Analysis Toolbox#
Analysis Toolbox Demo¶
This notebook demonstrates post-fit analysis helpers: ROI statistics, ROI timecourses, and group-level comparisons. The example synthesizes a small batch study, so it runs without bundled datasets.
[1]:
from pathlib import Path
import json
import shutil
import numpy as np
import matplotlib.pyplot as plt
from mrax.analysis import ROI, collect_roi_stats, extract_timecourse, analyze_groups
from mrax.core.batch import run_batch_studies
from mrax.core.synthetic import make_example_suite
from mrax.data_struct import Quantity, Study, load_study_results
Run a small batch study¶
Create four synthetic subjects, fit a T1 inversion-recovery model for each subject, and persist the generated results under tmp/analysis_toolbox_demo.
[2]:
demo_root = Path.cwd() / "tmp" / "analysis_toolbox_demo"
inputs_root = demo_root / "inputs"
outputs_root = demo_root / "outputs"
for path in (inputs_root, outputs_root):
if path.exists():
shutil.rmtree(path)
path.mkdir(parents=True, exist_ok=True)
subjects = [
("control_01", 0, "control"),
("control_02", 1, "control"),
("treated_01", 2, "treated"),
("treated_02", 3, "treated"),
]
for name, seed, group in subjects:
study_dir = inputs_root / name
study_dir.mkdir(parents=True, exist_ok=True)
(study_dir / "config.json").write_text(json.dumps({"seed": seed, "group": group}))
def loader(study_dir: Path):
cfg = json.loads((study_dir / "config.json").read_text())
examples = make_example_suite(noise_level=0.03, seed=cfg["seed"])[:1]
study_globals = {"field_strength_mhz": Quantity(400.0, "MHz")}
return Study.from_examples(examples, study_globals=study_globals), {"config": cfg}
summaries = run_batch_studies(
studies_root=inputs_root,
study_loader=loader,
output_root=outputs_root,
analysis_kwargs={"num_steps": 3, "step_size": 0.02},
)
summaries
[2]:
[{'study_name': 'control_01',
'manifest_path': PosixPath('/tmp/mrax-notebook-smoke/tmp/analysis_toolbox_demo/outputs/control_01/study_manifest.json'),
'results': [{'name': 't1_ir',
'model': 't1_ir',
'fields': {'amplitude': Quantity(values=Array([[0.68209094, 0.68224174, 0.6835417 , 0.6861043 , 0.68232936,
0.6828738 , 0.6820199 , 0.6835348 , 0.6820076 , 0.6838535 ,
0.6821099 , 0.68606627, 0.6823191 , 0.68227303, 0.6821362 ,
0.68248117],
[0.7430966 , 0.7430551 , 0.7426947 , 0.715351 , 0.68526715,
0.68195516, 0.68180376, 0.68175155, 0.6817051 , 0.6817301 ,
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0.6853528 ],
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0.7425461 ],
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0.7408031 ],
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0.7064828 ],
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[0.74309283, 0.7430971 , 0.74307835, 0.7430046 , 0.74300927,
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0.6816524 ],
[0.74268305, 0.74285424, 0.7428627 , 0.7430068 , 0.74308497,
0.7430924 , 0.7430648 , 0.7429047 , 0.68234295, 0.6820088 ,
0.68174464, 0.68170226, 0.6816719 , 0.68165505, 0.6816522 ,
0.6816001 ],
[0.6820593 , 0.6857469 , 0.7412452 , 0.74295425, 0.7430819 ,
0.74309504, 0.7431188 , 0.74310315, 0.7430316 , 0.7120217 ,
0.6819575 , 0.6816913 , 0.68166226, 0.6816227 , 0.68162066,
0.6816158 ],
[0.6816944 , 0.6817793 , 0.68198496, 0.7413331 , 0.7430636 ,
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0.68243366, 0.6817075 , 0.6816401 , 0.68162125, 0.6816098 ,
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0.7396205 , 0.68181455, 0.6816685 , 0.68162394, 0.68161243,
