hardened , the bulla / temporal bone was dissected and the cochlea exposed .
this was then immersed in a 16% koh solution over 3 days followed by 2% hcl ( over 1 to 5 hours ) to dissolve the soft tissue and the bone of the cochlea .
the last step was the immersion of the sample in 16% koh for another day before it was washed with distilled water to remove the remaining tissue .  
corrosion cast specimens were freeze dried [ 9 , 14 , 15 ] using a micro - modulyo freeze drying system ( thermo fischer scientific inc . ) and then mounted on a scanning em stub .
the samples where gold sputtered and analyzed for sem with the hitachi 3400 ( hitachi , ltd . , chiyoda - ku , tokyo , japan ) using either secondary electrons at 5  kv or backscatter electrons at 15  kv .
the images where processed with photoshop cs ( adobe systems incorporated inc . ) and analyzed with imagej ( u.s . national institutes of health , bethesda , md , usa ) software .
representative images of corrosion casts of cochlear vasculature are shown in figures 14 . in figure 1 , from the pig , the overall shape of the cochlea is clearly evident , and its squat structure is different than that of the more elongated chinchilla cochlea of the shown in figure 4 . in most specimens ,
we attempt to fill all vasculature ( arteries , capillaries , and veins ) , but in some cases a partial cast of only the arterial supply can be useful to more easily image some structures .
the specimens of figures 35 are partially filled casts that allow visualization of the arterioles that feed the stria vascularis . note that these casts do not show the actual blood vessel themselves , but rather the interior lumen of the vessels .
samples of the convoluted arterioles that supply the stria vascularis of the pig are shown in figures 2 and 3 .
note particularly in figure 3 ( lower panel ) the structure of these vessels , which have been previously described as  cochlear glomeruli .
 figure 4 shows a corrosion cast from a chinchilla cochlea . in this case , the arterial supply and strial capillary beds and filled but not the veins . some of the convoluted arterioles that supply the stria vascularis are highlighted .
the degree of convolution in this species is not as great as in the pig .  
we have devised a simple method to quantify the degree of convolution in these vessels as illustrated in figure 5 .
a measurement of the convoluted length divided by the linear end - to - end length provides a convolution index . in figure 5 ,
the data graphs plot individual measurements from the pig ( left plot ) and from the chinchilla ( right ) .
the average convolution index can be noted from the slope of the linear regression drawn through the data sets . for the pig , on average
we have noted differences in the degree of arteriole convolution when comparing basal and apical cochlear regions within species , but we have not yet made a systematic study .
the arterioles feeding stria vascularis show a high degree of tortuosity , and we suppose that this physical structure can act to dampen ( or low - pass filter ) blood pulsations in the capillaries of the cochlea .
we have developed a straightforward mathematical model to account for the damping that can be achieved by convoluted arterioles .
the model describes the properties of an elastic walled tube having a series of convolutions ( bends ) as represented in figure 6 .
thus , the tube diameter is constant ; we assume a laminar flow of a newtonian liquid of undefined viscosity , and we make the assumption that liquid can only move forward in one direction .  
the resistance to fluid flow through the tube will in part depend on its length , and the convolutions provide a way of increasing the effective length of the tubes within the confined space of the cochlea . as shown in figure 5 ,
the lengths are increased from a factor of 1.33 ( chinchilla ) to 1.45 ( pig ) because of convolutions .
in addition , each bend in a tortuous vessel will further increase the resistance to flow , especially in very small diameter tubes such as arterioles .
importantly in this model the tube wall acts as an elastic solid , and this basic property has been chosen based on the known viscoelastic properties of small arterioles . in this
regard , franz and colleagues   have reported that the second - order arterioles in the cochlea of the guinea pig have two smooth muscle layers that are known to have viscoelastic properties .
the third - order arterioles feeding the stria have little or no smooth muscle but have vascular pericytes cells that envelope the vessels that also have some intrinsic elastic properties .
our model is based on a system with such viscoelastic properties . in a straight , elastic - walled tube
, a sinusoidal pressure change would cause an overall volume change due to the compliant walls .
however , in a convoluted , small diameter , elastic - walled vessel , each bend would add a resistance to flow such that tube segments before each bend would have increased viscoelastic distension .
this is equivalent to separating the tube into a number of nodes ( see figure 6 ) . for each node , not only
is there a reduction in overall pressure change between input and output , but also each node acts as a pressure reservoir , and there is a consequent phase change to the pressure signal output from each node . the overall output from this system with many nodes ( i.e.
, an arteriole with many convolutions ) is the summation and a degree of cancellation of out - of - phase signals . assuming that the vessels are elastic , overall fluid dynamics will be the result of a competitive relationship among nodes . each node is defined as the section of the vessel in front of a bend as illustrated in figure 6 .
equation ( 1 ) describes the elasticity and resistance of each node : 
 ( 1)dndt = n(n1)+n(n)f(x)n(n)k . 
 here n
is the pressure in any node , f(x ) is a function that describes the elasticity of the tube , and k a constant that represents the resistance due to tube .
we have modeled the tube wall elasticity based on known stress - strain curve data for an artery .
thus in ( 2 ) , properties of the elastic vessel walls are defined , where  is the maximal distension of the vessel ,  is the value at which the elasticity of the walls reached the mid value ( f(x ) = /2 ) , and  is the exponential value that describes the speed ( time constant ) at which the vessel returns at its initial position .   rather than a complex cardiovascular pressure waveform , we use a simple sinusoidal function ( 3 ) to simulate pulsatile blood flow : 
 ( 3)sin(x)+a . 
 here
,  is the pulsation amplitude of f(x ) = sin ,  ( angular frequency ) represents heart rate , and a represents the average pressure ( the average function position in the y - axis ) .
although the heart beat has a complex function , for our purposes it can be approximated as a sinusoidal function .
the resultant model is shown below , where every n , except the first and the last , represents a node : 
 ( 4)dn0dt=sin(x)+a , dn1dt = n0+n1n1n1()+(n1),dn(n)dt = n(n1)+n(n)n(n)n(n)()+(n(n))k . 

