aslprep.utils.cbf module

Functions for calculating CBF.

calculate_deltam_pasl(X, cbf, att, abat, abv)

Specify a model for use with scipy curve fitting.

The model is fit separately for each voxel.

This model is used to estimate cbf, att, abat, and abv for multi-PLD PCASL data.

Parameters:

• cbf (float) – Cerebral blood flow. Used for deltam_tiss calculation. Estimated by the model.

• att (float) – Arterial transit time. Used for deltam_tiss calculation. Estimated by the model.

• abat (float) – The arterial bolus arrival time, describing the first arrival of the labeled blood water in the voxel within the arterial vessel. Used for deltam_art calculation. Estimated by the model.

• abv (float) – Arterial blood volume. The fraction of the voxel occupied by the arterial vessel. Used for deltam_art calculation. Estimated by the model.

• X (numpy.ndarray of shape (n_plds/tis, 6)) – Dependent variables: labeleff, t1blood, m0_a, m0_b, tis, ti1s.

Returns:

deltam – Delta-M values for the voxel.

Return type:

numpy.ndarray of shape (n_tis,)

Notes

X breaks down into six variables:

labelefffloat

Labeling efficiency. In the case of background suppression, this combines alpha and alpha_bs, so we don’t need a separate term for alpha_bs. Used for both deltam_tiss and deltam_art calculation.

t1bloodfloat

Longitudinal relaxation time of arterial blood in seconds. Used for both deltam_tiss and deltam_art calculation.

m0_afloat

Equilibrium magnetization of tissue, calculated as M0a = SIpd / lambda, where SIpd is a proton density weighted image and lambda is the tissue/blood partition coefficient. SIpd is also already scaled by any user-provided scaling factor. Used for deltam_tiss calculation.

m0_bfloat

Equilibrium magnetization of arterial blood. Used for deltam_art calculation.

tisnumpy.ndarray

Inversion times in seconds.

ti1float

Bolus cutoff delay time. For Q2TIPS, this is the first delay time. For QUIPSSII, it’s the only one.

calculate_deltam_pcasl(X, cbf, att, abat, abv)

Specify a model for use with scipy curve fitting.

The model is fit separately for each voxel.

This model is used to estimate cbf, att, abat, and abv for multi-PLD PCASL data.

Parameters:

• cbf (float) – Cerebral blood flow. Used for deltam_tiss calculation. Estimated by the model.

• att (float) – Arterial transit time. Used for deltam_tiss calculation. Estimated by the model.

• abat (float) – The arterial bolus arrival time, describing the first arrival of the labeled blood water in the voxel within the arterial vessel. Used for deltam_art calculation. Estimated by the model.

• abv (float) – Arterial blood volume. The fraction of the voxel occupied by the arterial vessel. Used for deltam_art calculation. Estimated by the model.

• X (numpy.ndarray of shape (n_plds, 6)) – Dependent variables: labeleff, t1blood, m0_a, m0_b, plds, taus.

Returns:

deltam – Delta-M values for the voxel.

Return type:

numpy.ndarray of shape (n_plds,)

Notes

X breaks down into six variables:

labelefffloat

Labeling efficiency. If background suppression was performed, then this is already adjusted and combines alpha_bs as well. Used for both deltam_tiss and deltam_art calculation.

t1bloodfloat

Longitudinal relaxation time of arterial blood in seconds. Used for both deltam_tiss and deltam_art calculation.

m0_afloat

Equilibrium magnetization of tissue, calculated as M0a = SIpd / lambda, where SIpd is a proton density weighted image and lambda is the tissue/blood partition coefficient. Used for deltam_tiss calculation.

m0_bfloat

Equilibrium magnetization of arterial blood. Used for deltam_art calculation.

pldsnumpy.ndarray

Post-labeling delays. Used for both deltam_tiss and deltam_art calculation.

tausnumpy.ndarray

Labeling durations. Also known as LD. Used for both deltam_tiss and deltam_art calculation.

estimate_att_pcasl(deltam_arr, plds, lds, t1blood, t1tissue)

Estimate arterial transit time using the weighted average method.

The weighted average method comes from Dai et al.[1].

Parameters:

• deltam_arr (numpy.ndarray of shape (S, D)) – Delta-M array, averaged by PLD.

• plds (numpy.ndarray of shape (S, D)) – Post-labeling delays. w in Dai 2012. In case of a 2D acquisition, PLDs may vary by slice, and thus the plds array will vary in the spatial dimension. For 3D acquisitions, or 2D acquisitions without slice timing info, plds will only vary along the second dimension.