0.68160504],
[0.68166906, 0.6816749 , 0.6817141 , 0.6863515 , 0.74027157,
0.7430819 , 0.7431213 , 0.74312514, 0.74311996, 0.7430243 ,
0.68383425, 0.6817812 , 0.6817007 , 0.6816423 , 0.6816262 ,
0.6816244 ],
[0.68184483, 0.681838 , 0.68178993, 0.68456984, 0.68959475,
0.7418566 , 0.7428324 , 0.7430257 , 0.74152803, 0.74035823,
0.68271613, 0.6820309 , 0.6817781 , 0.68173194, 0.68167466,
0.6816559 ],
[0.6827251 , 0.68281454, 0.6824246 , 0.68618023, 0.6822656 ,
0.68244934, 0.68219686, 0.6829403 , 0.6820001 , 0.68501204,
0.6825542 , 0.68416804, 0.68326324, 0.6830336 , 0.6824102 ,
0.6824026 ]], dtype=float32), si_unit='1'),
't1': Quantity(values=Array([[2451.0042, 2450.9924, 2451.019 , 2451.067 , 2450.9758, 2451.0269,
2450.9536, 2451.019 , 2450.967 , 2451. , 2450.9907, 2451.0186,
2450.9875, 2451.0293, 2450.9902, 2450.9543],
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2451.0337, 2450.982 , 2450.974 , 2450.9292, 2451.005 , 2451.0403,
2452.1953, 2490.0293, 2599.2485, 2599.2266],
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2450.6584, 2450.68 , 2450.6816, 2450.948 , 2451.0796, 2451.1028,
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2450.9883, 2450.9631, 2450.968 , 2450.9502],
[2450.9895, 2451.0176, 2451.144 , 2451.2048, 2450.664 , 2450.7876,
2450.661 , 2450.6614, 2450.6804, 2450.676 , 2451.0825, 2451.032 ,
2450.9453, 2450.9583, 2450.9197, 2450.892 ],
[2450.9844, 2450.965 , 2451.1003, 2451.157 , 2450.665 , 2450.6738,
2450.6838, 2450.66 , 2450.666 , 2450.6812, 2450.6907, 2450.9827,
2450.9578, 2450.904 , 2450.893 , 2450.8838],
[2450.943 , 2450.9353, 2450.993 , 2451.0217, 2450.6921, 2450.6777,
2450.6792, 2450.6748, 2450.674 , 2450.686 , 2451.046 , 2450.964 ,
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[2450.9949, 2450.9749, 2450.9807, 2451.0176, 2451.0493, 2450.6926,
2450.6877, 2450.6858, 2450.69 , 2450.6912, 2450.9695, 2450.9937,
2450.9436, 2450.9377, 2450.9043, 2450.9092],
[2450.9827, 2450.983 , 2451.0076, 2451.0732, 2450.9792, 2451.0076,
2450.9675, 2450.99 , 2450.9287, 2450.9658, 2451.0012, 2451.0393,
2451.0032, 2450.983 , 2450.9822, 2450.962 ]], dtype=float32), si_unit='ms')},
'loss_history': [0.15132774412631989,
0.14381380379199982,
0.1369260996580124],
'cached': False}],
'metadata': {'config': {'seed': 0, 'group': 'control'}},
'study_dir': PosixPath('/tmp/mrax-notebook-smoke/tmp/analysis_toolbox_demo/inputs/control_01')},
{'study_name': 'control_02',
'manifest_path': PosixPath('/tmp/mrax-notebook-smoke/tmp/analysis_toolbox_demo/outputs/control_02/study_manifest.json'),
'results': [{'name': 't1_ir',
'model': 't1_ir',
'fields': {'amplitude': Quantity(values=Array([[0.6822252 , 0.6823839 , 0.6839408 , 0.68228877, 0.6820798 ,
0.6831264 , 0.6822702 , 0.6823908 , 0.6822631 , 0.6846213 ,
0.6821853 , 0.68461674, 0.68264514, 0.682621 , 0.6822236 ,
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[0.6816895 , 0.68169343, 0.6817601 , 0.68219596, 0.74291927,
0.74308765, 0.74310994, 0.7431202 , 0.743093 , 0.7429749 ,
0.7072856 , 0.6819312 , 0.6816661 , 0.6816423 , 0.68162847,
0.68162113],
[0.68181974, 0.6819553 , 0.6819781 , 0.6821021 , 0.6834799 ,
0.7196619 , 0.74258935, 0.74301046, 0.7428989 , 0.73720545,
0.6833024 , 0.6820794 , 0.6817877 , 0.6817106 , 0.6816779 ,
0.68166465],
[0.6823212 , 0.68455577, 0.68242085, 0.6825844 , 0.6928078 ,
0.6820986 , 0.6825319 , 0.68278486, 0.68217915, 0.68345153,
0.6837263 , 0.6830403 , 0.6821558 , 0.68209946, 0.68222785,
