1. RUTGERS UNIVERSITY
Final Research Paper
Biointerface between fibriongen and 316L
stainless steel
Michael Infante
5/9/2012
Prof. Prabhas Moghe
155:531

2. 1
Introduction
Coronary heart disease (also called coronary artery disease) is a life threatening disorder that
involves the restriction of blood vessels that supply blood to the heart. Coronary stents are an
important and potentially lifesaving treatment for coronary artery disease. Stents are used to
increase blood flow through coronary arteries
that have become blocked by a buildup of
plaque. The treatment involves expanding the
stent until the artery reaches its original
diameter, which increases blood flow. The
procedure for inserting a stent is fairly
straightforward and the basic process of
inserting a stent is shown in Figure 1. The
closed stent is wrapped around a collapsed
balloon and placed at the end of a catheter
tube. This catheter is inserted into the artery
until the stent reaches the blockage. The
balloon is then inflated until the stent is fully
opened and the artery is returned to a
diameter that allows adequate blood flow.
The balloon is then deflated once again and
the catheter and balloon are removed from
the body. Since the goal of a coronary stent
is to keep the artery open and unblocked, so
that blood can flow freely and oxygen can be
delivered to the heart, the effectiveness of a stent can be measured by how well it resists the
growth of scar tissue and prevents the formation of blood clots. One common material used in
the construction of stents in 316L stainless steel. 316L stainless steel is widely used because it
has a low carbon content and is resistant to corrosion which is a function of its face-centered
cubic crystalline structure. Since the introduction of stents as a treatment option for heart
disease drug coatings have been added to further improve the body’s reaction to the implant
and reduce the immune response. Drug-eluting or drug coated stents were designed to help
slow the growth of scar tissue (cell proliferation) and the blockade of the stents (restenosis) that
develop over time. The basic design of drug coated stents is fairly simple. It consists of a
standard stent that is coated in a polymer, which houses the drug. The polymer releases the
drug after the stent is placed within the body. The drug is released into the walls of the arteries
and helps to prevent thrombus and restenosis. Two common drug-eluting stents are the
CypherTM
and TAXUSTM
stents which are rapamycin and paclitaxel-eluting respectively. To
understand how well a stent will perform in the body it is useful to know how proteins in the
blood will react to the surface once it is implanted. One such protein, fibrinogen, is very
important because it is one of the most plentiful proteins that circulates through the body.
Fibrinogen has a symmetrical structure that is dimeric and is made up of three sets of
intertwined polypeptide chains. These chains are denoted as α, β, and γ. Another reason
fibrinogen is so important is that it is one of the first blood proteins that will adsorb onto the
surface of a stent and it plays an important role in the coagulation cascade. During coagulation
fibrinogen is converted into fibrin, which is then cross-linked with clotting factors to form clots.
The dangers of clot formation and restenosis are a major concern after the implantation of a
stent, which means it is very important to understand how much fibrinogen will adsorb to the
surface as well as how strong the adhesive force is between the stainless steel and fibrinogen
molecules. Since it is clear that fibrinogen plays a key role in the success or failure of a stent it
is important to characterize these interactions between fibrinogen and the surface of the stent.
Figure 1. A pictorial representation of the process of
inserting a stent into a coronary artery. Source:
http://www.drugrecalllawyerblog.com/Stent%20%2801-28-
10%29.jpg

3. 2
For this project the biointerface between fibrinogen and 316L stainless steel will be studied. To
better understand how effective drug coatings are in the prevention of restenosis and clot
formation two drug coatings will also be included in the research. CypherTM
, the rapamycin-
eluting stent and TAXUSTM
, the paclitaxel-eluting stent will be studied alongside the uncoated
stainless steel stent. The goal of studying these three systems in conjunction is to determine
how much better a drug-eluting stent will perform under the same conditions as a traditional
uncoated stent. To study these aspects of the biointerface two techniques have been chosen;
Atomic Force Microscopy (AFM) and Ellipsometry. AFM will be used to study the strength of the
attractive force between fibrinogen and 316L stainless steel. AFM has been chosen for this work
over other cell adhesion assays because of its ease of operation, analysis and interpretation.
Ellipsometry will be used to determine the total amount of protein that can be adsorbed onto the
surface. The major advantage of ellipsometry and the reason it was chosen over other methods
to measure total mass of protein adsorbed is that it provides other information about the
biointerface in addition to the thickness of the film, which will be used to calculate the mass.
