swanson and clark, "dimensions and geometric relationships"
TRANSCRIPT
8/12/2019 Swanson and Clark, "Dimensions and Geometric Relationships"
http://slidepdf.com/reader/full/swanson-and-clark-dimensions-and-geometric-relationships 1/13
W. MILTON SWANSON and RICHARD E. CLARKPressure
Dimensions and Geometric Relationships of the Human Aortic Value as a Function of
Print ISSN: 0009-7330. Online ISSN: 1524-4571Copyright © 1974 American Heart Association, Inc. All rights reserved.is published by the American Heart Association, 7272 Greenville Avenue, Dallas, TX 75231Circulation Research
doi: 10.1161/01.RES.35.6.8711974;35:871-882Circ Res.
http://circres.ahajournals.org/content/35/6/871
World Wide Web at:The online version of this article, along with updated information and services, is located on the
http://circres.ahajournals.org//subscriptions/
is online at:Circulation ResearchInformation about subscribing toSubscriptions: http://www.lww.com/reprints
Information about reprints can be found online at:Reprints:
document.Permissions and Rights Question and Answerabout this process is available in thelocated, click Request Permissions in the middle column of the Web page under Services. Further informationEditorial Office. Once the online version of the published article for which permission is being requested is
can be obtained via RightsLink, a service of the Copyright Clearance Center, not theCirculation Research
Requests for permissions to reproduce figures, tables, or portions of articles originally published inPermissions:
at RHODE ISLAND HOSP on May 20, 2014http://circres.ahajournals.org/ Downloaded from at RHODE ISLAND HOSP on May 20, 2014http://circres.ahajournals.org/ Downloaded from
8/12/2019 Swanson and Clark, "Dimensions and Geometric Relationships"
http://slidepdf.com/reader/full/swanson-and-clark-dimensions-and-geometric-relationships 2/13
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
at RHODE ISLAND HOSP on May 20, 2014http://circres.ahajournals.org/ Downloaded from
8/12/2019 Swanson and Clark, "Dimensions and Geometric Relationships"
http://slidepdf.com/reader/full/swanson-and-clark-dimensions-and-geometric-relationships 3/13
872 SWANSON, CLARK
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
2) .
f = F r e e e d g e ( c m ) ( F i g . 2).
h = Height from ven tricu lar tra ct base
plane to top of annulus fibrosis (Fig.
2).I = Length (cm) (Fig. 2).p = Press ure (dynes/cmJ).x, y = Coordinates.
a = Leaflet angle (Figs. 2, 9).= Angles (Fig. 9). f = Free edge angle (Fig. 2).a = Stress (dynes/cm
2).
FMURE 1
a: Series 8 valve molds, 0 to 100 mm Hg. b: 80-mm Hg mold mated with left ventricle mold.
Circulation Research VoL 35 December 1971
at RHODE ISLAND HOSP on May 20, 2014http://circres.ahajournals.org/ Downloaded from
8/12/2019 Swanson and Clark, "Dimensions and Geometric Relationships"
http://slidepdf.com/reader/full/swanson-and-clark-dimensions-and-geometric-relationships 4/13
AORTIC VALVE DIMENSIONS AND GEOMETRY 873
SUBSCRIPTS
a = —
m =
s =V
Aorta.Center.Maximum.
Sinus of Valsalva.Ventricular tract.
SUPERSCRIPTS
* = Dimensionless q uan tity referred to dv.# = Dimens ionless q uan t i ty re fe rred to
that quantity at zero pressure.
Results
The valves listed in Tables 1-4 were chosen
for evaluation. Previous series were develop-
mental and had too few casts to yield signifi-
cant data.
The dimensions obtained from cast meas-
urements are listed in Tables 2-4. Figure 2illustrates the valve region and shows repre-
sentative dimensions. Graphic illustrations
of dimensionless variations with pressure
are presented in Figures 3-5. Dimensions
were reduced to dimensionless variables (de-
noted by asterisks) with respect to the diam-
eter, dv, of the left ventricle immediately
below the aortic valve for two reasons: dv is
the flow inlet diameter, and it varies very
little with pressure. The average variation of
dv with pressure from 20 mm Hg to 120 mm
Hg was approximately 10% (Fig. 3).
For calculating the flow conditions
through the valve region (5), the sinus di-
mensions d^*, dsm*, and s* are significant
along with the leaflet length €c* and the
center and maximum coaptation dimensions
Q* and Cm*. dv was measured as the diameter
of an indentation ring formed at the annularattachment (Fig. 2). The inlet flow diameter
is slightly smaller than dv by the thickness of
TABLE 2
Dimensional Quantities
Series
4
5
6
7
8
AverageAverage at 100
mm Hg
P(m m Hg)
0
2040
60
0
20
20
40
60
80
0
20
20
50
80
0
2040
70
10 0
12 0
0
20
40
60
80
10 0
(1 )
d v
(mm)
23.6
25.227.228.022.222.622.222.022.622.623.026.626.824.826.023.5
24.025.026.626.827.023.024.625.024.825.025.0
(2 )
d .