0.68371826]], dtype=float32), si_unit='1'),
't1': Quantity(values=Array([[2450.965 , 2450.9946, 2450.9976, 2450.9749, 2450.9722, 2451.0132,
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2450.9426, 2450.9226, 2450.9197, 2450.8906],
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2450.9614, 2450.8992, 2450.8953, 2450.892 ],
[2450.9546, 2450.971 , 2450.971 , 2451.0198, 2450.686 , 2450.6821,
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[2450.974 , 2451.0117, 2451.0042, 2451.0037, 2450.9958, 2450.7583,
2450.689 , 2450.6892, 2450.689 , 2450.6936, 2450.9797, 2450.9675,
2450.9697, 2450.934 , 2450.9277, 2450.9214],
[2450.9946, 2450.9814, 2451.0076, 2450.9702, 2451.0415, 2450.9692,
2450.9797, 2450.9941, 2450.9702, 2451.0032, 2450.9805, 2451.028 ,
2450.9587, 2450.964 , 2450.9739, 2451.0242]], dtype=float32), si_unit='ms')},
'loss_history': [0.150870680809021,
0.14339159429073334,
0.13653187453746796],
'cached': False}],
'metadata': {'config': {'seed': 1, 'group': 'control'}},
'study_dir': PosixPath('/tmp/mrax-notebook-smoke/tmp/analysis_toolbox_demo/inputs/control_02')},
{'study_name': 'treated_01',
'manifest_path': PosixPath('/tmp/mrax-notebook-smoke/tmp/analysis_toolbox_demo/outputs/treated_01/study_manifest.json'),
'results': [{'name': 't1_ir',
'model': 't1_ir',
'fields': {'amplitude': Quantity(values=Array([[0.6840635 , 0.68246615, 0.6824025 , 0.6823969 , 0.68219155,
0.6859856 , 0.68218327, 0.68274003, 0.68375576, 0.68296057,
0.68260694, 0.6940091 , 0.6822574 , 0.6836015 , 0.6823665 ,
0.68184596],
[0.74310863, 0.74307024, 0.74283046, 0.7427845 , 0.6832082 ,
0.68192667, 0.6817856 , 0.68172425, 0.68167526, 0.68175465,
0.6817727 , 0.68201536, 0.6819208 , 0.68260914, 0.69655573,
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[0.7431198 , 0.7431408 , 0.74308574, 0.74308497, 0.7163158 ,
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't1': Quantity(values=Array([[2450.9875, 2451.0042, 2451.0015, 2450.982 , 2451.0002, 2451.0015,
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'loss_history': [0.1519847810268402,
0.14443373680114746,
0.1375051885843277],
'cached': False}],
'metadata': {'config': {'seed': 2, 'group': 'treated'}},
'study_dir': PosixPath('/tmp/mrax-notebook-smoke/tmp/analysis_toolbox_demo/inputs/treated_01')},
{'study_name': 'treated_02',
'manifest_path': PosixPath('/tmp/mrax-notebook-smoke/tmp/analysis_toolbox_demo/outputs/treated_02/study_manifest.json'),
'results': [{'name': 't1_ir',
'model': 't1_ir',
'fields': {'amplitude': Quantity(values=Array([[0.6819282 , 0.6821133 , 0.6820945 , 0.68258524, 0.6831481 ,
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't1': Quantity(values=Array([[2450.9714, 2450.9382, 2450.9402, 2450.983 , 2451.049 , 2450.9731,
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[2450.9658, 2450.9355, 2450.9958, 2450.9653, 2450.7627, 2450.686 ,
2450.689 , 2450.689 , 2450.6824, 2450.6914, 2451.0054, 2450.9502,
2450.9612, 2450.9336, 2450.9136, 2450.9077],
[2450.982 , 2450.988 , 2450.9907, 2450.9985, 2450.999 , 2450.9514,
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'loss_history': [0.15260642766952515,
0.1450989693403244,
0.13821451365947723],
'cached': False}],
'metadata': {'config': {'seed': 3, 'group': 'treated'}},
'study_dir': PosixPath('/tmp/mrax-notebook-smoke/tmp/analysis_toolbox_demo/inputs/treated_02')}]
ROI statistics for parameter maps¶
Load one subject's manifest and extract ROI statistics from the fitted maps.
