Scaffolds For Tissue Engineering Applications - First Review (27 Jan 2009)
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Micro/Nanoporous Scaffolds for Tissue Engineering Applications Department of Chemical Engineering and Materials Science Amrita School of Engineering Coimbatore – 641 105 January 2009
First Review By Divya Haridas (CB105PE012) Karthikeyan G (CB105PE023) Krishna Priya C (CB105PE025) Premika G (CB105PE028) Guide Dr. Murali Rangarajan. Ph.D Co-Guide Dr. Nikhil K Kothurkar. Ph.D
Scaffolds-Overview
Scaffolds play a critical role during cell adhesion, proliferation and differentiation Cell Adhesion occurs between cell membrane and the implanted scaffold surface via the receptorligand bonds Following implantation, the gradually degrading scaffolds is continuously subjected to load due to the growing tissues Effect of stress – detachment of bonding forces undesirable However, little is known of the interaction between the scaffold and the bone
Need for Modeling
Once implanted, there is only very limited access to the adhered scaffolds Any control over the healing response is also lost upon implantation Surgical intervention to possibly reengineer any treatment also would prove to be an invasive procedure At this point, the scaffold modeling process takes over, modifying the design and mechanical characteristics of the scaffold on its own
Cell Adhesion
Cell adhesion is the binding of cell to another cell or to a surface or matrix
Cell adhesion is regulated by specific cell adhesion molecules that interact with other molecules
Cell adhesion on Biomaterials
The adhesion involves two phases – the attachment phase and the adhesion phase Attachment phase – involves short term events like physicochemical linkages between cells and materials involving ionic forces, van der Walls forces, etc. Adhesion phase – involves long term events like interaction between extracellular matrix proteins, cell membrane proteins and cytoskeleton proteins Protein interactions with ligands, other proteins, or surfaces are controlled by the complex array of intermolecular and intersurface forces
Peeling Model
Assumes attachment pattern similar to that of peeling
Simple model that captures essential physics
The model consists of two regions 1. the free zone and 2. the adhesive zone
General approach Analyze the membrane mechanics for each zone separately Requires continuity of the solutions at the interface between the two zones
One Dimensional Peeling Model
Evan A. Evans, 1985. Detailed mechanism of membranemembrane adhesion and separation, Biophysical Journal, 48, 175-183
Peeling Model - Assumptions
Scaffold Membrane
Rigid, flat, non-porous, solid surface
Cell Membrane
Thin elastic shell, Axisymmetric
Forces of separation = Tension induced during adhesive contact formation.
The adhesion forces are finite range interactions Hence membrane is studied under two zones
Peeling Model- Forces Forces A cell membrane adhered to the scaffold will be subjected to a combination of internal and external forces External forces acting includes Ligand-receptor Interactions ( Major Force) Electrostatic interactions at the surface (Approximated)
van der Waals forces of attraction (Approximated) Steric forces of repulsion (Approximated) The shape of the cell is then obtained by solving for the internal forces when the cell is subject to the external forces, at equilibrium
Leckband D., 2000. Measuring the forces that control protein interactions, Annual Review Biophysics Biomolecular Structure 29, 1-26
One Dimensional Peeling Model
Dong Kong, Baohua Ji, Lanhong Dai, 2008. Nonlinear mechanical model of cell adhesion, Journal of Theoretical Biology 250, 75-84
Peeling Model
The forces acting is given as an empirical formula : Linear :
fn - strength of the bond lb - bond length
Nonlinear :
L - bond extension C - dimensionless parameter characterizing the nonlinearity of force–extension relationship of bond and the ability of bond Evan having A. Evans, 1985. Detailed mechanism of membrane-membrane adhesion and large deformation separation, Biophysical Journal, 48, 175-183
Governing Equations
Free Zone
Where s = arc length bond k= local curvature
Adhesive Zone
f = adhesive bond force of a single n = bond density
Solution for free zone – Linear and Non Linear Boundary Conditions
Changing the variables from Ɵ to X we get
Boundary Conditions
Solution for free zone – Linear and Non Linear The solutions of free zone are functions of local angle θ, the external force Tex , the Macroscopic angle θ0 is shown as follows
The elastic constitutive relation for membrane is given by bending moment is proportional to the change in curvature