• lds (numpy.ndarray) – Labeling durations. tau in Dai 2012.

• t1blood (float) – T1 relaxation rate for blood.

• t1tissue (float) – T1 relaxation rate for tissue.

Returns:

att_arr – Arterial transit time array.

Return type:

numpy.ndarray

Notes

This function was originally written in MATLAB by Jianxun Qu and William Tackett. It was translated to Python by Taylor Salo. Taylor Salo modified the code to loop over voxels, in order to account for slice timing-shifted post-labeling delays.

Please see https://shorturl.at/wCO56 and https://shorturl.at/aKQU3 for the original MATLAB code.

The code could probably be improved by operating on arrays, rather than looping over voxels. It is also overkill for 3D acquisitions, where PLD doesn’t vary by voxel.

License

MIT License

Copyright (c) 2023 willtack

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the “Software”), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED “AS IS”, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

References

[1] (1,2)

Weiying Dai, Philip M Robson, Ajit Shankaranarayanan, and David C Alsop. Reduced resolution transit delay prescan for quantitative continuous arterial spin labeling perfusion imaging. Magnetic resonance in medicine, 67(5):1252–1265, 2012.

estimate_cbf_pcasl_multipld(deltam_arr, scaled_m0data, plds, tau, labeleff, t1blood, t1tissue, unit_conversion, partition_coefficient)

Estimate CBF and ATT for multi-delay PCASL data.

Parameters:

• deltam_arr (numpy.ndarray of shape (S, P)) – Control-label values for each voxel and PLDs. S = sample (i.e., voxel). P = Post-labeling delay (i.e., volume).

• scaled_m0data (numpy.ndarray of shape (S,)) – The M0 volume, after scaling based on the M0-scale value.

• plds (numpy.ndarray of shape (S, P)) – Post-labeling delays. One value for each volume in deltam_arr.

• tau (numpy.ndarray of shape (P,) or (0,)) – Label duration. May be a single value or may vary across volumes/PLDs.

• labeleff (float) – Estimated labeling efficiency.

• t1blood (float) – The longitudinal relaxation time of blood in seconds.

• t1tissue (float) – The longitudinal relaxation time of tissue in seconds.

• unit_conversion (float) – The factor to convert CBF units from mL/g/s to mL/ (100 g)/min. 6000.

• partition_coefficient (float) – The brain/blood partition coefficient in mL/g. Called lambda in the literature.

Returns:

• att_arr (numpy.ndarray of shape (S,)) – Arterial transit time map.

• cbf (numpy.ndarray of shape (S,)) – Estimated cerebrospinal fluid map, after estimating for each PLD and averaging across PLDs.

Notes

Delta-M values are first averaged over time for each unique post-labeling delay value.

Arterial transit time is estimated on a voxel-wise basis according to Dai et al.[1].

CBF is then calculated for each unique PLD value using the mean delta-M values and the estimated ATT.

CBF is then averaged over PLDs according to Juttukonda et al.[2], in which an unweighted average is calculated for each voxel across all PLDs in which PLD + tau > ATT.

References

[2]

Meher R Juttukonda, Binyin Li, Randa Almaktoum, Kimberly A Stephens, Kathryn M Yochim, Essa Yacoub, Randy L Buckner, and David H Salat. Characterizing cerebral hemodynamics across the adult lifespan with arterial spin labeling mri data from the human connectome project-aging. Neuroimage, 230:117807, 2021. URL: https://doi.org/10.1016/j.neuroimage.2021.117807, doi:10.1016/j.neuroimage.2021.117807.

estimate_t1(metadata)

Estimate the relaxation rates of blood and gray matter based on magnetic field strength.

t1blood is set based on the scanner’s field strength, according to Zhang et al.[3], Alsop et al.[4]. If recommended values from these publications cannot be used (i.e., if the field strength isn’t 1.5T, 3T, 7T), then the formula from Zhang et al.[3] will be applied.

t1tissue is set based on the scanner’s field strength as well, according to Wright et al.[5]. At the moment, field strengths other than 1.5T, 3T, and 7T are not supported and will raise an exception.

Parameters:

metadata (dict) – Dictionary of metadata from the ASL file.

Returns:

• t1blood (float) – Estimated relaxation rate of blood based on magnetic field strength.

• t1tissue (float) – Estimated relaxation rate of gray matter based on magnetic field strength.

References

[3] (1,2)

Xiaofei Zhang, Esben T Petersen, Eidrees Ghariq, JB De Vis, AG Webb, Wouter M Teeuwisse, Jeroen Hendrikse, and MJP Van Osch. In vivo blood t1 measurements at 1.5 t, 3 t, and 7 t. Magnetic resonance in medicine, 70(4):1082–1086, 2013.