[3]:
manifest = summaries[0]["manifest_path"]
data = load_study_results(manifest)
exp = data["experiments"]["t1_ir"]
maps = exp["fitted_maps"]
mr_image = exp["mr_image"]
mask = np.zeros(mr_image.shape[-2:], dtype=bool)
mask[4:12, 4:12] = True
roi = ROI("center", mask)
rows = collect_roi_stats(maps, [roi], stats=("mean", "variance"))
rows
[3]:
[{'map': 'amplitude',
'roi': 'center',
'stat': 'mean',
'value': 0.7074053883552551,
'unit': '1'},
{'map': 'amplitude',
'roi': 'center',
'stat': 'variance',
'value': 0.0008956128731369972,
'unit': '1'},
{'map': 't1',
'roi': 'center',
'stat': 'mean',
'value': 2452.32373046875,
'unit': 'ms'},
{'map': 't1',
'roi': 'center',
'stat': 'variance',
'value': 137.02313232421875,
'unit': 'ms'}]
ROI timecourse¶
Reduce the ROI in the raw image stack to a timecourse.
[4]:
timecourse = extract_timecourse(mr_image, roi, stat="mean")
ti = exp["observables"].get("TI")
ti_vals = np.asarray(ti.values) if ti is not None else np.arange(timecourse.shape[0])
fig, ax = plt.subplots(figsize=(4, 3))
ax.plot(ti_vals, timecourse, marker="o")
ax.set_xlabel("TI (ms)")
ax.set_ylabel("ROI mean signal")
ax.set_title("ROI timecourse")
plt.show()
Timecourse plotting and animation¶
The arrays returned by MRax analysis helpers can be plotted directly with matplotlib.
[5]:
from matplotlib.animation import FuncAnimation, PillowWriter
from mrax.analysis.timecourse_processing import mean_timecourses_by_label, nan_gaussian_filter, apply_baseline
def plot_timecourses(image_series, label_mask, times, *, dilution=None, baseline_frames=50, smooth_sigma=2.0, labels=None, infusion_times=None, time_scale=60.0, time_unit="min", save_path=None):
series = np.asarray(image_series, dtype=float)
times_arr = np.asarray(times, dtype=float)
raw_timecourses, label_values = mean_timecourses_by_label(
series,
label_mask,
baseline_frames=0,
smooth_sigma=smooth_sigma,
dilution=dilution,
)
timecourses = raw_timecourses.copy()
if baseline_frames > 0:
for idx in range(timecourses.shape[1]):
timecourses[:, idx] -= np.nanmean(timecourses[:baseline_frames, idx])
fig, ax = plt.subplots(figsize=(7.2, 4.2))
for infusion_time in infusion_times or []:
ax.axvline(x=infusion_time, color="gray", linestyle="--", linewidth=1)
labels = labels or {label: str(label) for label in label_values}
for idx, label in enumerate(label_values):
ax.plot(times_arr / time_scale, raw_timecourses[:, idx], label=labels.get(label, str(label)), linewidth=2)
ax.set_xlabel(f"Time ({time_unit})")
ax.set_ylabel("Parameter Value")
ax.legend(loc="upper right")
if save_path:
fig.savefig(save_path, dpi=300, bbox_inches="tight")
plt.close(fig)
return timecourses
def plot_mean_timecourses(timecourses, label, times, *, groups=None, infusion_times=None, vmin=None, vmax=None, label_index=0, time_scale=60.0, time_unit="min"):
data = np.asarray(timecourses, dtype=float)
times_arr = np.asarray(times, dtype=float)