Where km0 is stress free curvature B – bending modulus The local balance of moments in the membrane surface is given by the relation transverse Shear equal to gradient bending moment
Free zone curvature :
Solution for adhesive zone - Linear
Tangential forces remains the same but normal forces gets modified fn is the sum of the attractive and repulsive forces Fn is the maximum force at which the bond will break Bond length scale lb is the maximum stretch required to reach the peak force
Solution for adhesive zone - Linear
The work done in either breaking or forming the cross bridges when the membrane is brought from large separations to equilibrium contact is given as
Adhesion energy per unit contact area is given as
Solution for adhesive zone - Linear
Adhesive stress
When the membrane angle is less than θ ≤ 30°
Solution for adhesive zone - Linear
Solving
Solution for adhesive zone
Variation in tension term is of higher order i.e. smaller compared to bending stress term
Where, Ɵα - ratio of adhesion and bending energies t - ratio of tension and bending
Solution for constants
At the edge of contact zone i.e. s = 0 and
C2 /
=1
Θ=
1
K=-
Q/B = [(
C2 -
2 1
2
C1
C2 + 2 2 2
-
2 1
1 2
)
1
C1 +
2 2
+2
1 2
[(
= lb
2 1
-
C1 ]C2 +
2
2 2
)
2
+2
2 1
]C1
2
C1 value is solved using Newton’s method and values are obtained from a C program
Adhesion energy per unit area vs ratio of adhesion to bending (deformation) energies Picture 11
The approximation that tension T is constant is reasonable for: large bending (small θ ) and strong adhesion (large θ0)
Contact Angle (θ0) vs. Adhesion/Bending Energy (θα)
Contact angle is large when adhesion is strong and free contact angle is large
Future work
Linear Model Obtain the contour of the cell membrane as function of Bending Modulus Tension Adhesion
This translates as obtaining contour of the cell membrane as a function of B Θ 0
Future work
Adhesive zone – Nonlinear Modeling :
From experimental data on osteoblast adhesion on scaffolds, find a nonlinear force-extension model
Use this model to obtain equilibrium adhesion profiles of osteoblasts on flat scaffold surfaces
Extend this model to curved scaffold surfaces
Thank you
First Review By Divya Haridas (CB105PE012) Karthikeyan G (CB105PE023) Krishna Priya C (CB105PE025) Premika G (CB105PE028) Guide Dr. Murali Rangarajan. Ph.D Co-Guide Dr. Nikhil K Kothurkar. Ph.D
Scaffolds-Overview
Scaffolds play a critical role during cell adhesion, proliferation and differentiation Cell Adhesion occurs between cell membrane and the implanted scaffold surface via the receptorligand bonds Following implantation, the gradually degrading scaffolds is continuously subjected to load due to the growing tissues Effect of stress – detachment of bonding forces undesirable However, little is known of the interaction between the scaffold and the bone
Need for Modeling
Once implanted, there is only very limited access to the adhered scaffolds Any control over the healing response is also lost upon implantation Surgical intervention to possibly reengineer any treatment also would prove to be an invasive procedure At this point, the scaffold modeling process takes over, modifying the design and mechanical characteristics of the scaffold on its own
Cell Adhesion
Cell adhesion is the binding of cell to another cell or to a surface or matrix
Cell adhesion is regulated by specific cell adhesion molecules that interact with other molecules
Cell adhesion on Biomaterials
The adhesion involves two phases – the attachment phase and the adhesion phase Attachment phase – involves short term events like physicochemical linkages between cells and materials involving ionic forces, van der Walls forces, etc. Adhesion phase – involves long term events like interaction between extracellular matrix proteins, cell membrane proteins and cytoskeleton proteins Protein interactions with ligands, other proteins, or surfaces are controlled by the complex array of intermolecular and intersurface forces
Peeling Model
Assumes attachment pattern similar to that of peeling
Simple model that captures essential physics
The model consists of two regions 1. the free zone and 2. the adhesive zone
General approach Analyze the membrane mechanics for each zone separately Requires continuity of the solutions at the interface between the two zones
One Dimensional Peeling Model
Evan A. Evans, 1985. Detailed mechanism of membranemembrane adhesion and separation, Biophysical Journal, 48, 175-183
Peeling Model - Assumptions
Scaffold Membrane
Rigid, flat, non-porous, solid surface
Cell Membrane
Thin elastic shell, Axisymmetric
Forces of separation = Tension induced during adhesive contact formation.