This other information, such as surface roughness and refractive index, can provide for
information about what happens at the interface, but will not be considered in this work.
Together these techniques should give a complete picture of how fibrinogen will react in the
presence of these stents and should also provide important insights into how well they will
perform when placed in the human body.
Principles
In this section the principles behind the two techniques being used in the experiment will be
discussed. Before getting into the specifics of Atomic Force Microscopy it is first necessary to
understand the forces that can exist between two cells or molecules. When two molecules
approach one another they can experience van der Waals forces, electrostatic forces, and
attractive or repulsive other forces. For the molecules to adhere to one another the forces of
attraction must overcome the forces of repulsion. The driving force for overcoming the repulsive
forces is that the molecules lower their total energy, which is what leads to adhesion. Since
adhesion is dependent on the strength of the force between the molecules it can be modeled as
a reversible reaction with an equilibrium constant. By knowing this equilibrium constant the force
per bond can be calculated and this leads to insights about the interactions in the system. Many
systems exist to study adhesion strength, but AFM is
easy to operate and provides reliable data that is
easy to analyze and interpret. AFM systems consist
of a cantilever that has a sharp tip called a probe, a
sample surface, a laser, and a detector. A schematic
of AFM is provided here in Figure 2. The schematic
shows the positioning of the cantilever and the probe
over the sample surface. The cantilever is usually
made of silicon or silicon nitride. The probe is
specifically designed to gather information about the
surface and has a radius of curvature on the order of
nanometers. The probe is used to scan the surface
of the sample and can measure van der Waals,
electrostatic, chemical bonding and other forces
when it is in the vicinity of the sample surface. The
forces between the probe and the sample surface
cause the cantilever to deflect. This force can be
calculated, using Hooke’s Law as the model,
because the cantilever acts as a spring. To use
Figure 2. A schematic of a typical AFM setup.
Source:
http://www.mtholyoke.edu/~menunez/Research
Page/AFM_mechanism.gif

4. 3
Hooke’s Law the spring constant (k) of the cantilever must be known. Typically values of the
spring constant for the cantilever vary from 0.1 N/m to 50 N/m. The laser is used to measure the
deflection of the cantilever because changes in the distance from the surface can happen on the
nanoscale. AFM usually operates using one of three main settings: contact, non-contact, and
intermittent mode. In contact mode the probe is in close contact with the sample surface. The
force is measured by the deflection of the cantilever. This deflection is compared to a reference
value of the deflection. If the deflection varies from the reference value then a feedback
controller raises or lowers the sample so that a constant value of the deflection is maintained.
This mode is generally used when the overall force is repulsive otherwise the probe has a
tendency to stick to the sample. One disadvantage of contact mode is that it can be destructive
since the probe is touching the sample surface. Non-contact mode keeps the cantilever above
the surface at a distance of 50 to
150 Å. This mode does not
damage the surface since there
is no contact, which overcomes
the major drawback of contact
mode. During operation the
cantilever oscillates above
sample and the long range
forces between molecules can
be measured. A feedback
controller maintains a constant
amplitude of oscillation and also
allows the creation of a
topographic map of the sample.