if data.ndim == 3 and data.shape[1] == times_arr.size:
data = data[..., label_index][:, None, :]
elif data.ndim == 2 and data.shape[0] == times_arr.size:
data = data[:, label_index][None, None, :]
group_names = list(groups) if groups is not None else [f"Group {i+1}" for i in range(data.shape[0])]
fig, ax = plt.subplots(figsize=(7.2, 4.2))
for infusion_time in infusion_times or []:
ax.axvline(x=infusion_time, color="gray", linestyle="--", linewidth=1)
for group_idx, group_name in enumerate(group_names):
group_data = data[group_idx]
mean_tc = np.nanmean(group_data, axis=0)
sem_tc = np.nanstd(group_data, axis=0) / np.sqrt(max(1, group_data.shape[0]))
line, = ax.plot(times_arr / time_scale, mean_tc, lw=2, label=group_name)
ax.fill_between(times_arr / time_scale, mean_tc - sem_tc, mean_tc + sem_tc, color=line.get_color(), alpha=0.25)
ax.set_xlabel(f"Time ({time_unit})")
ax.set_ylabel(label)
if vmin is not None or vmax is not None:
ax.set_ylim(vmin, vmax)
ax.legend(frameon=False, loc="upper right")
return fig
def map_animation(image_series, reference, times, save_path, *, dilution=None, vmin=0.0, vmax=0.0005, infusion_times=None, baseline_frames=5, smooth_sigma=1.0, fps=30, dpi=300):
series = np.asarray(image_series, dtype=float)
if smooth_sigma and smooth_sigma > 0:
series = nan_gaussian_filter(series, sigma=smooth_sigma)
if dilution is not None:
dil = apply_baseline(np.asarray(dilution, dtype=float), baseline_frames=baseline_frames, mode="divide", axis=0)
with np.errstate(invalid="ignore", divide="ignore"):
series = series / np.clip(dil, 1e-2, None)
times_arr = np.asarray(times, dtype=float)
baseline = np.nanmean(series[:baseline_frames], axis=0)
fig, ax = plt.subplots(figsize=(5, 5))
ax.imshow(reference, cmap="gray")
im = ax.imshow(series[0] - baseline, vmin=vmin, vmax=vmax, cmap="jet")
ax.axis("off")
plt.colorbar(im, ax=ax)
title = ax.set_title(f"t={times_arr[0]:.2f}")
def update(frame):
im.set_array(series[frame] - baseline)
title.set_text(f"t={times_arr[frame]:.2f}")
return [im, title]
anim = FuncAnimation(fig, update, frames=series.shape[0], blit=True)
anim.save(save_path, writer=PillowWriter(fps=fps), dpi=dpi)
plt.close(fig)
label_mask = np.zeros(mr_image.shape[-2:], dtype=int)
label_mask[4:12, 4:12] = 1
timecourses = plot_timecourses(
mr_image,
label_mask,
times=ti_vals * 1e-3,
infusion_times=[5],
)
plot_mean_timecourses(
timecourses[None, ...],
label="Signal",
times=ti_vals * 1e-3,
groups=["control"],
label_index=0,
)
[5]:
[6]:
animation_path = outputs_root / "roi_animation.gif"
map_animation(
mr_image,
reference=mr_image[0],
times=ti_vals * 1e-3,
save_path=str(animation_path),
)
animation_path
[6]:
PosixPath('/tmp/mrax-notebook-smoke/tmp/analysis_toolbox_demo/outputs/roi_animation.gif')
Group summaries and comparisons¶
Use the batch output root to compare groups. Members can be study folder names
(inside outputs_root) or explicit manifest paths.