the graphical representation of this model is shown in the lower panel of figure 6 .
the sinusoidal signal input ( left ) is unchanged in the model if there are zero nodes .
increasing node number ( increasing bends in a convoluted blood vessel ) clearly attenuates the transmitted pressure changes .
in the present study , we used a corrosion casting technique and sem imaging in order to assess the vasculature within the cochlea of chinchilla and pig .
a number of previous studies have employed such methods to visualize and describe in detail the cochlear vasculature in various mammalian [ 16 , 1922 ] and avian   species .
we present results from the pig ( sus scrofa ) and chinchillas ( chinchilla laniger ) , species not previously investigated in detail .
as described by others , we , observe the tortuous vessels that supply the capillary beds of stria vascularis .
tange   described corrosion casts of the adult rat inner ear and noted that apical and basal cochlear regions were supplied by the arteria cochleae propia and the arteria vestibulocochlearis , respectively .
images from that study showed convolutions of feeding arterioles but not a detailed description . in the guinea pig , franz and
colleagues   described the feeding vessels to stria vascularis as the  cochlear glomeruli ,  as schwalbe previously described them over a century ago .
these tortuous vessels are very similar to those found in the pig cochlea of the present study ( see lower panel of figure 3 in particular ) .
these authors suggested that these tortuous vessels served to  reduce blood pressure by mechanical friction . 
others ( e.g. , [ 13 , 20 , 24 ] ) have also observed these contorted vessels and generally suggested a role for blood flow regulation . of interest , iwagaki and
colleagues   have studied age - related changes to cochlear vessels in mice and observe that in the neonate , vessels of the spiral ligament are less tortuous than in more mature animals . in this altricious species final cochlear development occurs some time after birth and it appears that the increased vessel convolutions might correspond with hearing onset and thus have some functional significance .  
we strongly suggest that the vessel convolutions serve to attenuate cardiovascular pulse signals reaching the capillary beds stria vascularis . in most peripheral capillary beds ,
thus , shore reported [ 4 , 25 ] that in the peripheral capillary beds of the human finger there are cardiovascular pulse signals ranging from 0.5  mmhg ( 67  pa ) to 12  mmhg ( 1560  pa ) .
she used a direct cannulation of the capillaries with glass micropipette . for almost all capillary networks , it is of no detriment to have some pulsatile flow ; however , in the stria vascularis of the cochlea it would pose a real problem . if in stria vascularis there were pulse pressure fluctuation at the lower end of the range reported for skin capillaries , for example , 0.5  mmhg ( 67  pa ) and if this was transmitted into cochlear endolymphatic space it would certainly interfere with cochlear function .
it is unclear exactly how a low - frequency pulsation would affect hair cell function , but it is suffice to note that detection hair cells can detect acoustic signals of 20  pa ( 0  db spl ) . a constantly pulsing pressure signal , many orders of magnitude larger than 20  pa , would be a problem . the mathematical model presented here is intended to simply illustrate how a tortuous and elastic vessel can attenuate pulsating pressure signals .
as previously discussed , the model is relatively simple and does not incorporate some features that would clearly align it more closely with the actual vascular system .
the exact shapes and dimensions of the arterioles are not modeled , nor is the non - newtonian nature of blood and its possible laminar or turbulent flow characteristics .
using corrosion cast techniques , we have described the tortuous arterioles that supply the capillary beds of stria vascularis .
we suggest that such vessel structure has an important role in dampening cardiovascular pulse signals that would otherwise interfere with cochlear function .
we have presented a mathematical model to demonstrate the essential elements of this cardiac pulse attenuation system .
 the mammalian ear has an extraordinary capacity to detect very low - level acoustic signals from the environment . 
 sound pressures as low as a few pa ( 10  db spl ) can activate cochlear hair cells . to achieve this sensitivity 
 , biological noise has to be minimized including that generated by cardiovascular pulsation . 
 generally , cardiac pressure changes are transmitted to most peripheral capillary beds ; however , such signals within the stria vascularis of the cochlea would be highly disruptive . 
 not least , it would result in a constant auditory sensation of heartbeat . 
 we investigate special adaptations in cochlear vasculature that serve to attenuate cardiac pulse signals . 
 we describe the structure of tortuous arterioles that feed stria vascularis as seen in corrosion casts of the cochlea . 
 we provide a mathematical model to explain the role of this unique vascular anatomy in dampening pulsatile blood flow to the stria vascularis . 
1. Introduction
2. Materials and Methods
3. Results
4. Mathematical Model of Tortuous Vessels
5. Discussion
6. Conclusions