In intermittent mode (also called
tapping mode) the tip is alternately put in contact with the surface and then raised above the
surface. The cantilever oscillates in a similar fashion as in non-contact mode, but in this case
the tip makes contact with the sample on every oscillation. The oscillations of the cantilever
have large amplitude, usually greater than 20 nm, and that amplitude is held constant as it
moves across the surface. Forces acting on the cantilever alter the amplitude of the oscillation,
so a feedback controller is used to keep the amplitude constant. These forces and deflections
are recorded and used to measure and characterize features of the sample surface. Intermittent
mode also has the advantage of doing less damage then contact mode and avoids problems
that are associated with friction, sticking, and electrostatic forces. By attaching a microsphere
that is coated with protein to the probe it is possible to determine the force that exists between
the protein and the surface that is being studied. This method used by Bremmell, et. al. provides
the means to study the adhesion strength of fibrinogen onto the stainless steel surfaces that is
used here. The second technique that is being utilized in this research is Ellipsometry. The
basic concepts of ellipsometry require some knowledge about light. Light is an electromagnetic
wave that is made up of two components; an electric and a magnetic field. As a light wave
propagates the two components of the wave oscillate in phase with one another, but are
perpendicular to each other and to the direction of travel. Ellipsometry relies on the use of plane
polarized light to measure changes on the surface of a sample. Plane polarized light means that
the electric field component of all of the waves are oscillating in only one plane, which is still
perpendicular to the direction of propagation. Light emitted from a source will have random
polarizations so the light must first be polarized before it contacts the sample. For the
experiment a sample is immobilized in the experimental apparatus so that data can be collected
as time passes and the protein is adsorbed onto the surface. When the experiment begins the
plane polarized light hits the sample and the light becomes elliptically polarized and that change
is measured and recorded. The schematic provided in Figure 3 shows how the beam of
Figure 3. The plane polarized light becoming elliptically polarized during
ellipsometry. Source: http://www.tcd.ie/Physics/Surfaces/images/elli_dia.JPG

5. 4
polarized light experiences a shift in phase and the polarization changes after it makes contact
with the sample. After the first data set is collected the initial polarization is changed by a wave
retarder and the experiment is repeated. The data sets are compared and the difference
between the two enables the calculation of Ψ and ∆ using the complex reflectance ratio. The
equation for the complex reflectance ratio, which is used in the analysis of the raw data, is given
here (Equation 1).
ρ = rp/rs =tan(Ψ)exp(i∆)
ρ is the complex reflectance ratio, rp and rs are the amplitudes of the components of the
polarized wave that are parallel and perpendicular to the plane of incidence, and Ψ and ∆ are
the parameters that are calculated. Once Ψ and ∆ have been calculated an optical model can
be used to extract useful information about the system. This information may include the film
thickness, the refractive index, the surface roughness, and the crystallinity of the sample. This
technique is very useful since it is easily reproducible, does not need a reference sample and
can measure the presence of very thin films on a surface. These advantages make ellipsometry
ideal for use with biological systems, which are often much more sensitive and cannot easily be
studied by highly destructive techniques. Once the film thickness is calculated from the optical
model, then the total amount of protein that has adsorbed onto the surface can be determined.
Approach
The goal of this experiment is to determine the adhesion strength and total mass of fibrinogen
adsorbed onto the surface
of a stainless steel stent.
Three different cases will
be considered for the
purposes of this
experiment. The surfaces
will consist of uncoated
316L stainless steel
(referred to as SS),
CypherTM
(rapamycin-
eluting) coated 316L
stainless steel (referred to
as RES), and TAXUSTM
(paclitaxel-eluting) coated
316L stainless steel
(referred to as PES). The
coated stainless steel
surfaces were prepared by
spray coating. The liquid
coatings were expelled from a micro syringe and then focused using ultrasonic atomization
equipment. The focused liquid was then sprayed directly onto the surfaces and allowed to dry
for 24 hours. The setup of the coating process is shown in Figure 4. The RES and PES coated
surfaces each contained 100 μg of the drugs. Fibrinogen solutions were prepared by dissolving
fibrinogen powder (bovine plasma fibrinogen, 92% clottable, Sigma, USA) into a phosphate-
buffered saline solution at 37 °C (PBS, pH 7.4, Sigma, USA). The fibrinogen solutions had a
concentration of 100 μg/ml. These methods for preparing the steel surfaces (Pan, et. al) and the
fibrinogen powder (Berlind, et. al) are taken from literature. Now that the basic conditions and
goals of the experiment have been established the setup for each of the experiments can be
explained. The AFM images were taken at multiple positions on each stainless steel surface
Figure 4. Spray coating setup. Source:
Pan, C.J., J. T. (2007). Improved blood compatibility of rapamycin-eluting stent by
incorporating curcumin. Colloids and Surfaces B: Biointerfaces, 105-111.
