May 11, 2012 Brain tissue temperature dynamics during functional activity Greggory Rothmeier Department of Physics and Astronomy Georgia State University Atlanta, GA 30303 Friday, May 11, 12 

Why should you care about brain temperature? ✤ Numerous conditions including severe head injury, stroke and brain ischemia show better clinical outcomes when treated with induced hypothermia. ✤ Current methods for measuring brain temperature are invasive. ✤ Current models of brain temperature can’t reproduce the variety of experimental results.1,2 2 1 J.G. McElligott and R. Melzack, Experimental Neurology 17, 293-312 (1967). 2 G Zeschke and V G Krasilnikov, Acta Biologica Et Medica Germanica 35, 935-41 (1976). Friday, May 11, 12 

fMRI and BOLD Hemoglobin responds to the fMRI's magnetic field differently depending on the oxidative state: ✤ Deoxygenated: paramagnetic ✤ Oxygenated: diamagnetic Deoxyhemoglobin alters the local magnetic susceptibility, thereby producing a slight change in the local MR signal. Images from http://harveymillican.files.wordpress.com/2011/05/mri.jpg and http://www.martinos.org/neurorecovery/images/fMRI_labeled.png 3 Friday, May 11, 12 

fMRI and BOLD With less deoxy-hemoglobin present, the local MR signal increases and gives rise to a blood oxygenation level dependent (BOLD) signal change. Figure modified from Richard B Buxton, Kâmil Uludağ, David J Dubowitz, and Thomas T Liu, NeuroImage 23, S220-33 (2004). 4 Friday, May 11, 12 

Calculating temperature from BOLD 5 Friday, May 11, 12 

Previous Temperature Models ✤ Single-voxel Approaches ✤ Treat the region of interest as an average voxel deep within the brain ✤ Surrounding voxels are a heat sink ✤ Predict a decrease in temperature after an increase in activity ✤ Multi-voxel Approaches ✤ Treat each voxel independently and respect the location of each voxel ✤ Capable of predicting an increase or a decrease in temperature after increased activity based on a voxel’s location 6 Friday, May 11, 12 

3-D Penne’s Bioheat Equation From Christopher M Collins, Michael B Smith, and Robert Turner, Journal of Applied Physiology (Bethesda, Md. : 1985) 97, 2051-5 (2004). 7 ⇢c dT dt = kr2T ⇢ blood wc blood (T T blood ) + Q m Friday, May 11, 12 

3-D Penne’s Bioheat Equation From Christopher M Collins, Michael B Smith, and Robert Turner, Journal of Applied Physiology (Bethesda, Md. : 1985) 97, 2051-5 (2004). 7 Tissue Density Specific heat Thermal conductivity Blood perfusion Heat released by metabolism ⇢c dT dt = kr2T ⇢ blood wc blood (T T blood ) + Q m Friday, May 11, 12 

3-D Penne’s Bioheat Equation From Christopher M Collins, Michael B Smith, and Robert Turner, Journal of Applied Physiology (Bethesda, Md. : 1985) 97, 2051-5 (2004). 7 } } } Conduction Convection Heat Production ⇢c dT dt = kr2T ⇢ blood wc blood (T T blood ) + Q m Friday, May 11, 12 

Our Approach Combines a model for heat transfer in the brain with a model of calculating the normalized changes in blood flow, f(t), and metabolism of oxygen, m(t). 8 From Greggory H Rothmeier, A. G. Unil Perera, and Mukeshwar Dhamala, Physical Review Letters, In Review (2012). ⇢c dT dt = kr2T ⇢ blood f(t)wc blood (T T blood ) + m(t)Q m Friday, May 11, 12 

Our Approach 9 From Greggory H Rothmeier, A. G. Unil Perera, and Mukeshwar Dhamala, Physical Review Letters, In Review (2012). Friday, May 11, 12 

Our Approach 9 From Greggory H Rothmeier, A. G. Unil Perera, and Mukeshwar Dhamala, Physical Review Letters, In Review (2012). Friday, May 11, 12 

Calculations Procedure 10 Friday, May 11, 12 

The Segmented Head ✤ Segmented using SPM8 ✤ Tissue-specific parameters used during calculations 11 From Greggory H Rothmeier, A. G. Unil Perera, and Mukeshwar Dhamala, Physical Review Letters, In Review (2012). Tissue f0 100 ml/ ( g min ) ⇢ kg/m3 c J kg 1 C 1 k W m 1 C 1 Qm W/m3 Skin 12 1,100 3,150 0.342 1,100 Bone 3 1,080 2,110 0.65 26.1 Soft Tissue 3.8 1,041 3,720 0.4975 687 Cerebrospinal Fluid (CSF) 0 1,007 3,800 0.50 0 Gray Matter 67.1 1,035.5 3,680 0.565 15,575 White Matter 23.7 1,027.4 3,600 0.503 5,192 Friday, May 11, 12 