[7]:
groups = {
"control": ["control_01", "control_02"],
"treated": ["treated_01", "treated_02"],
}
results = analyze_groups(
groups,
output_root=outputs_root,
experiment_name="t1_ir",
rois=[roi],
map_names=["t1"],
stats=("mean",),
p_adjust="fdr_bh",
)
results["group_summary"]
[7]:
[{'group': 'control',
'experiment': 't1_ir',
'map': 't1',
'roi': 'center',
'stat': 'mean',
'count': 2.0,
'nan_count': 0.0,
'mean': 2452.281494140625,
'variance': 0.003567814826965332,
'std': 0.05973118805921519,
'sem': 0.04223632812499999,
'median': 2452.281494140625,
'min': 2452.2392578125,
'max': 2452.32373046875,
'p25': 2452.2603759765625,
'p75': 2452.3026123046875,
'unit': 'ms'},
{'group': 'treated',
'experiment': 't1_ir',
'map': 't1',
'roi': 'center',
'stat': 'mean',
'count': 2.0,
'nan_count': 0.0,
'mean': 2454.6890869140625,
'variance': 0.08044984936714172,
'std': 0.28363682653552186,
'sem': 0.20056152343749997,
'median': 2454.6890869140625,
'min': 2454.488525390625,
'max': 2454.8896484375,
'p25': 2454.5888061523438,
'p75': 2454.7893676757812,
'unit': 'ms'}]
[8]:
results["comparisons"]
[8]:
[{'experiment': 't1_ir',
'map': 't1',
'roi': 'center',
'stat': 'mean',
'group_a': 'control',
'group_b': 'treated',
'n_a': 2.0,
'n_b': 2.0,
'mean_a': 2452.281494140625,
'mean_b': 2454.68896484375,
'mean_diff': -2.407470703125,
't_stat': -11.746614794850906,
't_p': 0.04431433472445087,
'effect_size_d': -11.746614794850906,
'effect_size_g': -6.712351311343374,
'np_test': 'mannwhitney',
'np_stat': 0.0,
'np_p': 0.3333333333333333,
'unit': 'ms',
't_p_fdr_bh': 0.04431433472445087}]
Plot group distributions and significance¶
Visualize per-subject distributions and group summaries with significance markers.
[9]:
def _grouped_values(rows, *, experiment, map_name, roi, stat):
grouped = {}
for row in rows:
if row.get("experiment") == experiment and row.get("map") == map_name and row.get("roi") == roi and row.get("stat") == stat:
grouped.setdefault(str(row.get("group")), []).append(float(row.get("value", np.nan)))
return grouped
def _significance_label(p_value):
if p_value is None or not np.isfinite(p_value):
return "n/a"
if p_value <= 0.001:
return "***"
if p_value <= 0.01:
return "**"
if p_value <= 0.05:
return "*"
return "n.s."
def plot_group_distributions(subject_rows, *, experiment, map_name, roi, stat, comparisons=None, kind="box"):
grouped = _grouped_values(subject_rows, experiment=experiment, map_name=map_name, roi=roi, stat=stat)
order = sorted(grouped)
values = [grouped[name] for name in order]
fig, ax = plt.subplots(figsize=(5.2, 3.6))
positions = np.arange(len(order))
if kind == "violin":
ax.violinplot(values, positions=positions, showmedians=True)
else:
ax.boxplot(values, positions=positions, widths=0.6, patch_artist=True)
rng = np.random.default_rng(0)
for idx, group_vals in enumerate(values):
ax.scatter(np.full(len(group_vals), positions[idx]) + rng.normal(0, 0.04, len(group_vals)), group_vals, s=16, color="#2f2f2f", alpha=0.65)
ax.set_xticks(positions)
ax.set_xticklabels(order)
ax.set_ylabel(stat)
ax.set_title(f"{experiment} - {map_name} - {roi}")
return fig
def plot_group_summary(summary_rows, *, experiment, map_name, roi, stat, comparisons=None, value_key="mean", error_key="sem"):
rows = [row for row in summary_rows if row.get("experiment") == experiment and row.get("map") == map_name and row.get("roi") == roi and row.get("stat") == stat]
order = sorted(str(row.get("group")) for row in rows)
by_group = {str(row.get("group")): row for row in rows}
means = [float(by_group[group].get(value_key, np.nan)) for group in order]
errors = [float(by_group[group].get(error_key, np.nan)) for group in order]
fig, ax = plt.subplots(figsize=(5.2, 3.6))
positions = np.arange(len(order))
ax.bar(positions, means, yerr=errors, capsize=4, color="#88aadd", alpha=0.8)
ax.set_xticks(positions)
ax.set_xticklabels(order)
ax.set_ylabel(f"{value_key} ({stat})")
ax.set_title(f"{experiment} - {map_name} - {roi}")
return fig
fig = plot_group_distributions(
results["subject_stats"],
comparisons=results["comparisons"],
experiment="t1_ir",
map_name="t1",
roi="center",
stat="mean",
kind="box",
)
plt.show()
[10]:
fig = plot_group_summary(
results["group_summary"],
comparisons=results["comparisons"],
experiment="t1_ir",
map_name="t1",
roi="center",
stat="mean",
)
plt.show()