(1)

6. 5
using a Molecular Imaging Pico Scan AFM (Agilent Technologies, USA) to determine the
adhesion forces. The imaging was done in non-contact mode using a scan rate of 1 Hz. The
probe tip was made of Si3N4 and had a radius of curvature of 20 nm. To attach the fibrinogen to
the probe tip, glass microspheres were first incubated in the fibrinogen solution for 1 hr to
adhere the protein molecules to the surface, were then rinsed with PBS, and then these
microspheres were then attached to the probe tip using Epikote heat-sensitive resin (Bremmell,
et. al). The cantilever had a length of 225 nm, a width of 45nm, and a thickness of 2.5 μm. The
resonant frequency of the cantilever was 60 kHz. The images were flattened to remove any
parabolic curvature in the data using a flattening algorithm (Planefit). Each scan covered an
area of 5 μm by 5 μm. Three measurements were taken on each sample and two samples of
each material were used. These conditions match those used by Zhijun Bai, et. al. The
ellipsometry experiment was performed in situ using a variable angle spectroscopic ellipsometer
(VASE, J.A. Woollam Co. Inc.) that had an angle of incidence of 68° in the spectral range of
350-1050 nm. For rinsing, a flow
system was employed that
consisted of a glass cell that
contained a magnetic stirring bar.
This system is shown in Figure 5. All
incubations performed for this
experiment were done at a pH of
7.4 and were incubated for a total of
30 minutes. After each incubation
was completed the cell was rinsed
with PBS at a flow rate of 3.0 ml/min
for 30 minutes to remove the
adsorbed protein from the surfaces.
The use of peristaltic pumps
allowed the experiment to be
completed without being exposed to
air. Data acquisition was done using
WVASE (J.A. Woollam Co. Inc.)
software. Three samples of each
material were tested and five
experiments were done for each
sample. These conditions for the
ellipsometry experiments (Berlind,
et. al) were chosen because they have the potential to produce data that is relevant to actual
conditions in the body and can be compared to previously obtained literature values.
Expected Data Outcomes
After analyzing the data from the AFM experiments, the goal is to calculate the adhesion force
for the different surfaces and to see what information this data will provide about which surface
is the most useful for biological applications. To find the adhesion strength a model is needed
for how the data relates to the force. Since the difference between the point of zero deflection
and the point of maximum deflection is known, Hooke’s Law can be used to calculate the forces.
Hooke’s Law (Equation 2) is shown here.
F=-k*(x-x0)
F is the adhesion force, k is the spring constant, which is known to be 3 N/m, x0 is the point of
zero deflection, and x is the point of maximum deflection of the tip. Using this relation the
Figure 5. Flow rinsing system for the ellipsometry setup. Source:
Berlind, T., M. P. (2010). Formation and cross-linking of fibrinogen layers
monitored with in situ spectroscopic ellipsometry. Colloids and Surfaces B:
Biointerfaces, 410-417.
(2)

7. 6
Figure 6. The adhesion strengths of uncoated stainless steel, rapamycin coated
stainless steel, and paclitaxel coated stainless steel.
Figure 7. The total mass adsorbed on the surface of uncoated stainless steel, rapamycin coated
stainless steel, and paclitaxel coated stainless steel.
adhesion strengths are
determined to be 3.09
± 0.27 nN for untreated
stainless steel, 1.13 ±
0.22 nN for the
rapamycin-eluting
stent and 1.52 ± 0.23
nN for the paclitaxel
eluting stent. (All data
is theoretical and only
meant to show general
trends) These values
are displayed
graphically in Figure 6.
By inspection it is
obvious that the
adhesion strength is
strongest between
fibrinogen and the bare
stainless steel (SS). It
is also apparent that
the adhesion strengths
for the paclitaxel-
eluting stent is the next
strongest followed
closely by the
rapamycin-eluting
stent. These outcomes
make sense because
the reason for drug
coating a stent is to
slow the body’s
response after
implantation of the
stent. The results for
SS and RES compare
well to literature data.
No literature data was
available for
comparison for the
paclitaxel-eluting stent.
Since the goal of the
ellipsometry
experiments was to
calculate the amount of
fibrinogen that had been adsorbed onto the surfaces the data from those experiments had to be
analyzed before any conclusion can be made. The only information that can be taken directly
from the experiments is Ψ and ∆ so some optical model is needed. This analysis was done
using WVASE (J.A. Woollam Co. Inc.) software, which had built in optical models that were
used to calculate the film thickness on the surfaces. Once that was obtained the mass of
adsorbed protein could be calculated directly from the thickness of the fibrinogen film using
0
0.5
1
1.5
2
2.5
3
3.5
4
SS RES PES
Adhesion Strength (nN)
0
20
40
60
80
100
120
140
160
SS RES PES
Mass adsorbed (ng/cm2)

8. 7
Figure 8. Literature data for the total amount of fibrinogen adsorbed on the surface of uncoated
stainless steel (SS) and rapamycin coated stainless steel (RES).
