Gas Embolotherapy: Vascular Microbubbles for Cancer Treatment
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Gas Embolotherapy: Vascular Microbubbles for Cancer Treatment Joseph L. Bull, Brijesh Eshpuniyani, Andres J. Calderon, Tao Ye, and J. Brian Fowlkes Department of Biomedical Engineering The University of Michigan [email protected] http://www.umich.edu/~joebull. Introduction.

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Gas Embolotherapy: Vascular Microbubbles for Cancer Treatment

Joseph L. Bull, Brijesh Eshpuniyani, Andres J. Calderon, Tao Ye, and J. Brian Fowlkes

Department of Biomedical Engineering

The University of Michigan

[email protected]

http://www.umich.edu/~joebull


Introduction Treatment

  • Embolotherapy involves using emboli to starve tumors by occluding the blood flow to them

  • Previous work has focused on using solid emboli

  • Embolotherapy is well-suited for treatment of renal and hepatocellular carcinoma—these don’t respond well to chemotherapy and surgical resection is difficult

  • Currently embolotherapy for tumors is primarily used as a last resort after conventional treatment modalities have failed

  • Infarction of healthy tissue is a concern in using these methods


Introduction Treatment

  • We are developing a gas embolotherapy technique that will allow selective delivery of emboli to tumors

  • The bubbles originate as 6 μm-diameter liquid droplets of dodecafluoropentane (DDFP, C5F12) mixed in saline and albumin, and are injected into the vascular system

  • The boiling point of DDFP is 29 EC at atmospheric pressure

  • The droplets are small enough to pass through capillary beds, allowing them to circulate until the next stage of the treatment


Acoustic Droplet Vaporization Treatment

  • The droplets may be non-invasively vaporized at a strategic location, increasing their volume ~125 times

  • Example driving: 3.5 MHz and 33 cycle tone burst at 1.5 to 10 MPa

  • Pressure threshold decreases with increasing frequency


Transport of Emboli Treatment

  • Emboli are transported by blood flow until they become lodged

  • Life of static DDFP is O(days) in blood

  • Goal of treatment is to occlude flow to most of tumor

  • Successful treatment has been observed with 78% necrosis (De Signi 1997)

For more details, see: Bull J.L. Critical Reviews in Biomedical Engineering 33(4): 299-346, 2005.


  • Embolotherapy Research Topics Treatment

    • Droplet vaporization, bubble expansion, and potential to rupture/damage vessels

    • Bubble transport

      • Gravitational effects

      • Single and multiple bifurcations

    • Bubble sticking

      • Surface tension effects

      • Adhesion involving surface active molecules

    • Homogeneity of occlusion, multiple bifurcations, and effect of multiple doses

    • Interaction of bubbles with endothelium and blood-borne proteins and phospholipids

    • Drug delivery and functionalization in addition to occlusion

  • Methods

    • Animal experiments

    • Bench top experiments

    • Computational and theoretical models


Bubble vaporization expansion in a rigid tube
Bubble Vaporization/Expansion in a Rigid Tube Treatment

  • Motivation: potential bio-effects, such as vessel rupture and endothelial injury, could be induced by flow stresses on the vessel wall

  • Assumptions: Axisymmetric, isothermal flow; Rigid, impermeable tube wall; Viscous, incompressible liquid; Ideal gas inside bubble, initially high pressure; Constant surface tension

  • T. Ye and J.L. Bull. Direct Numerical Simulations of Micro-Bubble Expansion in Gas Embolotherapy. Journal of Biomechanical Engineering 126(6): 745-759, 2004.


Physical scales
Physical Scales Treatment

  • Tube dimension and initial bubble diameter

    • Tube diameter, D: 36 μm

    • Tube length, L: 36 μm × 32 = 1.152 mm

    • Initial bubble diameter, di: 0.1, 0.3, 0.5, 0.7, and 0.9 times tube diameter

      • 3.6 μm, 10.8 μm, 18 μm, 25.2 μm, 32.4 μm

  • Velocity scale, U, range: 1.628 m/s to 3.440 m/s

  • Time scale, T, range: 10.5 × 10-6 s to 22.1 × 10-6 s

  • Stress scale range: 2540 to 11340 Pa


Initial bubble diameter 0 5
Initial Bubble Diameter = 0.5 Treatment

  • Re = 428, We = 6.93, St = 10.5, Pinitial= 176

    • Time interval is 0.25 dimensionless unit (10.5 × 10-6 s / unit)


