Sholl analysis in Skan#
Skan provides a function to perform Sholl analysis, which counts the number of processes crossing circular (2D) or spherical (3D) shells from a given center point. Commonly, the center point is the soma, or cell body, of a neuron, but the method can be used to compare general skeleton structures when a root or center point is defined.
%matplotlib inline
%config InlineBackend.figure_format='retina'
import matplotlib.pyplot as plt
import numpy as np
import zarr
neuron = np.asarray(zarr.open('../example-data/neuron.zarr.zip'))
fig, ax = plt.subplots()
ax.imshow(neuron, cmap='gray')
ax.scatter(57, 54)
ax.set_axis_off()
plt.show()
---------------------------------------------------------------------------
FileExistsError Traceback (most recent call last)
Cell In[2], line 4
1 import numpy as np
2 import zarr
----> 4 neuron = np.asarray(zarr.open('../example-data/neuron.zarr.zip'))
6 fig, ax = plt.subplots()
7 ax.imshow(neuron, cmap='gray')
File /opt/hostedtoolcache/Python/3.12.11/x64/lib/python3.12/site-packages/zarr/api/synchronous.py:200, in open(store, mode, zarr_version, zarr_format, path, storage_options, **kwargs)
162 def open(
163 store: StoreLike | None = None,
164 *,
(...) 170 **kwargs: Any, # TODO: type kwargs as valid args to async_api.open
171 ) -> Array | Group:
172 """Open a group or array using file-mode-like semantics.
173
174 Parameters
(...) 198 Return type depends on what exists in the given store.
199 """
--> 200 obj = sync(
201 async_api.open(
202 store=store,
203 mode=mode,
204 zarr_version=zarr_version,
205 zarr_format=zarr_format,
206 path=path,
207 storage_options=storage_options,
208 **kwargs,
209 )
210 )
211 if isinstance(obj, AsyncArray):
212 return Array(obj)
File /opt/hostedtoolcache/Python/3.12.11/x64/lib/python3.12/site-packages/zarr/core/sync.py:163, in sync(coro, loop, timeout)
160 return_result = next(iter(finished)).result()
162 if isinstance(return_result, BaseException):
--> 163 raise return_result
164 else:
165 return return_result
File /opt/hostedtoolcache/Python/3.12.11/x64/lib/python3.12/site-packages/zarr/core/sync.py:119, in _runner(coro)
114 """
115 Await a coroutine and return the result of running it. If awaiting the coroutine raises an
116 exception, the exception will be returned.
117 """
118 try:
--> 119 return await coro
120 except Exception as ex:
121 return ex
File /opt/hostedtoolcache/Python/3.12.11/x64/lib/python3.12/site-packages/zarr/api/asynchronous.py:345, in open(store, mode, zarr_version, zarr_format, path, storage_options, **kwargs)
343 else:
344 mode = "a"
--> 345 store_path = await make_store_path(store, mode=mode, path=path, storage_options=storage_options)
347 # TODO: the mode check below seems wrong!
348 if "shape" not in kwargs and mode in {"a", "r", "r+", "w"}:
File /opt/hostedtoolcache/Python/3.12.11/x64/lib/python3.12/site-packages/zarr/storage/_common.py:349, in make_store_path(store_like, path, mode, storage_options)
345 store = FsspecStore.from_url(
346 store_like, storage_options=storage_options, read_only=_read_only
347 )
348 else:
--> 349 store = await LocalStore.open(root=Path(store_like), read_only=_read_only)
350 elif isinstance(store_like, dict):
351 # We deliberate only consider dict[str, Buffer] here, and not arbitrary mutable mappings.
352 # By only allowing dictionaries, which are in-memory, we know that MemoryStore appropriate.
353 store = await MemoryStore.open(store_dict=store_like, read_only=_read_only)
File /opt/hostedtoolcache/Python/3.12.11/x64/lib/python3.12/site-packages/zarr/abc/store.py:83, in Store.open(cls, *args, **kwargs)
67 """
68 Create and open the store.
69
(...) 80 The opened store instance.
81 """
82 store = cls(*args, **kwargs)
---> 83 await store._open()
84 return store
File /opt/hostedtoolcache/Python/3.12.11/x64/lib/python3.12/site-packages/zarr/storage/_local.py:114, in LocalStore._open(self)
112 async def _open(self) -> None:
113 if not self.read_only:
--> 114 self.root.mkdir(parents=True, exist_ok=True)
115 return await super()._open()
File /opt/hostedtoolcache/Python/3.12.11/x64/lib/python3.12/pathlib.py:1311, in Path.mkdir(self, mode, parents, exist_ok)
1307 """
1308 Create a new directory at this given path.
1309 """
1310 try:
-> 1311 os.mkdir(self, mode)
1312 except FileNotFoundError:
1313 if not parents or self.parent == self:
FileExistsError: [Errno 17] File exists: '../example-data/neuron.zarr.zip'
This is the skeletonized image of a neuron. The cell body, or soma, has been manually annotated by a researcher based on the source image. We can use the function skan.sholl_analysis to count the crossings of concentric circles, centered on the cell body, by the cell’s processes.
import pandas as pd
from skan import Skeleton, sholl_analysis
# make the skeleton object
skeleton = Skeleton(neuron)
# define the neuron center/soma
center = np.array([54, 57])
# define radii at which to measure crossings
radii = np.arange(4, 45, 4)
# perform sholl analysis
center, radii, counts = sholl_analysis(
skeleton, center=center, shells=radii
)
table = pd.DataFrame({'radius': radii, 'crossings': counts})
table
We can visualize this using functions from skan.draw and matplotlib.
from skan import draw
# make two subplots
fig, (ax0, ax1) = plt.subplots(nrows=1, ncols=2, figsize=(8, 4))
# draw the skeleton
draw.overlay_skeleton_2d_class(
skeleton, skeleton_colormap='viridis_r', vmin=0, axes=ax0
)
# draw the shells
draw.sholl_shells(center, radii, axes=ax0)
# fiddle with plot visual aspects
ax0.autoscale_view()
ax0.set_facecolor('black')
ax0.set_ylim(75, 20)
ax0.set_xlim(20, 80)
ax0.set_aspect('equal')
# in second subplot, plot the Sholl analysis
ax1.plot('radius', 'crossings', data=table)
ax1.set_xlabel('radius')
ax1.set_ylabel('crossings')
plt.show()