Biofilm Mechanics from nano to macro scale

1. A Combined Experimental and Numerical Study of
Biofilm Detachment
Presented by: Ashkan Safari
Supervisors: Prof. Alojz Ivankovic
Prof. Eoin Casey
1
"Biofilms are responsible for over 80% of
microbial infections in the body“
(US National Institutes of Health)

2. The big picture
2
Undefined Compression
AFM Retraction
Adhesive Joint Failure Test
FV simulation (OpenFOAM)
Mode I Mode II
CZM: Max & GIC
E(t)

3. Biofilm Mechanics, What We Know?
3
• A composite material: cells, EPS, and micro (and macroscale) voids.
• Biofilm detachment: increase in external forces or decrease in interface forces.
• Heterogeneous structure in time and space,
• A combined advanced microscopy methods & various modes of loadings.
• Mechanically heterogeneous, throughout thickness and on the surface.
• Isotropic or anisotropic?
• Strain rate dependency of mechanical properties.
• Viscoelastic fluid or viscoelastic solid?
• Burger model, Standard linear solid and generalised Maxwell models (No spring).
• Ductile Failure behaviour.
Ductile failure
Liquid fraction? Viscoelastic solid
He, Y., et al. (2013), ." PLoS One 8(5): e63750 Aggarwal, S. and R. M. Hozalski
(2010). Biofouling 26(4): 479-486
Wilking, J. N., et al., (2011). MRS Bulletin 36(05): 385-391.

4. This Study: Goals & Methods Used
4
Biofilm maturation, more EPS….• Defining the linear viscoelastic behaviour
• Prony series & Hereditary integral form
• Comparing different test methods at micro and macroscale levels
• Evaluation of elastic modulus at macroscale level:
• Mechanical heterogeneity: Indentation & multiple Hertz model fitting
• Adhesion effect: Retraction and JKR-based method
• Evaluation of failure at biofilm-glass interface under bulk mechanical loads
• CZM applicability for mode I and II interfacial separation
• AFM retraction analysis for a pure adhesive separation
• CZM-base FSI for biofilm detachment under fluid shear stress
Undefined mixed culture mature
biofilm from wastewater system
v
Realistic intact biofilm structureBiofilm sample in this study
𝐸 𝑡 = 𝐸0 +
𝑖=1
𝑀
𝐸𝑖 𝑒−(𝑡 𝜏 𝑖
𝜎 𝑡 =
0
𝑡
𝐸 𝑡 − 𝜏
𝑑𝜀(𝜏
𝑑𝑡
𝑑𝜏

5. Creep & Stress Relaxation : Rheometry of Different Biofilm Samples
5

6. Stress Relaxation: Compression vs. Rheometry
6
A
B
C
A B C
𝐸 𝑏𝑜𝑛𝑑
𝐸
=
1 + 3𝜐
1 − 𝜐
1 + 𝜐
𝑆2
1 + 3𝜐 1 − 2𝜐 𝑆2 𝐸 𝑏𝑜𝑛𝑑 =1.8E
𝜐 =0.46
*Williams, J. G. and C. Gamonpilas (2008). International Journal of Solids and Structures 45(16): 4448-4459.
S= 𝑎 ℎ = 1.6

7. Compressive Relaxation: Effect of Change in Loading Velocity
7

8. AFM Indentation and Retraction: Hertz vs. JKR
Distance
Contact line X=0
-X
+X
Indentation
Retraction
• Initial nonlinear part due to EPS,
• Variation in EPS, different indentation depths,
• Hertz model used, but better to use JKR,
• Structural/mechanical homogeneity throughout depth,
• Higher indentation, stiffer biofilm due to void closure.
Δ
Padh
𝐸 =
−3𝑃𝑎𝑑ℎ
𝑅
3 ∆𝛿
1 + 4−2 3
−3 2
𝐹 =
𝐸
1 − 𝜈2
𝑎2
+ 𝑅2
2
𝑙𝑛
𝑅 + 𝑎
𝑅 − 𝑎
− 𝑎𝑅 ; 𝛿 =
𝑎
2
𝑙𝑛
𝑅 + 𝑎
𝑅 − 𝑎
8
Hertz model Simplified JKR based displacement*
*Grunlan, J. C., X. Xia, D. Rowenhorst and W. W. Gerberich (2001). "Preparation and evaluation of tungsten tips relative to diamond for nanoindentation of soft
materials." Review of Scientific Instruments 72(6): 2804-2810.