The adhesion forces are finite range interactions Hence membrane is studied under two zones
Peeling Model- Forces Forces A cell membrane adhered to the scaffold will be subjected to a combination of internal and external forces External forces acting includes Ligand-receptor Interactions ( Major Force) Electrostatic interactions at the surface (Approximated)
van der Waals forces of attraction (Approximated) Steric forces of repulsion (Approximated) The shape of the cell is then obtained by solving for the internal forces when the cell is subject to the external forces, at equilibrium
Leckband D., 2000. Measuring the forces that control protein interactions, Annual Review Biophysics Biomolecular Structure 29, 1-26
One Dimensional Peeling Model
Dong Kong, Baohua Ji, Lanhong Dai, 2008. Nonlinear mechanical model of cell adhesion, Journal of Theoretical Biology 250, 75-84
Peeling Model
The forces acting is given as an empirical formula : Linear :
fn - strength of the bond lb - bond length
Nonlinear :
L - bond extension C - dimensionless parameter characterizing the nonlinearity of force–extension relationship of bond and the ability of bond Evan having A. Evans, 1985. Detailed mechanism of membrane-membrane adhesion and large deformation separation, Biophysical Journal, 48, 175-183
Governing Equations
Free Zone
Where s = arc length bond k= local curvature
Adhesive Zone
f = adhesive bond force of a single n = bond density
Solution for free zone – Linear and Non Linear Boundary Conditions
Changing the variables from Ɵ to X we get
Boundary Conditions
Solution for free zone – Linear and Non Linear The solutions of free zone are functions of local angle θ, the external force Tex , the Macroscopic angle θ0 is shown as follows
The elastic constitutive relation for membrane is given by bending moment is proportional to the change in curvature
Where km0 is stress free curvature B – bending modulus The local balance of moments in the membrane surface is given by the relation transverse Shear equal to gradient bending moment
Free zone curvature :
Solution for adhesive zone - Linear
Tangential forces remains the same but normal forces gets modified fn is the sum of the attractive and repulsive forces Fn is the maximum force at which the bond will break Bond length scale lb is the maximum stretch required to reach the peak force
Solution for adhesive zone - Linear
The work done in either breaking or forming the cross bridges when the membrane is brought from large separations to equilibrium contact is given as
Adhesion energy per unit contact area is given as
Solution for adhesive zone - Linear
Adhesive stress
When the membrane angle is less than θ ≤ 30°
Solution for adhesive zone - Linear
Solving
Solution for adhesive zone
Variation in tension term is of higher order i.e. smaller compared to bending stress term
Where, Ɵα - ratio of adhesion and bending energies t - ratio of tension and bending
Solution for constants
At the edge of contact zone i.e. s = 0 and
C2 /
=1
Θ=
1
K=-
Q/B = [(
C2 -
2 1
2
C1
C2 + 2 2 2
-
2 1
1 2
)
1
C1 +
2 2
+2
1 2
[(
= lb
2 1
-
C1 ]C2 +
2
2 2
)
2
+2
2 1
]C1
2
C1 value is solved using Newton’s method and values are obtained from a C program
Adhesion energy per unit area vs ratio of adhesion to bending (deformation) energies Picture 11
The approximation that tension T is constant is reasonable for: large bending (small θ ) and strong adhesion (large θ0)
Contact Angle (θ0) vs. Adhesion/Bending Energy (θα)
Contact angle is large when adhesion is strong and free contact angle is large
Future work
Linear Model Obtain the contour of the cell membrane as function of Bending Modulus Tension Adhesion
This translates as obtaining contour of the cell membrane as a function of B Θ 0
Future work
Adhesive zone – Nonlinear Modeling :
From experimental data on osteoblast adhesion on scaffolds, find a nonlinear force-extension model
Use this model to obtain equilibrium adhesion profiles of osteoblasts on flat scaffold surfaces
Extend this model to curved scaffold surfaces
Thank you
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