Biofilm Mechanics

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)

The big picture

2

Undefined Compression

AFM Retraction

Adhesive Joint Failure Test

FV simulation (OpenFOAM)

Mode I Mode II

CZM: Max & GIC

E(t)

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): 479-486Wilking, J. N., et al., (2011). MRS Bulletin 36(05): 385-391.

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

𝐸𝑖𝑒 −(𝑡 𝜏𝑖

𝜎 𝑡 =

0

𝑡

𝐸 𝑡 − 𝜏 𝑑휀(𝜏

𝑑𝑡𝑑𝜏

Creep & Stress Relaxation : Rheometry of Different Biofilm Samples

5

Stress Relaxation: Compression vs. Rheometry

6

AB

C

A B C

𝐸𝑏𝑜𝑛𝑑

𝐸=

1 + 3𝜐1 − 𝜐1 + 𝜐

𝑆2

1 + 3𝜐 1 − 2𝜐 𝑆2 𝐸𝑏𝑜𝑛𝑑 =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

Compressive Relaxation: Effect of Change in Loading Velocity

7

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

2𝑙𝑛

𝑅 + 𝑎

𝑅 − 𝑎− 𝑎𝑅 ; 𝛿 =

𝑎

2𝑙𝑛

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.

Finite Volume Numerical Method - Linear Viscoelastic Model

9

Finite Volume Discretization in OpenFOAM

𝜕

𝜕𝑡

𝑉

𝜌𝐵𝜑 𝑑𝑉 +

𝑆

𝜌𝐵𝜑𝒗. 𝒏 𝑑𝑆

=

𝑆

𝜑𝑔𝑟𝑎𝑑𝜙. 𝒏 𝑑𝑆 +

𝑉

𝑞𝜙𝑉 𝑑𝑉

Continuum mechanics formulations

𝜕

𝜕𝑡

𝑉

𝜌𝐵𝜑 𝑑𝑉 +

𝑆

𝜌𝐵𝜑𝒗. 𝒏 𝑑𝑆 =

𝑆

𝜞𝜑𝑔𝑟𝑎𝑑𝜙. 𝒏 𝑑𝑆 +

𝑉

𝒒𝜙𝑉 𝑑𝑉

𝜕𝜌𝐵𝜑

𝜕𝑡+ 𝛻. 𝜌𝐵𝜑𝒗 = 𝛻. 𝜞𝜑𝛻𝜑 + 𝒒𝜑𝑉

𝜕𝜌

𝜕𝑡+ 𝛻. 𝜌𝒗 = 0

𝜕𝜌𝑣

𝜕𝑡+ 𝛻. 𝜌𝒗𝒗 = 𝛻. 𝜎

𝝈 𝑡 = 0

𝑡

2𝜇(𝑡 − 𝜏 𝛿𝜺(𝜏

𝛿𝜏𝑑𝑡 + 𝑰

0

𝑡

𝜆 𝑡 − 𝜏 𝑡𝑟 𝛿𝜺(𝜏

𝛿𝜏𝑑𝑡

𝛿𝝈 𝑡 = 2𝜇 𝑡 − 𝜏 𝛿𝜺 𝜏 + 𝜆 𝑡 − 𝜏 𝑡𝑟𝛿𝜺 𝜏 𝑰

𝛿𝜺 𝜏 =1

2𝛻𝛿𝒖 𝜏 + 𝛻𝛿𝒖 𝜏 𝑇

𝐵𝜑=1

𝐵𝜑= 𝒗

• 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

𝛿𝑐

𝜎. 𝑑𝛿

Interface stress distribution

(/E ratio)

CZM

Homogeneous cohesive crack

Interfacial crack

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

Separation Energy & Maximum Traction – JKR Contact Model

12

Padh

𝑅03 =

3

4

6𝜋𝑅2∆𝛾

𝐸𝑅𝑝𝑓 = 0.63𝑅0

𝐴𝑝𝑓 = 𝜋𝑅𝑝𝑓2

𝜎𝑠𝑒𝑝𝑎𝑟𝑎𝑡𝑖𝑜𝑛 =𝑃𝑎𝑑ℎ

𝐴𝑝𝑓𝑃𝑎𝑑ℎ = −

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)

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)

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

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

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.

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.