[4]

David C. Alsop, John A. Detre, Xavier Golay, Matthias Günther, Jeroen Hendrikse, Luis Hernandez-Garcia, Hanzhang Lu, Bradley J. MacIntosh, Laura M. Parkes, Marion Smits, Matthias J. P. van Osch, Danny JJ Wang, Eric C. Wong, and Greg Zaharchuk. Recommended Implementation of Arterial Spin Labeled Perfusion MRI for Clinical Applications: A consensus of the ISMRM Perfusion Study Group and the European Consortium for ASL in Dementia. Magnetic resonance in medicine, 73(1):102–116, January 2015. URL: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4190138/ (visited on 2020-04-13), doi:10.1002/mrm.25197.

[5]

PJ Wright, OE Mougin, JJ Totman, AM Peters, MJ Brookes, R Coxon, PE Morris, M Clemence, ST Francis, RW Bowtell, and others. Water proton t 1 measurements in brain tissue at 7, 3, and 1.5 t using ir-epi, ir-tse, and mprage: results and optimization. Magnetic Resonance Materials in Physics, Biology and Medicine, 21:121–130, 2008. URL: https://doi.org/10.1007/s10334-008-0104-8, doi:10.1007/s10334-008-0104-8.

fit_deltam_multipld(deltam_arr, scaled_m0data, plds, labeleff, t1blood, partition_coefficient, is_casl, tau=None, ti1=None)

Estimate CBF, ATT, aBAT, and aBV from multi-PLD PCASL data.

This function uses the general kinetic model specified by Woods et al.[6].

Parameters:

• deltam_arr (numpy.ndarray of shape (n_voxels, n_volumes)) – Subtracted (control - label) signal.

• scaled_m0data (numpy.ndarray of shape (n_voxels,)) – M0 data, after any scaling requested by the user.

• plds (numpy.ndarray of shape (n_voxels, n_volumes)) – Post-labeling delay values. This uses the TI values for PASL data.

• labeleff (float) – Labeling efficiency, also referred to as alpha. In the case of background suppression, this combines alpha and alpha_bs, so we don’t need a separate term for alpha_bs.

• t1blood (float) – Longitudinal relaxation time of arterial blood in seconds. Used for both deltam_tiss and deltam_art calculation.

• partition_coefficient (float) – Brain partition coefficient (lambda in Alsop 2015). Generally 0.9.

• is_casl (bool) – True if is (P)CASL sequence.

• tau (float or numpy.ndarray or None, optional) – Label duration. May be a single value or may vary across volumes/PLDs. Only defined for (P)CASL data.

• ti1 (float or None, optional) – TI1. Only defined for PASL data.

Returns:

• cbf (numpy.ndarray of shape (n_voxels,)) – Cerebral blood flow.

• att (numpy.ndarray of shape (n_voxels,)) – Arterial transit time.

• abat (numpy.ndarray of shape (n_voxels,)) – Arterial bolus arrival time.

• abv (numpy.ndarray of shape (n_voxels,)) – Arterial blood volume.

• failures (numpy.ndarray of shape (n_voxels,)) – Boolean array indicating whether the model fit failed for each voxel. False indicates success, True indicates failure.

Notes

This model does not include a separate term for T1,tissue, but we could expand it to do so in the future.

References

[6]

Joseph G Woods, Eric Achten, Iris Asllani, Divya S Bolar, Weiying Dai, John A Detre, Audrey P Fan, Maria Fernández-Seara, Xavier Golay, Matthias Günther, Jia Guo, Luis Hernandez-Garcia, Mai-Lan Ho, Meher R. Juttukonda, Hanzhang Lu, Bradley J. MacIntosh, Ananth J. Madhuranthakam, Henk J.M.M. Mutsaerts, Thomas W. Okell, Laura M. Parkes, Nandor Pinter, Joana Pinto, Qin Qin, Marion Smits, Yuriko Suzuki, David L. Thomas, Matthias J.P. van Osch, Danny J.J. Wang, Esther A.H. Warnert, Greg Zaharchuk, Fernando Zelaya, Moss Zhao, and Michael A. Chappell. Recommendations for quantitative cerebral perfusion mri using multi-timepoint arterial spin labeling: acquisition, quantification, and clinical applications. OSF Preprints, 2023. URL: https://doi.org/10.31219/osf.io/4tskr, doi:10.31219/osf.io/4tskr.