molecular weight of the fibrinogen from the study, 340 kDa (Sigma, USA). The values obtained
for the mass absorbed were keep in units of ng/cm2
so that they could easily be compared with
literature values. The fibrinogen adsorption onto the surfaces were determined to be 140.5 ± 6.5
ng/cm2
for untreated stainless steel, 38.8 ± 2.6 ng/cm2
for the rapamycin-eluting stent and 47.2
± 2.9 ng/cm2
for the paclitaxel eluting stent (This data is also theoretical). A similar trend is seen
in the total mass adsorbed to that which was seen for the adhesion strengths. The results
clearly show that uncoated stainless steel has the greatest amount of fibrinogen adsorbed onto
it’s surface. Again the two drug coated surfaces have similar results, which are much lower than
the uncoated stent. These results are shown graphically in Figure 7. For comparison a graphical
representation of
literature data has been
included. This includes
literature data for the total
protein adsorption of bare
stainless steel (SS) and
stainless steel coated
with rapamycin (RES),
but no data for the total
adsorption of fibrinogen
onto the paclitaxel coated
surface. This data is
shown in Figure 8 and
has the same trend that
was observed in the data
in the present study. Now
that the adhesion strength
and total protein
adsorption have been
calculated for each of the
different surfaces it is
obvious that both of the
drug-eluting stents have
less of fibrinogen adsorbed onto their surfaces and the fibrinogen adheres to those surfaces
with less force.
Interpretations
The first thing to notice about both of these experiments is that the results follow similar trends.
In the AFM experiment the adhesion strength of fibrinogen on an uncoated stainless steel
surface was shown to be more than double that of the surfaces that were drug eluting. This
means quite simply that it will take more force for a fibrinogen molecule to adhere to the drug
coated surface and that these molecules will need to come into closer proximity to these
surfaces before they can overcome the repulsive forces and adhere. Similarly after analyzing
the ellipsometry measurements the uncoated stainless steel had more than twice as much
fibrinogen adhered to it’s surface then the drug coated surfaces. So under the same conditions
and incubation times the drug coated surface will have less to protein on their surfaces. Thus
fibrinogen has a lower affinity for these surfaces and will not adhere to them as often or in such
a large quantity. Knowing this the question can be asked, what does that mean in terms of how
these materials will perform when formed into stents and placed in the human body? Since we
know that fibrinogen is not only one of the first proteins that will adhere to a foreign material that
is placed in the body, but it is also instrumental in the clotting process, it can be inferred that the

9. 8
drug coated stents will have a much greater chance of success when used in the body. There
are multiple reasons behind this prediction. The first reason comes directly from this experiment
and is due to the fact that the adhesion strength is lower for the drug eluting stents. This means
that as a fibrinogen molecule flows through the artery it will have a much harder time forming a
lasting bond with these surfaces when compared with the uncoated stainless steel stents. If the
fibrinogen molecules do attach to the surface, it will be harder for them to remain attached. The
lower force of adhesion between the surface and the fibrinogen molecule mean that the other
forces that are acting on the molecule, such as the force due to the flow of the blood, can result
in the proteins being desorbed from the stent surface. For any kind of major buildup of
fibrinogen to happen on these drug coated surfaces a much greater amount of time will have to
pass when they are compared to the uncoated surface, meaning a longer useful life of the stent.