(mm)
19.7
21.623.127.517.818.118.519.921.021.420.123.524.826.528.918.2
19.721.224.024.927.023.025.226.627.030.130.7
(3 )
h
(mm)
20.0
19.320.319.815.115.715.715.715.615.719.520.019.0
19.519.517.8
17.817.618.018.518.017.317.717.317.417.717.8
(4)
<t>
51
4645
37
43
44
43
41
36
39
51
4 5
42
39
34
52
4944
41
39
32
34
32
31
29
25
23
40
32
(5 )
a
23
1920
23
15
15
15
17
20
20
15
17
16
22
24
9
1013
13
15
17
23
23
24
25
27
29
20
22
(6)
E,, x 1 0-3
(dynes/cm1)
2.22.2
2.4
5.3
5.2
5.2
5.0
5.3
1.6
1.6
2.1
2.4
3.33.1
3.2
3.3
3.4
3.0
3.3
3.6
3.8
4.0
3.3
3.5
See text for abbreviations.
Circulation Research, Vol. 35 , December I97i
at RHODE ISLAND HOSP on May 20, 2014http://circres.ahajournals.org/ Downloaded from
8/12/2019 Swanson and Clark, "Dimensions and Geometric Relationships"
http://slidepdf.com/reader/full/swanson-and-clark-dimensions-and-geometric-relationships 5/13
8/12/2019 Swanson and Clark, "Dimensions and Geometric Relationships"
http://slidepdf.com/reader/full/swanson-and-clark-dimensions-and-geometric-relationships 6/13
AORTIC VALVE DIMENSIONS AND GEOMETRY 875
TABLE 4
Dimensionless Quantities Relative to Zero Pressure Value
Series
4
5
6
7
8
P
(m m Hg)
0
20
40
60
0
20
20
40
60
80
0
20
20
5080
0
20
40
70
10 0
12 0
0
20
40
60
80
10 0
(1 )
d v *
1.001.071.151.241.001.020.990.991.021.021.001.161.17
1.081.131.001.021.061.131.141.151.001.071.091.081.091.09
(2 )
d . '
1.001.091.161.391.001.011.031.111.181.201.001.171.23
1.321.441.001.081.161.321.371.481.001.091.151.171.311.33
3)
h *
1.000.971.020.991.001.041.041.041.031.041.001.030.97
1.001.001.001.000.991.011.041.011.001.021.001.011.021.03
(4 )
d . '
1.001.121.231.301.001.021.021.061.081.101.001.261.28
1.361.481.001.081.131.221.261.271.001.061.131.151.201.23
(5 )
d . n '
1.001.131.231.351.001.051.031.081.131.141.001.251.27
1.341.481.001.061.121.161.191.251.001.081.161.161.201.22
(6 )
fr*
1.001.091.121.171.001.041.041.031.071.041.001.131.10
1.101.141.001.021.041.101.131.141.001.051.021.041.071.08
7)
e
1.000.991.011.081.001.041.051.051.041.051.001.101.12
1.131.201.001.111.161.161.161.231.001.011.031.011.071.07
See text for abbrev i a t i ons .
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.
at RHODE ISLAND HOSP on May 20, 2014http://circres.ahajournals.org/ Downloaded from
8/12/2019 Swanson and Clark, "Dimensions and Geometric Relationships"
http://slidepdf.com/reader/full/swanson-and-clark-dimensions-and-geometric-relationships 7/13
876 SWANSON, CLARK
5 1.0LLJ
I I
ZxLU H-
uos
L U
0.8 h
0.6
0.4 0 40 80 120
PRESSURE-p (mm Hg)FIGURE 4
Dimensionless leaflet center length, tr*, as a function ofpressure, p.
(8) for this type of comparison. This modulus
is not constant but increases with increasing
load. The marked nonlinear behavior of aor-
tic leaflets gives values of E from 2 x 105 to 6
x 107 dynes/cm
2 (9, 10).