Initial bubble diameter 0 51
Initial Bubble Diameter = 0.5 Treatment

  • Pressure and shear stress along the top wall at various times

    • Stress : 11338.8 N/m2 per dimensionless unit


Effect of initial bubble size
Effect of Initial Bubble Size Treatment

  • Pressure and shear stress along the top wall at time = 2.5

    • Time: 10.5 × 10-6 s per dimensionless unit

    • Stress : 11338.8 N/m2 per dimensionless unit


Rigid tube conclusions
Rigid Tube Conclusions Treatment

  • Wall pressure peaks near the beginning of expansion, proportional to initial bubble pressure

  • Larger initial bubbles result in higher pressure and shear stress on the wall

  • The peak shear stress usually occurs when the bubble moves close to the wall, lagging behind peak pressure in time

  • Higher viscosity and surface tension reduce the peak shear stress, as does lower initial pressure


Bubble expansion in a flexible tube
Bubble Expansion in a Flexible Tube Treatment

  • Flexible wall with stiffness and tension components

  • T. Ye and J.L. Bull Microbubble expansion in a flexible tube. Journal of Biomechanical Engineering, 128(4): 554-563, 2006.


Mathematical model
Mathematical Model Treatment

  • Similar to rigid model with the addition of a flexible wall

  • Dimensionless wall equation (tension and elasticity)

  • Wall stiffness, s , and tension, t


Comparison of rigid and flexible tube wall bubble evolution for d i 0 5
Comparison of Rigid and Flexible Tube Wall Bubble Evolution for di = 0.5

Rigid Tube Wall

Flexible Tube Wall

  • Re = 427.59, We = 6.93, St = 10.47


Streamlines for d i 0 3
Streamlines for for di = 0.3

  • Streamline snapshots

t (dimensionless) = 0, 0.4, 0.8, 1.2, 1.6, 2, time scale = 10.5 μs


Flexible tube conclusions
Flexible Tube Conclusions for

  • The bubble expansion results in an increase of local tube volume, which generates liquid in flow at the open ends of the tube

  • In flow and flow due to expanding bubble result in complex flow patterns and stagnation points

  • Maximum wall pressure occurs near the bubble during the early stage of expansion

  • High shear stresses concentrate at the center of the tube close to the bubble and near the open ends of the tube

  • Larger initial bubble diameters result in higher shear stress


Emboli Transport for

  • A bubble may be initially carried along by the flow without contacting the vessel walls

  • The bubble then dries the walls of the vessel, but may still be swept along by the flow

  • If the driving pressure is insufficient to over come the surface tension forces on the bubble, the bubble will become lodged

  • Understanding the dynamics of bubble sticking is essential to knowing how to achieve a homogeneous distribution of bubbles and subsequently a uniform necrosis of the tumor


Bubble splitting in a single bifurcation

for

Bubble Splitting in a Single Bifurcation

Objective: determine effects of flow rate, bubble size, and gravity on splitting ratio of the bubble in a single bifurcation

Calderón A.J., Fowlkes J.B., and Bull J.L. Bubble splitting in bifurcating tubes: a model study of cardiovascular gas emboli transport. Journal of Applied Physiology, 99: 479-487, 2005.


Bubble splitting in a single bifurcation bench top experiments
Bubble Splitting in a Single Bifurcation—Bench Top Experiments

  • Constant flow rate, Q, is provided by syringe pump

  • Pressure at the outlets is held constant setting elevation of the two reservoirs Experiments matched Re = ρUDp/μ, Ca = U∙µ/, and Bo* = ρgDp2sin(θ)/σ to physiological values

  • Effects of roll angle, θ, bubble length, and flow rate examined in artery and arteriole models

  • Measured splitting ratio, Lb/Lt, of bubbles lengths in daughter branches after bubble completely split, and recorded dynamics of splitting


Bubble splitting in a single bifurcation theory
Bubble Splitting in a Single Bifurcation—Theory Experiments

  • Considered one dimensional flow

  • Poiseuille flow ahead of bubble

  • “Bretherton problem” approach to model the motion of long bubbles

  • Governing equations

    • Conservation of mass

    • Conservation of momentum

  • Interfacial stress and kinematic boundary conditions


Splitting ratio vs capillary number
Splitting Ratio vs. Capillary Number Experiments

Arteriole Model

Artery Model

θ

θ

Experiments θ = 0° □, θ = 15° Δ, θ = 30° ○, θ = 45° ◊, θ = 60° , θ = 90° . Theory θ = 0° ―――, θ = 15° ―― ――, θ = 30° ―― – ―― , θ = 45° …, θ = 60° ――― ―――, θ = 90° ―― – – ――.

