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8/12/2019 Swanson and Clark, "Dimensions and Geometric Relationships"
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Dimensions and Geometric Relationships of the Human
Aortic Value as a Function of Pressure
W. Milton Swanson and Richard E. Clark
ABSTRACTIn a continuing effort to develop improved prosth etic h ear t valves, a redefini-
tion of the anatomy of the human aortic valve as a function of stress wasundertaken. Dimensions and geometric relationships of the hum an aortic valveas a function of intraaortic pressure between 0 and 120 mm Hg were obtainedfrom a series of silicone rubber valve casts. The axial length of the valve regionwas found to vary negligibly with press ure, but significant variations ingeometry and angular dimensions were seen. The leaflet atta chm ent annulusforms an ellipse at the plane of intersec tion with th e cylindrical surfacepassing from the left ven tricular tra ct through the aorta. Deductions fromstress considerations for the measured geometry indicate that the loadedleaflet is a section of a cylindrical surface. The equation for this developedsurface was obtained, and a prosthetic design was determined using averagevalues at 100 mm Hg. The leaflet is developable onto a plane with a cutrequired along part of the junction line between the initially cylindrical partand the plane coapting surfaces. Optimum valve shape mandates a base anglebetween the cylindrical leaflet and the center axis of 70° a =20-22°, where a isthe leaflet angle).
KEY WORDS aortic valve structu releaflet sha pe and d imensionsprosthetic valve design
aortic modulusstresses in valve leaflets
• An accurate definition of the geometry of
the aortic valve is necessary prior to develop-
ment and fabrication of a prosthetic valve.
As part of a program to determine the geom-
etry and stru ctu re of the human aortic
valve, silicone rubber molds were cast under
pressure. Measurements considered to be im-
portant were made and analyzed. Prelimi-
nary studies in our laboratory have demon-
strated the sensitivity of in-plane stresses to
the geometry of this structure during dias-
tole and systole (1). Previous investiga tions
by Wood et al. (2) and Sauvage et al. (3)
utilized pig hearts and a freezing technique
under pressure. Recently, Mercer et al. (4)
have investigated the geometry of the hu-
man aortic leaflet via a molding technique at100 mm Hg of pressure. The present paper is
a report on our 2-year investigation of the
geometry and proportionalities of the human
aortic valve from which important design
conclusions can be drawn. Accurate knowl-
From the Departments of Mechanical Engineering andCardiothoracic Surgery, Washington University, St.Louis, M issouri 63130.
This work was supported in part by U- S. Public HealthService Grant HL-13803 from the National Heart andLung Institute .
Received January 31, 1974. Accepted for publication
August 8, 1974.Circulation R esearch VoL 35 December 197k
edge of valve and sinus region geometry is
required for flow calculations yielding infor-
mation on leaflet motion during opening and
closing (5).