9. Finite Volume Numerical Method - Linear Viscoelastic Model
9
Finite Volume Discretization in OpenFOAM
𝜕
𝜕𝑡
𝑉
𝜌𝐵 𝜑 𝑑𝑉 +
𝑆
𝜌𝐵 𝜑 𝒗. 𝒏 𝑑𝑆
=
𝑆
𝜑 𝑔𝑟𝑎𝑑𝜙. 𝒏 𝑑𝑆 +
𝑉
𝑞 𝜙𝑉 𝑑𝑉
Continuum mechanics formulations
𝜕
𝜕𝑡
𝑉
𝜌𝐵 𝜑 𝑑𝑉 +
𝑆
𝜌𝐵 𝜑 𝒗. 𝒏 𝑑𝑆 =
𝑆
𝜞 𝜑 𝑔𝑟𝑎𝑑𝜙. 𝒏 𝑑𝑆 +
𝑉
𝒒 𝜙𝑉 𝑑𝑉
𝜕𝜌𝐵 𝜑
𝜕𝑡
+ 𝛻. 𝜌𝐵 𝜑 𝒗 = 𝛻. 𝜞 𝜑 𝛻𝜑 + 𝒒 𝜑𝑉
𝜕𝜌
𝜕𝑡
+ 𝛻. 𝜌𝒗 = 0
𝜕𝜌𝑣
𝜕𝑡
+ 𝛻. 𝜌𝒗𝒗 = 𝛻. 𝜎
𝝈 𝑡 =
0
𝑡
2𝜇(𝑡 − 𝜏
𝛿𝜺(𝜏
𝛿𝜏
𝑑𝑡 + 𝑰
0
𝑡
𝜆 𝑡 − 𝜏 𝑡𝑟
𝛿𝜺(𝜏
𝛿𝜏
𝑑𝑡
𝛿𝝈 𝑡 = 2𝜇 𝑡 − 𝜏 𝛿𝜺 𝜏 + 𝜆 𝑡 − 𝜏 𝑡𝑟𝛿𝜺 𝜏 𝑰
𝛿𝜺 𝜏 =
1
2
𝛻𝛿𝒖 𝜏 + 𝛻𝛿𝒖 𝜏 𝑇
𝐵 𝜑=1
𝐵 𝜑= 𝒗

10. • Total work of adhesion vs. pure interfacial
separation energy
• Dissimilar bimaterial stress distribution
• Local stress concentration at the free
interface edge
• CZM for interfacial crack
Biofilm-Glass Dissimilar Bimaterial Failure: Cohesive Zone Model
10
𝑊𝑎𝑑ℎ = ∆𝛾(1 + 𝜑
𝐺𝑐 =
0
𝛿 𝑐
𝜎. 𝑑𝛿
Interface stress distribution
(/E ratio)
CZM
Homogeneous cohesive crack
Interfacial crack

11. Experimental Evaluation of Biofilm-glass Interfacial Separation
11
A B
A
B
C
D
C D
Mode I interfacial failure
A B C D
A
B
C
D
Mode II interfacial failure

12. Separation Energy & Maximum Traction – JKR Contact Model
12
Padh
𝑅0
3
=
3
4
6𝜋𝑅2
∆𝛾
𝐸
𝑅 𝑝𝑓 = 0.63𝑅0
𝐴 𝑝𝑓 = 𝜋𝑅 𝑝𝑓
2
𝜎𝑠𝑒𝑝𝑎𝑟𝑎𝑡𝑖𝑜𝑛 =
𝑃𝑎𝑑ℎ
𝐴 𝑝𝑓
𝑃𝑎𝑑ℎ = −
3
2
∆𝛾𝜋𝑅
• Cohesive or adhesive pull-off force?
• Microscale separation energy from AFM retraction 4 orders of
magnitude smaller than total failure energy (bulk butt joint test)

13. average= 66.6 Pa
Numerical Prediction of Mode I and II Separation Initiation
13
B
Material Properties Value
Prony Coefficients
E0, E1 (Pa) 339.6, 100.2
t1, (sec) 8.58
Density,  (kg/m3) 1000
Poisson’s Ratio,  (-) 0.46
CZM Properties Value
Mode I Maximum Traction (Pa) 205
Mode I Separation Energy (mJ/m2) 0.033
Mode II Maximum Traction (Pa) 150
Mode II Separation Energy (mJ/m2) 0.033
B
average= 59.2 Pa
 Biofilm: /E=0.001 Pa-1 (E=1 kPa & =0.46)
 Glass: /E=5x10-12 Pa-1 (E=50 GPa & =0.25)