The width of the coaptation at the center,c,., decreased with incre asing pre ssu re as a
consequence of a greater increase in diame-
ter than in length. The coaptation surface
then peeled back as the diameter of the
leaflet supporting structure increased with
increasing pressure. Also, because of the
small rate of increase of dv with pressure, the
sinuses bulged out over this base diameter
producing an increase in the angle of the
lower leaflet surface, a and a decrease in the
angle of the free edge, <f>, as indicated in
Table 2
(columns 5 and 4,
respectively) and in
Figures 6 and 7. The free edge length, f,
increased only slightly at the expense of a
decrease in coaptation width (c,. and 0 , and
it increased as a increased and decreased
(i.e., da increase d m ore th an dv). This
behavior was also evid ent from sectio ns
through one of the sinuses at three different
pressures (Fig. 7a). Sauvage et al. (3) also
indicated a slight increase in f with pressure;
the ir dimensionless r esu lts (3, Figs. 1-14) are
quite similar to ours and give f* =0.58 at 100
mm Hg for pig hearts compared with f* =0.62
for human hearts. They indicated that <£
decreases from 34° to 24° when pressures are
increased from 80 mm Hg to 120 mm Hg with
<f> = 28° at 100 mm Hg compared with our value
of 0 =32° at 100 mm Hg. These results are as
close as can be expected considering the dif-
ference of species. The most obvious signifi-
cant structural or geometric difference is in
the configuration of the sinuses of Valsalva
(6, Figs. 1-6). In addition to the difference in
species, freezing also produces a variation
effect on tissue properties (9).
Uncertainties based on errors from re-
peated measurements of basic qua ntities
were 5 for f*, <j>, and c*, 4 for a 3% for <?c*,
and 2 for other dimensionless quantities.
These values are close to the maximum rela-
tive variations of data points from smoothedcurves.
Since th e leaflets meet at an angle at the
noduli Aranti and since th e pressure loading
is balanced across the coapting surfaces,
there can be no stress along the free edge or
in t he coapting surfaces in the central region
except for the compressive stress equal to
the pressure.
LEAFLET STRUCTURE
Striations on the surfaces of the casts ad-
jacent to the leaflets indicated a fibrous
structure across the leaflet on the aortic
'0 40 80 120
PRESSURE p (mmHg)FIGURES
Dimensionless overall vertical height, h* , as a function ofpressure, p.
Circulation Research Vol. 35 December 197U
at RHODE ISLAND HOSP on May 20, 2014http://circres.ahajournals.org/ Downloaded from
8/12/2019 Swanson and Clark, "Dimensions and Geometric Relationships"
http://slidepdf.com/reader/full/swanson-and-clark-dimensions-and-geometric-relationships 8/13
AORTIC VALVE DIMENSIONS AND GEOMETRY 877
oz6 0
u 40
40 80 120
PRESSURE-p (mm Hg)FIGURE a
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
at RHODE ISLAND HOSP on May 20, 2014http://circres.ahajournals.org/ Downloaded from
8/12/2019 Swanson and Clark, "Dimensions and Geometric Relationships"
http://slidepdf.com/reader/full/swanson-and-clark-dimensions-and-geometric-relationships 9/13
8/12/2019 Swanson and Clark, "Dimensions and Geometric Relationships"
http://slidepdf.com/reader/full/swanson-and-clark-dimensions-and-geometric-relationships 10/13
AORTIC VALVE DIMENSIONS AND GEOMETRY 879
FIGURES
Views of aortic valve, a: View from left ventricle, b : Sideview iv plane of attachment line, c: Section throughcontour b of Figure Ha.
attachment line section is jus t the one-third
chord of the dv circle or 0.866 relative to dv.
The relative length of the elliptical contour
is 1/4 of the major axis length or 0.45. The
contours of the attachment annulus come
together at the top in a vertical short com-
missure section as indicated in Figure 10a, c,
and d. The center coaptation also turns up to
the vertical (Fig. 10a).
The platform projection of the leaflet in
Figure lOe is obtained from laying out chord
lengths on the projections from 10a as calcu-lated from arc len gths from 10c. The leaflet
contour chord length is obtained from the
cylindrical leaflet surface contour in Figure
10c and is just x=dv0/2 or x*=6/2, where 0 is the
angle out from the center along the leaflet arc
whose radius is dv/2. The longitudinal coordi-
nate obtained from projection onto the plane
perpendicular to the axis of the leaflet is
_ dr l - cosfl)V 2tany
Substituting 6 = 2x* into this expi-ession for ygives
Circulation Research Vol. J.5. December 1971
tany
for the equation of the leaflet contour. Fig-ure lOf is a layout of the vertical coapting
plane surfaces as the projection from Figure
10a and b. The bottom curves are parts of
ellipses formed by the intersection of the
coaptation planes with the leaflet cylinder
section. The two coapting planes from Figure
lOf are reconstructed on Figure lOe to be
coincident at the commissure attachment
point and tangent to the top curve of the
cylindrical leaflet section there.
The light internal lines of Figure 10 are
represen tative of the collagen load-carrying
fiber bundles. The load in the top point of thecylindrical section (Fig. lOe) is carried by the
fibers running down through the coaptation
zones (two fiber lines are illustrated). The
parts of the coaptation surfaces above the
lines to the point are unstressed (except for
the compressive pressure loading).