Methods
Fresh human hearts were obtained at autopsy,stored at 4°C, and used within 1-3 days afterdeath. The specimens consisted of two to threediameters of aorta beyond the sinuses of Valsalvaand one-half to one diameter of tissue on the leftventricle side. The aor ta was held with th reehemostats hung on ring-stand hook arms. Then,40-50 ml of low-viscosity room temperature-vul-canizing silicone rubber (RTV GE-11) was pre-pared. The coronary ar ter ies w ere at first tied off,bu t it was late r found t ha t coronary leak age couldbest be eliminated by plugging them with siliconerubber beads, 4-5 mm in diameter. Part of thesilicone rubber was injected into the sinus pocketswith a 20-ml syringe and a 6-cm tube extension toallow filling from the bottom up to eliminate airpockets. When the preparation was nearly full, agrooved stopper with a 5-cm length of glass tubein it was slowly pushed into the aorta, filling thetube. The aorta was secured to the stopper withumbilical tape around the groove. The remainingsilicone rubber was poured into a large reservoirsyringe connected to the stopper tube with a shortpiece of flexible tubing, and the reservoir syringewas then suspended on a ring s tand. A tubethrough a s topper in the top of the reservoirsyringe was connected thr ough a T-tube to a
87 1
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standard sphygmomanometer. The pressure wasgradually increased to the desired casting pres-sure and maintained during th e cure. A jar ofsaline was placed around the aorta to maintain amoist condition and a tem pe ra tu re of 37°C. Thisslightly warm temperature also accelerated thecure. A period of about 2 hours was required for aminimum stable-dimension c ure. The cast wasremoved, and the procedure was repeated at thenext pressure. With this technique, five or sixcasts could be made in 1 day. The d eterio ratingeffect of the casting procedure on the elasticproperties of the ao rta was determined by repeat-ing the preparation of a cast at 20 mm Hg. Thischeck cast was made on th ree series (series 5 and6 of Table 2 and one other) after the last cast atmaximum pressure had been made. No significantdimensional variations were found. One serieswas also repeated at 50 mm Hg, and no significantvaria tion s were noted. The series 8 casts are
shown in Figure 1.
Data on subject aortas are presented in Table 1.The significant dimensions recorded in Tables 2-4were measured with vernier calipers to the near-est 0.1 mm. In some critical cases, several sets ofreadings were taken for one dimension and aver-aged to determine repeatability. The variationsobtained were usually within 0.2 mm or about 1%.Dimensions involving the three separate sinusesand leaflets were average for the three. The non-coronary sinus was usually, but not always, thesmallest.
A profile trac ing of the sinus region in a planeperpendicular to the center axis was made andplanimetered to obtain the maximum sinus areafrom _yvhich an equ iva lent area-averaged diame-ter, d,, was determined. Each cast tracing wasplanimetered ten times to get an acc urate meas-
TABLE 1
Valve Origin
Valve series
45
6T»
Age
(years)
293929
M4f
Sex
FMFFM
urement. The ten measurements usually did notvary by more tha n 1%. When the variation waslarger, more readings were taken. The circum-scribing sinus diameter, dsm, was also recorded .
Nomenclaturec = C o a p t a t i o n ( F i g . 2 ).d = D i a m e t e r ( m m ) (F i g . 2).E = E l a s t i c m o d u l u s ( d yn e s / c m * ).E d = E l a s t i c m o d u l u s b a s e d on a o r t i c d i a m e -
t r a l s t r a i n : E,, = A p / A da /d a ) ( d y n e s /cm
ferred to as pressure modulus in ref. 6: Ed =Ap/(da/da). The range 1.6 x 10
5 < Ert < 5.3 x
105 dynes/cm1
in Table 2 is in the range ofpublished data for pig aortas (Ed = 2 x 10
s
dynes/cm2 [6]) and for the femoral artery (2 x105
< i^ < 6 x 106 dynes/cm
2 [3, 7]). This
relatively large range of values for a physio-logical property is not unusual . The modulusde te rmined in th is ma nner m ight includeinaccuracies because of the method of deter-mining the strain Ad
a/d
a. The uncertainty for
Ed varied from about 100% a t 20 mm Hg toabout 10% at 80 mm Hg. The max imum localdata variation for Ed values calculated froma smoothed curve of Ap vs. (da* - 1) was 15%.More accurate means determined using spe-cial s t ra in tes t ing apparatus (8) give tru emoduli and yield values of the circumferen-tial modulus E for the aorta of about 4 x 10
6
dynes/cm2 at 10% strain. Values of Ed were
converted to E by m ultiplying by d/2t, whichwas a bout 10 (where t is the wall thickness).The average resulting E of approximately 5
x 10s
dynes/cm2
was close to published da taCirculation Research, VoL 35, December 1S7J,
SYMBOL SERIES
1.4
oD
A
•
•
mY2Lm
0 40 80 120
PRESSURE-p mm Hg)FIGURES
Relative dimensional variation of inlet diameter, djwith
pressure, p.
