Perfusion Imaging¶

This guide covers Arterial Spin Labelling (ASL) quantification using the qmri.perfusion module.

Overview¶

Arterial Spin Labelling (ASL) is a non-invasive MRI technique for measuring cerebral blood flow (CBF). It uses magnetically labelled arterial blood water as an endogenous tracer.

The qmri.perfusion module provides:

ASL quantification (qmri.perfusion.asl): White Paper consensus equations
General Kinetic Model (qmri.perfusion.gkm): Full GKM signal generation

ASL Basics¶

ASL works by:

Labelling: Inverting the magnetisation of inflowing arterial blood
Waiting: Allowing labelled blood to flow into the imaging region
Imaging: Acquiring "label" and "control" images
Subtraction: Computing the perfusion-weighted difference signal

The difference signal (\(\Delta M = \text{control} - \text{label}\)) is proportional to CBF.

ASL Labelling Schemes¶

Pseudo-Continuous ASL (pCASL)¶

The recommended clinical standard. Uses a train of RF pulses to continuously label blood.

Key parameters:

Label duration (\(\tau\)): Typically 1.5-2.0 s
Post-label delay (PLD): Typically 1.5-2.0 s
Labelling efficiency (\(\alpha\)): Typically 0.85

Pulsed ASL (PASL)¶

Uses a single inversion pulse to create a labelled bolus.

Key parameters:

Bolus duration (\(TI_1\)): Typically 0.7-1.0 s
Inversion time (\(TI\)): Typically 1.5-2.0 s
Labelling efficiency (\(\alpha\)): Typically 0.98

ASL Quantification¶

pCASL/CASL Quantification¶

The White Paper consensus equation for pCASL:

\[ f = \frac{6000 \cdot \lambda \cdot \Delta M \cdot e^{PLD/T_{1,b}}}{2 \cdot \alpha \cdot T_{1,b} \cdot M_0 \cdot (1 - e^{-\tau/T_{1,b}})} \]

where \(f\) is perfusion in ml/100g/min.

import numpy as np
from qmri.perfusion import asl

# Image data
control = np.array([1000.0, 1050.0, 980.0])
label = np.array([950.0, 1000.0, 935.0])
m0 = np.array([2000.0, 2100.0, 1950.0])

# Quantify perfusion
result = asl.quantify_pcasl(
    control=control,
    label=label,
    m0=m0,
    label_duration=1.8,      # seconds
    post_label_delay=1.8,    # seconds
    label_efficiency=0.85,   # typical for pCASL
    t1_blood=1.65,          # seconds at 3T
    partition_coefficient=0.9  # ml/g
)

print(f"CBF: {result.perfusion} ml/100g/min")

PASL Quantification¶

The White Paper equation for PASL:

\[ f = \frac{6000 \cdot \lambda \cdot \Delta M \cdot e^{TI/T_{1,b}}}{2 \cdot \alpha \cdot TI_1 \cdot M_0} \]

from qmri.perfusion import asl

result = asl.quantify_pasl(
    control=control,
    label=label,
    m0=m0,
    bolus_duration=0.7,      # TI1 in seconds
    inversion_time=1.8,      # TI in seconds
    label_efficiency=0.98,   # typical for PASL
    t1_blood=1.65,
    partition_coefficient=0.9
)

print(f"CBF: {result.perfusion} ml/100g/min")

General Kinetic Model¶

The qmri.perfusion.gkm module implements the Buxton General Kinetic Model for simulating ASL signals.

GKM Theory¶

The GKM calculates the magnetisation difference as:

\[ \Delta M(t) = 2 M_{0,b} f \lbrace c(t) \ast [r(t) \cdot m(t)] \rbrace \]

where:

\(c(t)\) = delivery function (arterial input)
\(r(t) = e^{-ft/\lambda}\) = residue function
\(m(t) = e^{-t/T_1}\) = magnetisation relaxation

The model accounts for:

Arterial transit time (ATT)
Label duration
T1 relaxation of blood and tissue
Perfusion rate

Using the Full GKM¶

import numpy as np
from qmri.perfusion import gkm

result = gkm.signal_gkm(
    perfusion_rate=60.0,        # ml/100g/min
    transit_time=1.0,           # arterial transit time (s)
    m0_tissue=1000.0,
    label_duration=1.8,         # seconds
    signal_time=3.6,            # PLD + tau
    label_efficiency=0.85,
    partition_coefficient=0.9,
    t1_blood=1.65,
    t1_tissue=1.3,
    label_type="pcasl"          # or "pasl"
)

print(f"Delta M: {result.delta_m}")

Using the Simplified GKM¶

The simplified version assumes the bolus has fully arrived:

from qmri.perfusion import gkm

result = gkm.signal_gkm_simplified(
    perfusion_rate=60.0,
    transit_time=1.0,
    m0_tissue=1000.0,
    label_duration=1.8,
    signal_time=3.6,
    label_efficiency=0.85,
    partition_coefficient=0.9,
    t1_blood=1.65,
    label_type="pcasl"
)

GKM Arrival States¶

The GKM models three temporal phases:

Not arrived (\(t \leq \delta\)): No labelled blood has reached tissue
Arriving (\(\delta < t < \delta + \tau\)): Bolus is arriving
Arrived (\(t \geq \delta + \tau\)): Entire bolus has arrived

where \(\delta\) is the arterial transit time and \(\tau\) is the label duration.