The entire geometry is essentially deter-
mined by the angle a (since 3 = y). The
comm issure heig ht (0.37) and the ce nte r
coaptation h eigh t (0.17) do not affect the
final shape of the cylindrical part of the
leaflet or its load-carrying ability and stress.
The size of the split necessary to allow a
development of the coapting surfaces with
the cylindrical surface with contiguity at the
attachment lines shown in Figure lOe is also
determined by a. The value 20° < a < 25°
minimizes this separation and the size of the
slit window where the fold line diverges.
If the leaflet thickness were uniform, the
stress would be cr = pd/2t, since it is a th in
mem brane (t < < d) with a uniform radius
(cylindrical section). The maximum value of
the pressure, p, is about 100 mm Hg at valve
closure. The maximum membrane stress isthen on the order of 27 x 10
5 dynes/cm
2 for a
leaflet thickness of 0.5 mm.
Discussion
The design geometry derived from valve
cast measurements is an averaged repre-
sentative geometry for the aortic heart
valve. The simple cylindrical geometry of the
load-carrying part of the leaflet gives a uni-
form stress resultant (load per unit thick-
ness) equal to pd/2.
This derived simplified geometry does nottake into account variations from one leaflet
at RHODE ISLAND HOSP on May 20, 2014http://circres.ahajournals.org/ Downloaded from
8/12/2019 Swanson and Clark, "Dimensions and Geometric Relationships"
http://slidepdf.com/reader/full/swanson-and-clark-dimensions-and-geometric-relationships 11/13
880 SWANSON, CLARK
FIGURE 10
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
at RHODE ISLAND HOSP on May 20, 2014http://circres.ahajournals.org/ Downloaded from
8/12/2019 Swanson and Clark, "Dimensions and Geometric Relationships"
http://slidepdf.com/reader/full/swanson-and-clark-dimensions-and-geometric-relationships 12/13
8/12/2019 Swanson and Clark, "Dimensions and Geometric Relationships"
http://slidepdf.com/reader/full/swanson-and-clark-dimensions-and-geometric-relationships 13/13
88 SWANSON CLARK
kg). This downward force is balanced primar-ily by the distributed pressure force on thecurved wall of the aortic arch.
References
1. GOULD PL CATALOGLU A DH TT G CHATTOPA
DHYAY A, CLARK R E: Stress analysis of th e hu-
man aortic valve. National Symposium on Com-
puterized Structural Analysis and Design G«orgeWashington University 1972
2. WOOD SJ, ROBEL SB, SAUVAGE LR : Technique for
study of heart valves. J Thorac Cardiovasc Surg46:369- 385 , 1963
3. S A U V A G E LR , V I G G E R S RF , B E R G E R K, R O B E L SB,
SAWYER PN WOOD SJ: Pro sthetic Repla cemen t of
the Aortic Valve. Springfield Illinois Charles C
Thomas 1972
4. MERCER JL BENEDECTY M BAHNSON HT: Geomet ryand construction of th e aortic leaflet. J ThoracCardiovasc Surg 65:511-518 1973
5. SWANSON WM CLARK RE: Aortic valve leaflet mo-
tion during systole. Circ Res 32:42-48 1973
6. MOZERSKY DJ , SUMNER DS: Transcuta neous meas-
urement of th e elastic properties of the humanfemoral artery. Circulation 46:948-955 1972
7. A R N D T J O , KOBERG: Die Druc k-Dur chme sser-Bez ie-
hung der in takten A. Femoralis des wachen
Menschen un d ihre Beein flussung durch Nora-drenalin-Infusionen. Pfluegers Arch 318:130-1461970
8. MINNS RJ , SODIN PD : Role of the fibrous compo-nents an d ground subst ance in the mechanicalproperties of biological tissues: A preliminary in-
vestigation. J Biomechanics 6:153-165 19739. CLARK RE: Stress-strain characteristics of fresh and
frozen human aortic an d mitral leaflets and chor-dae tendineae. J Thorac Cardiovasc Surg 66:202-208, 1973
10. CLARK RE, BUTTERWORTH GAM: Charac te riza tionof the mechanics of human aortic an d mitral valveleaflets. Surg Forum 22:134-135 1971
11. SWANSON WM CLARK RE: Motion and stresses in
aortic valve leaflet during systole. American Soci-ety of Mechanical Engin eers Paper 72-WA/BHF-51972
12. CLARK RE, FlNKE EH: Scanning an d light micro-scopy of human aortic leaflets in stressed and
relaxed states. Cardiovasc Surg 67:792-804 1974
Circulation Research VoL 35 December I97i