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Bottom leaflet surface a ngle, a, variation with pressure, p.
(b )FMURE7
a: Sections through a sinus vertical center plane at SO 60and 80 mm Hg. b: Cylindrical sections at SO, 50, an d 80mm Hg . Tick marks indicate leaflet attachment points.
surface (Fig. 8). These striations were in aplane perpendicular to the axis of the cylin-drical leaflet surface and extended from oneattachment to the other. Mating casts in the
left ventricle side had a smooth surface adja-cent to the leaflets. The leaflets are essen-tially thin flexible membranes, and they tendto form a cylindrical surface between theirpoints (or lines) of main support. Sectionsthrough the leaflet profiles along the stria-tion lines are shown in Figure 7b.
Since the leaflets end at a free edge in asection through the coaptation zone, therecan be no radial stress component in them.This conclusion is also corroborated by thefact that the radial profiles were essentiallystr aig ht (no significant definable cu rv atu re
in the radial direction [Figs. 8 and 9]). Theonly load stress component is then the cir-cumferential stress carried by the circumfer-ential collagen fiber structure.
LEAFLET THICKNESS
Leaflet molds were made on the series 8aortic molds. The fibrous structure in thecylindrical portions and in the coapting sur-faces closely resembled that indicated in Fig-ure s 8 and 10. As the molding press ure wasincreased, the coapting leaflet thickness de-creased. Measurements made on series 8
casts gave a 30% decrease in average thick-Circulation Research, VoL 35, December 1971,
ness measu red a t the m idpoint of th e coapt-ing surfaces from 0.48 mm to 0.32 mm (Fig.11). Variations were large from one leaflet toanother on the same valve at a given pres-
sure. At 100 mm Hg, thickness varied from0.22 mm to 0.4 mm.
OVERALL STRUCTURE
The valve structure consists of thin flexi-ble sheets (the leaflets) freely suspended be-tween the attachments, forming interleafletseals along the coaptation zone.
Details of an idealized valve structure areshown in Figure 9. Figure 9a is a view look-ing from the left ventricle side. The load-carrying collagen fibers appear in the angledview of the bottom side of the leaf-
let as ellipses. The attachment annulus linewhich forms the three-way intersection ofthe leaflets with the sinus and ventriculartract walls projects into a circle (the leftventr icular out le t t ract d iameter) in th isview. A section in the plane of the circulararc through the leaflet is shown in Figure 9c.The leaflet contour b in Figure 9c is one-third of a circle. The adjoining sinus contouris also nearly circular. The leaflet and sinuscurvatures are parallel at their l ine of at-tachment intersection with the left ventricu-lar outflow tract wall yielding a load-stress
balance, as indicated by the arrows in Figure
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a: Side -profile through attachment plane, b: View from left ventricular side, c: Sectionthrough cylindrical leaflet profile, d: P rojected attachment line profile, c: Developedsurface of leaflet, f: Planar layout of coapting surfaces. Dimensions are relative to dr* =
1.0.
40 80 120PRESSURE-mm Hg
FIGURE 11
Coapting leaflet thickness as a function of pressure.
to another, specifically observed variationsin attachment line geometry between coro-nary and noncoronary leaflets. These varia-tions were not included because of the objec-tive of obtaining a simplified geometry thatcould be fabricated for clinical installationand because the variations were not largeenough to be considered as physiologicallys ignif icant for pros thet ic valve ins tal la-tion.
The leaflet and attachment load stressesare max imum a t va lve c losu re . Bend ingstresses during the folding wave motion dur-ing valve opening are an order of magnitudesmaller than the static load stresses followingvalve closure (11).
Since the free edge is always unloaded orunstressed, its length should not change sig-nificantly. As the diameter at the top of the
commissure increases with pressure, the freeCirathtion Raearch VoL 35 December 197i
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