Parameter Choices and Their Effects¶

Label Duration (τ)¶

Value	Effect
Short (1.0 s)	Lower signal, less T1 decay
Long (2.0 s)	Higher signal, more T1 decay, longer scan

Recommendation: 1.8 s is a good compromise for pCASL.

Post-Label Delay (PLD)¶

Value	Effect
Short (1.0 s)	Higher signal but ATT sensitivity
Long (2.5 s)	Lower signal but robust to ATT variation

Recommendations:

Young healthy adults: 1.8 s
Elderly or vascular disease: 2.0-2.5 s
Children: 1.5 s

T1 of Blood (T₁,ᵦ)¶

Field strength dependent:

Field	T1 blood (s)
1.5T	1.35
3T	1.65
7T	2.1

Blood-Brain Partition Coefficient (λ)¶

Grey matter: 0.98 ml/g
White matter: 0.82 ml/g
Whole brain average: 0.9 ml/g (commonly used)

Labelling Efficiency (α)¶

Method	Typical \(\alpha\)
pCASL	0.85
PASL	0.98
CASL	0.95

Volume Processing¶

Both ASL quantification functions handle multi-dimensional data:

import numpy as np
from qmri.perfusion import asl

# 3D ASL data
control_3d = np.random.rand(64, 64, 30) * 1000 + 1000
label_3d = control_3d - np.random.rand(64, 64, 30) * 50  # ~5% difference
m0_3d = np.random.rand(64, 64, 30) * 500 + 2000

result = asl.quantify_pcasl(
    control=control_3d,
    label=label_3d,
    m0=m0_3d,
    label_duration=1.8,
    post_label_delay=1.8
)

print(f"CBF map shape: {result.perfusion.shape}")  # (64, 64, 30)

Complete Example: ASL Processing Pipeline¶

import numpy as np
from qmri.perfusion import asl, gkm

# Simulate a voxel with known perfusion
true_cbf = 60.0  # ml/100g/min
true_att = 1.2   # seconds

# Generate GKM signal
pld = 1.8
tau = 1.8
signal_time = pld + tau

gkm_result = gkm.signal_gkm(
    perfusion_rate=true_cbf,
    transit_time=true_att,
    m0_tissue=1000.0,
    label_duration=tau,
    signal_time=signal_time,
    label_efficiency=0.85,
    partition_coefficient=0.9,
    t1_blood=1.65,
    t1_tissue=1.3,
    label_type="pcasl"
)

# Simulate control and label images
m0 = 1000.0
control_signal = m0  # No labelling effect
label_signal = m0 - gkm_result.delta_m

# Add noise
noise_std = 5.0
control_noisy = control_signal + np.random.normal(0, noise_std)
label_noisy = label_signal + np.random.normal(0, noise_std)
m0_noisy = m0 + np.random.normal(0, noise_std)

# Quantify CBF
asl_result = asl.quantify_pcasl(
    control=np.array([control_noisy]),
    label=np.array([label_noisy]),
    m0=np.array([m0_noisy]),
    label_duration=tau,
    post_label_delay=pld,
    label_efficiency=0.85,
    t1_blood=1.65,
    partition_coefficient=0.9
)

estimated_cbf = asl_result.perfusion[0]
error = 100 * (estimated_cbf - true_cbf) / true_cbf
print(f"True CBF: {true_cbf:.1f} ml/100g/min")
print(f"Estimated CBF: {estimated_cbf:.1f} ml/100g/min")
print(f"Error: {error:+.1f}%")

Best Practices¶

Acquisition¶

Use pCASL as the default labelling scheme.
Acquire an M0 calibration image with long TR (>5 s).
Choose PLD based on expected ATT:
Longer PLD for vascular disease or elderly patients
Consider multi-PLD for ATT estimation
Use background suppression to reduce physiological noise.

Quantification¶

Use appropriate T1 blood value for your field strength.
Consider partial volume effects in grey/white matter boundaries.
Apply motion correction before averaging control-label pairs.

Mask low M0 regions to avoid division by small numbers:

mask = m0 > threshold
result = asl.quantify_pcasl(
    control=control[mask],
    label=label[mask],
    m0=m0[mask],
    ...
)

Quality Control¶

Inspect control-label subtraction images for artefacts.
Check for negative CBF values (may indicate motion or noise).
Verify M0 image quality (affects all voxels).
Compare with expected CBF ranges:
Grey matter: 50-80 ml/100g/min
White matter: 20-30 ml/100g/min

Typical CBF Values¶

Tissue/Region	CBF (ml/100g/min)
Grey matter	50-80
White matter	20-30
Whole brain	45-55
Cortical grey matter	60-80
Deep grey matter	40-60

References¶

Alsop, D.C., et al. "Recommended implementation of arterial spin-labeled perfusion MRI for clinical applications." MRM 73(1):102-116, 2015.
Buxton, R.B., et al. "A general kinetic model for quantitative perfusion imaging with arterial spin labeling." MRM 40(3):383-396, 1998.
Grade, M., et al. "A neuroradiologist's guide to arterial spin labeling MRI in clinical practice." Neuroradiology 57(12):1181-1202, 2015.