ANSYS FLUENT for Brain Research: Cranio-spinal system

Medical Image Mathematical Model

Cranium

Spinal canal

ANSYS FLUENT for Brain Research:Hydrocephalus

Normal Hydrocephalic

ANSYS FLUENT for Brain Research

ApplicationApplication

Intracranial DynamicsIntracranial Dynamics

ANSYS FLUENT Application: Intracranial dynamics

MR imaging

Geometry reconstruction

Grid generation

Computational results

PRESSURE

Medical Imaging

Computer Science 1st Principles: Math/Physics

ANSYS FLUENT Application: Intracranial dynamics

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0 20 40 60 80 100

% Cardiac Cycle

Flo

w R

ate

[ml/s

] PredictedMeasured

Third ventricle

4th ventricle

3rd ventricle

Pontine cistern

Aqueduct

ANSYS FLUENT Application: Intracranial dynamics

Vel

ocity

[m

/s]

Pre

ssur

e [P

a]

Normal

Linninger, A.A., M. Xenos, D.C. Zhu, M.R. Somayaji, S. Kondapalli, and R.D. Penn. Cerebrospinal fluid flow in the normal and hydrocephalic human brain. IEEE Trans. Biomed. Eng. 54:291-302, 2007.

ANSYS FLUENT Application: Intracranial dynamics

0 20 40 60 80 100-30

-20

-10

0

10

20

30

% Cardiac Cycle

Ve

loc

ity

Ma

gn

itu

de

[m

m/s

]

AqueductPontine Cistern

3rd Ventricle

4th Ventricle

4th ventricle

3rd ventricle

Pontine cistern

Aqueduct

(mm/s)

Mid systole(15% cc)

(mm/s)(mm/s)

Mid systole(15% cc)

(mm/s)

ANSYS FLUENT Application: Intracranial dynamics

Pressure [Pa]

CCJ

SAS

LV

V4

Mid systole(15% cc)

LV: lateral ventricle SAS: subarachnoid space

V4: fourth ventricle CCJ: cranio-cervical junction

Definition of Symbols/Abbreviations

0 20 40 60 80 100

500

550

600

650

700

% Cardiac Cycle

Pre

ssu

re [

Pa]

LV SAS V4 CCJ

38.5 39 39.5 40 40.5 41 41.5529

530

531

532

533

534

535

% Cardiac Cycle

Pre

ss

ure

[P

a]

LV SAS V4 CCJ

A

LV SAS V4 CCJLV SAS V4 CCJ

ANSYS FLUENT Application: Intracranial dynamics—Conclusions

II

I

III

IV

V

Description of Boundary Conditions

Cranio-Cervical Junction (fluid

exchange between cranium and spinal canal)

V

Subarachnoid SpaceIV

ParenchymaIII

Constant CSF Inflow (0.5 ml/min)II

Lateral Ventricle Wall (deformable boundary, red)

I

Cranio-Cervical Junction (fluid

exchange between cranium and spinal canal)

V

Subarachnoid SpaceIV

ParenchymaIII

Constant CSF Inflow (0.5 ml/min)II

Lateral Ventricle Wall (deformable boundary, red)

I

0 20 40 60 80 100 120 140 160 180 200100

150

200

250Basilar Arterial Blood Flow

ml/m

in

% Cardiac Cycle

a

b

c

Pressure gradients in the brain remain small (<1mmHg)

Blood flow and vasculature expansion

driving force for pulsatile CSF motion

TPG <

4 P

a

ANSYS FLUENT for Brain Research

ApplicationApplication

Drug DeliveryDrug Delivery

ANSYS FLUENT Application: Drug delivery to the human brain

Motivation: Validate invasive techniques for clinical practice

Geometrical Challenge:Reconstruction of brain anatomy from images

Physiological Challenge:Quantify brain anisotropy and heterogeneity from DTI

Drug Transport Challenge:Predict spatio-temporal drug distribution in 3d

Treatment Challenge:Propose optimal catheter positioning and CED parameters

Apparent water diffusion tensor in human brain from diffusion tensor imaging (DTI)

Axial view

( ) ( ) ( )

, ,

Cx v x C x C

tR C x S C x

+++++++++++++++++++++++++++++++++++++++ +++

eD

Drug transport—porous brain parenchyma

12 2

28.61 0.580 1.040

( ) 10 0.580 23.44 1.230 [m /s]