Experiments θ = 0° □, θ = 5° Δ, θ = 10° , θ = 15° , θ = 20° ◊, θ = 30° . Theory θ = 0° ―――, θ = 5° ―― ――, θ = 10° ―― – ―― , θ = 15° …, θ = 20° ――― ―――, θ = 30° ―― – – ――.

  • Capillary number, Ca = U∙µ/, indicates flow rate

  • Splitting ratio = Lb/Lt, is 1 if splitting is even


Bubble reversal
Bubble Reversal Experiments

  • Experiment

  • Theory


Single bifurcation bubble splitting conclusions

Higher flow rates will improve homogeneity and there is a critical flow rate below which bubbles will not split

Bubble size relative to vessel size affects splitting behavior

Theory captures behavior of experiments

Resolved apparent paradox between Chang et al. and Souders et al. studies

Acoustic droplet vaporization in small vessels could potentially lead to even distribution of microbubbles

Inertial, viscous, and surface tension forces are important—gravity doesn’t tell the whole story!

Single Bifurcation Bubble Splitting Conclusions


Bubble Lodging: Experiments and Theory critical flow rate below which bubbles will not split

  • Investigated bubble lodging a microfluidics bifurcation (PDMS)

  • Impose driving pressure and determine critical pressure for lodging and dislodging

Calderón A.J., Heo Y.S., Huh D., Futai N., Takayama S., Fowlkes J.B., and Bull J.L. A microfluidic model of bubble lodging in microvessel bifurcations. Applied Physics Letters, 89(24): Art. No. 244103, 2006.


Theoretical analysis
Theoretical Analysis critical flow rate below which bubbles will not split

  • A long bubble will lodge in a bifurcation of decreasing diameter if the pressure difference can be supported by a stationary bubble.


Bubble lodging states
Bubble Lodging States critical flow rate below which bubbles will not split

  • Two states (A & B) identified

  • State A occurred at a lower pressure

  • Bubble reversal often lead to bubble passing through one branch when dislodged (C)


Bubble Lodging and Dislodging Pressures critical flow rate below which bubbles will not split

*

*

*

*

*

*

*

(b)

  • Average lodging and dislodging pressures for each perimeter ratio.


Dimensionless Bubble Lodging Pressure vs. Diameter Ratio critical flow rate below which bubbles will not split

  • Theoretical curves and experimental data

  • Smaller hydraulic diameter ratio (daughter channel diameter : parent channel diameter) results in higher lodging pressure


Bubble lodging conclusions
Bubble Lodging Conclusions critical flow rate below which bubbles will not split

  • Expect microbubbles in gas embolotherapy to lodge in the microcirculation in vessels with diameters of 20 μm and less

  • Once lodged, bubbles tend to remain lodged

  • Bubbles tend to lodge at bifurcations, but can lodge in straight channels

  • Lodged bubbles occluded transport of microspheres—suggesting they would occlude transport of red blood cells

  • Follow up doses of microbubbles go to the un-occluded regions of the vasculature, indicating a strategy for occluding the entire tumor


Blood Flow Occlusion In Vivo critical flow rate below which bubbles will not split

  • Externalized rabbit kidney with vaporization in renal artery

  • The maximum regional ADV-induced reduction in renal perfusion was >90% with an average of >70% occlusion throughout the kidney.

Before ADV

After ADV

Embolized Kidney

Control

Kripfgans OD, et al., IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control. 52(7): 1101-1110, 2005.


Acknowledgements
Acknowledgements critical flow rate below which bubbles will not split

  • Collaborators (Department of Radiology, UMHS)

    • J. Brian Fowlkes, Oliver Kripfgans, Jon Rubin, David Williams

  • Students and postdoctoral fellows (present and past)

    • Work shown here: Andres Calderon, Brijesh Eshpuniyani, Tao Ye

    • Others in group: Khalil Khanafer, David Li, Yu-chun Lin, Molly O’Loughlin, Stan Samuel, Marty Schlicht, Robinson Seda, Balaji Srinivasan, Brad Steele, James Stephen, Doug Valassis, Zheng Zheng Wong

  • Funding

    • NIH R01EB006476

    • NIH EB003541

    • NSF BES-0301278

    • Whitaker Foundation RG-03-0017


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