14. FSI Study of Biofilm Detachment under Fluid Shear Stress
*Walter, M., et al., (2013). "Detachment characteristics of a mixed culture biofilm using particle size analysis." Chemical Engineering Journal 228(0): 1140-1147.
** Abe, Y. (2012). "Cohesiveness and hydrodynamic properties of young drinking water biofilms." water research 46, 1155-1166. 14
• Shear Induced Detachment Test in Flow Cell: Particle Size Analysis*:
• Frequency of sloughing/average size of particles (>5.0 μm2) increased
significantly at WSS above 0.04Pa (at 18 mm/s)
• FSI Simulation: Partitioned FSI approach: one-way coupling.
• Mode II CZM/ Dugdale type
• WSS of 0.04 Pa assumed as Max,
• of less than 0.00001 mJ/m2 by Inverse method (critical= 0.25 m).
• Hydrodynamic shear stress is 3 orders of magnitude lower than mechanically
measured value (global versus local properties).**
𝝈 = −𝑝𝑰 + 2𝜇 𝜺
𝜺 =
1
2
[𝛻𝒗 𝜏 + 𝛻𝒗 𝜏 𝑇
] Solve Fluid
Fixed Solid
Solve Solid
𝒗=
𝒅𝒖
𝑑𝑥
𝑷

15. FSI Simulation Results
15
At the highest flow velocity of 18 mm/s
water flow water flow
Just above the flow velocity of 2 mm/s

16. Conclusions
16
• Mature wastewater biofilm generally have a low elastic modulus.
• Mechanical properties of this mature biofilm do not depend on the mode of loading applied.
• Compressive elastic modulus of biofilm could be an overestimated (a bonded compression)
• Strain rate dependency of elastic modulus (at intermediate range).
• Viscoelastic solid behaviour described by Generalised Maxwell Model with a free spring.
• At microscale level, biofilm is considered mechanically inhomogeneous.
• significant influence of adhesion forces on the elastic properties.
• Macroscale adhesive joint failure evaluation methods as useful methods in order to investigate the interfacial failure for biofilms.
• Cohesive Zone Model can be used as a reliable approach to predict the separation initiation at the crack tip zone at the microscale level.
• Interfacial crack initiates due to a local stress concentration at dissimilar biofilm-glass interface edge.
• AFM retraction curve analysis as a useful method to obtain CZM parameters.
• Biofilm-glass interfacial failure energy is mainly associated with the bulk biofilm deformation than pure separation energy at the interface.
• The measured hydrodynamic separation stress (at global scale) and separation energy are found to be 4 orders of magnitude lower than
mechanically measured values by AFM (at local scale), giving a similar crack opening critical distance for both scales of testing.
• Uneven biofilm surface on the surface may lead to earlier detachment events due to an increase in shear stress at the localised areas.
• Individual biofilm aggregate can detach at earlier stage than a large carpet-like biofilm due to the local stress zone at biofilm-substrate interface.

17. Publications
17
Conference Publications
• Safari. A., Casey, E. and Ivankovic, A (2007) A fluid-structure interaction approach to the investigation of detachment from bacterial biofilms. Proceedings of 13th
Annual Conference Bioengineering in Ireland.
• Safari, A., Ivanković, A. and Tuković, Z (2008) Numerical Modelling of Viscoelastic Response of Bacterial Biofilm to Mechanical Stress. 14th Annual Conference
Proceedings of Bioengineering in Ireland.
• Safari, A., Walter, M., Casey, E., Ivankovic, A (2008) A two-phase flow model of biofilm detachment. Proceedings of the 31st Annual Meeting of the Adhesion Society,
Austin, USA.
• Safari, A., Ivanković, A. and Tuković, Z (2008) Numerical Modelling of Fluid-Biofilm. Proceeding of 8th World Congress on Computational Mechanics (WCCM8),
Venice, Italy.
• Safari. A., Ivankovic, A., Tukovic, Z (2009) Numerical modelling of viscoelastic response of biofilm to fluid flow stress. Proceedings of 6th International Congress of
Croatian Society of Mechanics (ICCSM), Dubrovnik, Croatia.
• Safari. A., Tukovic, Z., Casey, E., Ivankovic, A (2013) Cohesive Zone Modelling of Biofilm-Glass Interfacial Failure, Joint Symposium of Irish Mechanics Society &
Irish Society for Scientific & Engineering Computation, Dublin, Ireland.
Journal Publications
• Safari, A, Habimana, O, Allen, A, Casey, E (2014) The significance of calcium ions on Pseudomonas fluorescens biofilms: a structural, and mechanical study.
Biofouling, 30 :859-869.
• Walter, M., Safari, A., Ivankovic, A., Casey, E (2013) Detachment characteristics of a mixed culture biofilm using particle size analysis. Chemical Engineering
Journal, 228 :1140-1147.
Submitted Journal Publications
• Safari. A., Tukovic, Z., Walter, M., Casey, E., Ivankovic, A (Expected in 2015) Mechanical Properties of a Mature Biofilm from a Wastewater System - From
Microscale to Macroscale Level. For peer review in Biofouling.
• Safari. A., Tukovic, Z., Cardiff, Ph., Walter, M., Casey, E., Ivankovic, A (Expected in 2015) Investigation of the Interfacial Separation of a Mixed Culture
Mature Biofilm from a Glass Surface – A Combined Experimental and Cohesive Zone Modelling Study. For peer review in Biotechnology and Bioengineering.