1.040 1.230 21.04e x

D

Effective Diffusion Tensor of Growth Factor (GDNF) near the Putamen

A

V

q div dV

eD

Diffusion flux in anisotropic tissue:

tumortumor

White White mattermatter

cortexcortex

1

2

2V

1V

1

2tumortumor

White White mattermatter

cortexcortex

tumortumor

White White mattermatter

cortexcortex

1

2

2V

1V

1

2tumortumor

White White mattermatter

cortexcortex

1

2

2V

1V

1

2tumortumor

White White mattermatter

cortexcortex

tumortumor

White White mattermatter

cortexcortex

1

2

2V

1V

1

2

ANSYS FLUENT Application: Drug delivery to the human brain

ANSYS FLUENT Application: Drug delivery to the human brain

Axial slices

C

A

C

A

S

C

A

SC

A

SC

A

C

A

SC

A

S

C

A

SC

A

SC

A

C

A

S

C

A

SC

A

SC

A

C

A

SC

A

S

C

A

SC

A

S

high

low

Molecular weight = 27,000 kg/kmol; Flow rate = 4µl/min ; X0 = 3.7·10-3 mol/l, no reaction

ANSYS FLUENT for Brain Research

Drug DeliveryDrug Delivery

Additional ApplicationsAdditional Applications

ANSYS FLUENT Application: Drug distribution & catheter placement

Week #1 Week #4

Thalamus injection Injection into gray matter

A. Linninger, M.R. Somayaji, L. Zhang, M.S. Hariharan and R. Penn. Rigorous Mathematical Modeling Techniques for Optimal Delivery of Macromolecules to the Brain. IEEE Transaction on Biomedical Engineering, 55 (9): 2303-2313, 2008.

GDNF (neurotrophic factor) concentration field over time

mol/lWeek #2

Week #1 Week #4Week #2mol/l

Internal capsule injection Injection into white matter

ANSYS FLUENT Application: Drug distribution & catheter design

Concentration field over timelow high

0.1·10-6 m/s0.1·10-6 m/s0.1·10-6 m/s

0.1·10-6 m/s0.1·10-6 m/s0.1·10-6 m/s

Flow direction at week 3

Week #1 Week #3Week #2

ANSYS FLUENT Application: References

1. Linninger, A.A., M.R. Somayaji, T. Erickson, X. Guo, and R.D. Penn. Computational methods for predicting drug transport in anisotropic and heterogeneous brain tissue. Journal of Biomechanics. 41:2176-2187, 2008.

2. Linninger, A.A., M.R. Somayaji, M. Mekarski, and L. Zhang. Prediction of convection-enhanced drug delivery to the human brain. J Theor Biol. 250:125-138, 2008.

3. Linninger, A.A., M.R. Somayaji, L. Zhang, M.S. Hariharan, and R.D. Penn. Rigorous Mathematical Modeling Techniques for Optimal Delivery of Macromolecules to the Brain. Biomedical Engineering, IEEE Transactions on. 55:2303-2313, 2008.

4. Linninger, A.A., B. Sweetman, and R. Penn. Normal and hydrocephalic brain dynamics: the role of reduced cerebrospinal fluid reabsorption in ventricular enlargement. Ann. Biomed. Eng. 37:1434-47, 2009.

5. Linninger, A.A., M. Xenos, B. Sweetman, S. Ponkshe, X. Guo, and R. Penn. A mathematical model of blood, cerebrospinal fluid and brain dynamics. J. Math. Biol. 59:729-59, 2009.

6. Linninger, A.A., M. Xenos, D.C. Zhu, M.R. Somayaji, S. Kondapalli, and R.D. Penn. Cerebrospinal fluid flow in the normal and hydrocephalic human brain. IEEE Trans. Biomed. Eng. 54:291-302, 2007.

7. Morrison, P.F., R.R. Lonser and E.H. Oldfield, “Convective delivery of glial cell line-derived neurotrophic factor in the human putamen”, J Neurosurg, vol.107, pp. 74-83, Jul, 2007.

8. Salvatore, M.F., Y. Ai, B. Fischer, A.M. Zhang, R.C. Grondin, Z. Zhang, G.A. Gerhardt, D.M. Gash, “Point source concentration of GDNF may explain failure of phase II clinical trial”, Experimental Neurology, vol. 202, pp. 497-505, 2006.