The lower total adsorption of fibrinogen that was seen experimentally on these drug coated
surfaces gives another vital piece of information about how they will perform in vitro. Since the
fibrinogen molecules have a lower affinity for the surface when it is drug coated, there will be
less fibrinogen on the surface. This major reduction in protein attachment and therefore
blockage growth is one of the main reasons for the success of the drug coated stents. What has
been learned so far is that inside the body fibrinogen is not only less likely to adhere to the
surface of a drug coated stent, but once it does it will have a harder time staying attached. It is
also likely that drug coated stents will have less fibrinogen on their surfaces. Taking this
information and relating it back to the effectiveness of these materials as coronary stents, it is
clear that drug coated stents will likely be the best option. The advantage of these materials is
obvious when it is considered that fibrinogen is important in the coagulation cascade and the
formation of clots. By reducing the adsorption of fibrinogen on the surface of a stent, the chance
of forming a clot has effectively been reduced. This means that these stents will be far safer to
use in the body. It could also be possible that since less fibrinogen adheres to the surface that
this trend could hold true for other blood proteins as well. In this case the rate of cell proliferation
will be greatly reduced when the drug coated stents are used in place of their uncoated
counterparts. It can also be assumed that the growth of scar tissue over the stents will be
slowed and the chance of the artery becoming blocked again will be significantly reduced. Due
to the life threatening nature of this disease the advantages of drug coated stents are even
more important. The goal of these stents is to treat coronary heart disease, increase the
patient’s life expectancy and raise their quality of life. Having a stent that causes further
blockades of the coronary arteries or leads to the formation of clots will not be an effective
treatment. The stents would be rendered ineffective as a treatment for heart disease as they
would be potentially life threatening for the patients with the disease. The drug coated stents
can help these patients have a better long term outlook because they have the potential to last
longer and keep the arteries closer to their full diameter for a longer period of time. The reason
behind the use of these advanced materials is to treat this disease without the need for multiple
procedures or replacement stents. This means that not only will these patients have a better
outlook for the future, but they will spend less time dealing with costly surgical procedures, the
risks associated with the implantation of a stent, and the overall risks that they face as a result
of coronary heart disease. This hopefully means a longer, happier and healthier life for the
patient.
Caveats/Limitations
Despite the fact that these experiments were designed to look at specific aspects of the
interface between fibrinogen and stainless steel that will provide relevant information about the
biocompatibility of stainless steel and the experiments were carried out based on strict
standards of quality and safety, the conclusions that are drawn from them will have limitations.
The information and the insights that the data from these experiments provide may be

10. 9
extensive, but the range of its applicability to real life situations is fairly limited. To be truly
meaningful it needs to be supported by the work of other researchers. The first limitation of this
work is that it has been performed on surfaces that are flat. A real stent that is placed in the
body will have curved surfaces of varying geometries and this means that fibrinogen and other
blood proteins may react differently than what is predicted by this data. Proteins such as
fibrinogen may have greater adhesion rates because there is a greater surface area per unit
volume for the actual stents. Another caveat of this work is that information has only been
gathered for fibrinogen. The environment that the stent is placed into will be quite different from
the one that only contains fibrinogen. The information and conclusions gathered here may give
an idea of the general trends for these other blood materials, but there will be other factors that
cannot be foreseen and therefore are not considered when only fibrinogen is used to test the
surfaces. This means that it is hard to predict what will actually happen in the body. The present
work is also limited by the time scale over which the data was collected. These experiments
were performed on the order of hours and minutes, but a stent will in reality spend a much
greater amount of time in the human body. This could mean that as time passes the differences
in adhesion strength and total protein adsorption between the coated and uncoated stents may
become negligible as the drug becomes depleted. This also means great caution must be used
when interpreting any long term implications from the data collected in this study. The data is
meant to act as a guide to the general trends of coated versus uncoated stents and does not
provide any conclusive proof that drug coated stents are superior to uncoated stents in vitro.
Another caveat of this work is no testing was done to determine that all of the drug and stent
materials used in these experiments were safe. The assumption was made that the drug treated
stents have been used in human patients before and are therefore safe, but no validation was
done in this work. The final important factor that has not been considered is the economic
implications of using drug coated stents versus uncoated stents. If the cost of a drug coated
stent is much higher than the cost of an uncoated stent then it may be worth considering the
uncoated stent even if it means sacrificing the advantages that the drug coatings provide. This
determination would need to be based on the individual patient and could include factors such
as, the patient’s age, the patient’s level of health, and the individual prognosis of that patient.
With all of these limitations it is obvious that future work is necessary to definitively prove that
using drug coated stents is the best option. Some suggestions for future research include
performing the experiments on the actual stents, using other proteins or blood plasma in similar
experiments, and looking at which stents would be most effective for patients with varying
conditions and different backgrounds. By doing these experiments it may be possible to get a
full picture of what goes on in the body when a stent is implanted and determine which
treatment is the best for each patient. Knowing which treatment option can provide the highest
quality of life and the best overall prognosis for the patients will mean that doctors can do a
better job of prescribing the best treatment for each patient.

11. 10
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