Calculating metabolism and blood flow changes from BOLD From Roberto C Sotero and Yasser Iturria-Medina, Bulletin of Mathematical Biology 73, 2731-47 (2011). ✤ Resting state calculated (S0 ) ✤ fMRI data normalized to rest state (S(t)/S0) 12 Parameter Description Value ↵ steady state flow-volume relation 0.4 field-strength dependent parameter 1.5 A maximum BOLD signal change 0.22 a parameter from fitting E(f) vs f 0.4992 b parameter from fitting E(f) vs f 0.2216 c parameter from fitting E(f) vs f -0.9872 Friday, May 11, 12 

Calculating metabolism and blood flow changes from BOLD From Roberto C Sotero and Yasser Iturria-Medina, Bulletin of Mathematical Biology 73, 2731-47 (2011). ✤ Resting state calculated (S0 ) ✤ fMRI data normalized to rest state (S(t)/S0) 12 Parameter Description Value ↵ steady state flow-volume relation 0.4 field-strength dependent parameter 1.5 A maximum BOLD signal change 0.22 a parameter from fitting E(f) vs f 0.4992 b parameter from fitting E(f) vs f 0.2216 c parameter from fitting E(f) vs f -0.9872 Friday, May 11, 12 

Calculating Temperature Change 13 Friday, May 11, 12 

Calculating Temperature Change 13 Finite Difference Method Friday, May 11, 12 

Calculating Temperature Change 13 Finite Difference Method Friday, May 11, 12 

Calculating Temperature Change 13 Finite Difference Method Friday, May 11, 12 

Calculating Temperature Change 13 Finite Difference Method Friday, May 11, 12 

How does heat move between voxels? @ 2 T ( t ; x, y, z ) @y 2 ⇡ T ( t ; x, y + h, z ) 2 T ( t ; x, y, z ) + T ( t ; x, y h, z ) h 2 @ 2 T ( t ; x, y, z ) @z 2 ⇡ T ( t ; x, y, z + h ) 2 T ( t ; x, y, z ) + T ( t ; x, y, z h ) h 2 14 Friday, May 11, 12 

How does heat move between voxels? @ 2 T ( t ; x, y, z ) @y 2 ⇡ T ( t ; x, y + h, z ) 2 T ( t ; x, y, z ) + T ( t ; x, y h, z ) h 2 @ 2 T ( t ; x, y, z ) @z 2 ⇡ T ( t ; x, y, z + h ) 2 T ( t ; x, y, z ) + T ( t ; x, y, z h ) h 2 14 Friday, May 11, 12 

How is heat exchanged with the surrounding? ✤ Air is considered a heat sink and is kept at a constant temperature (24 °C) ✤ Voxels in contact with air conduct heat out, thereby lowering their temperatures ✤ This is turns causes voxels in contact with them to loose heat ✤ While important, this process is very slow 15 Friday, May 11, 12 

b Equilibrium Temperature ✤ Air is maintained at 24°C and all tissue voxels are started at 37°C ✤ Calculated by repeatedly applying the 3-D bioheat equation until the temperature stabilizes for every voxel 16 Distance through head From Greggory H Rothmeier, A. G. Unil Perera, and Mukeshwar Dhamala, Physical Review Letters, In Review (2012). y = -12 Friday, May 11, 12 

b Equilibrium Temperature ✤ Air is maintained at 24°C and all tissue voxels are started at 37°C ✤ Calculated by repeatedly applying the 3-D bioheat equation until the temperature stabilizes for every voxel 16 Distance through head From Greggory H Rothmeier, A. G. Unil Perera, and Mukeshwar Dhamala, Physical Review Letters, In Review (2012). y = -12 Friday, May 11, 12 

c d Synthetic BOLD Same BOLD signal, yet very different temperature changes 17 From Greggory H Rothmeier, A. G. Unil Perera, and Mukeshwar Dhamala, Physical Review Letters, In Review (2012). y = -12 Friday, May 11, 12 

Experimental BOLD Data Resting (20 s) Tapping (320 s) Resting (20 s) 18 Start Stop From Greggory H Rothmeier, A. G. Unil Perera, and Mukeshwar Dhamala, Physical Review Letters, In Review (2012) and Mukeshwar Dhamala, et al., NeuroImage 20, 918-26 (2003). ~ 25 mK x = -44 Friday, May 11, 12 

Conclusion The temperature change is spatially dependent, so the contribution from each voxel in the head must be considered in order to get an accurate calculation. 19 Friday, May 11, 12 

https://github.com/greggroth/temptools https://github.com/greggroth/thesis 20 Friday, May 11, 12