Cell/Nuclei Morphology¶

Cell/nuclei morphologies are often computed to quantify the shape of cells or nuclei. Different morphological metrics can be used, for example, to quantify differences in shapes between cell types or even within a cell type. For example, cells of some type can have varying shape based on their subtype or their localization in the tissue. If you need some intuition on what morphological metrics are, please check out this old but great slide deck from the University of Guelph.

In this notebook, We will be looking at the different shape metrics that can be computed with cellseg_gsontools.

The Data¶

We'll be taking a look at some glandular epithelial cells and their shapes espically. cellseg_gsontools provides a small example segmentation mask that contains a lot glandular epithelial cells.

In [1]:

from cellseg_gsontools.data import gland_cells

gc = gland_cells()
gc.plot(column="class_name", figsize=(10,10), legend=True)

from cellseg_gsontools.data import gland_cells gc = gland_cells() gc.plot(column="class_name", figsize=(10,10), legend=True)

Out[1]:

<Axes: >

In [2]:

gc

gc

Out[2]:

	type	geometry	class_name
0	Feature	POLYGON ((92.000 1083.984, 95.990 1079.993, 99...	glandular_epithel
1	Feature	POLYGON ((61.005 1085.988, 64.755 1086.000, 68...	glandular_epithel
2	Feature	POLYGON ((138.997 1093.988, 142.992 1092.988, ...	glandular_epithel
3	Feature	POLYGON ((109.005 1092.988, 115.995 1092.988, ...	glandular_epithel
4	Feature	POLYGON ((69.012 1091.997, 70.011 1094.994, 72...	glandular_epithel
...	...	...	...
1354	Feature	POLYGON ((1932.004 1671.988, 1936.755 1672.000...	glandular_epithel
1355	Feature	POLYGON ((1944.005 1691.988, 1951.996 1691.988...	glandular_epithel
1356	Feature	POLYGON ((1981.005 1723.988, 1985.996 1723.988...	glandular_epithel
1357	Feature	POLYGON ((1962.007 1726.990, 1965.005 1728.988...	glandular_epithel
1358	Feature	POLYGON ((1991.012 1739.997, 1992.011 1742.994...	glandular_epithel

1359 rows × 3 columns

Computing Morphological Metrics¶

We will compute all of the different morphological metrics that are available in cellseg_gsontools and then visualize them. The morphological metrics can be computed with the shape_metric-function. The available metrics are:

• Area
• Perimeter
• Solidity
• Major Axis Length
• Minor Axis Length
• Major Axis Angle
• Minor Axis Angle
• Convexity
• Compactness
• Circularity
• Eccentricity
• Elongation
• Equivalent Recatangular Index
• Rectangularity
• Squareness
• Sphericity
• Shape Index
• Fractal Dimension

In [3]:

from cellseg_gsontools.geometry import shape_metric

metrics = [
    "area",
    "solidity",
    "major_axis_len",
    "major_axis_angle",
    "minor_axis_len",
    "minor_axis_angle",
    "convexity",
    "compactness",
    "circularity",
    "eccentricity",
    "elongation",
    "equivalent_rectangular_index",
    "rectangularity",
    "squareness",
    "sphericity",
    "shape_index",
    "fractal_dimension"
]

gc = shape_metric(
    gc,
    metrics=metrics,
    parallel=True,
)

# compute perimeter
metrics.append("perimeter")
gc["perimeter"] = gc.length
gc

from cellseg_gsontools.geometry import shape_metric metrics = [ "area", "solidity", "major_axis_len", "major_axis_angle", "minor_axis_len", "minor_axis_angle", "convexity", "compactness", "circularity", "eccentricity", "elongation", "equivalent_rectangular_index", "rectangularity", "squareness", "sphericity", "shape_index", "fractal_dimension" ] gc = shape_metric( gc, metrics=metrics, parallel=True, ) # compute perimeter metrics.append("perimeter") gc["perimeter"] = gc.length gc

Out[3]:

	type	geometry	class_name	area	solidity	major_axis_len	major_axis_angle	minor_axis_len	minor_axis_angle	convexity	...	circularity	eccentricity	elongation	equivalent_rectangular_index	rectangularity	squareness	sphericity	shape_index	fractal_dimension	perimeter
0	Feature	POLYGON ((92.000 1083.984, 95.990 1079.993, 99...	glandular_epithel	520.239144	0.966439	42.279910	157.380527	15.206325	67.380527	0.998190	...	0.664169	0.933084	0.599828	0.777647	0.809179	0.842588	0.298672	0.607703	0.933084	99.392555
1	Feature	POLYGON ((61.005 1085.988, 64.755 1086.000, 68...	glandular_epithel	565.581197	0.979205	42.556314	164.055301	18.107017	74.055301	0.998635	...	0.720651	0.904966	0.549867	0.702213	0.733980	0.915058	0.377672	0.628537	0.904966	99.445024
2	Feature	POLYGON ((138.997 1093.988, 142.992 1092.988, ...	glandular_epithel	721.500898	0.992876	45.132745	157.165715	20.639463	67.165715	0.998725	...	0.764039	0.889310	0.609533	0.729744	0.774545	0.970325	0.417713	0.671005	0.889310	109.073619
3	Feature	POLYGON ((109.005 1092.988, 115.995 1092.988, ...	glandular_epithel	435.911486	0.982687	35.627477	165.963336	14.965253	75.963336	0.998602	...	0.734751	0.907502	0.575812	0.772660	0.817578	0.932899	0.370378	0.650374	0.907502	86.465279
4	Feature	POLYGON ((69.012 1091.997, 70.011 1094.994, 72...	glandular_epithel	302.260204	1.000000	22.618201	134.951251	14.843037	44.951251	1.000000	...	0.869898	0.754550	0.999997	0.836853	0.900327	1.107589	0.582249	0.807680	0.754550	66.078655
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
1354	Feature	POLYGON ((1932.004 1671.988, 1936.755 1672.000...	glandular_epithel	473.859283	1.000000	36.154051	155.225946	15.899675	65.225946	1.000000	...	0.767510	0.898108	0.687020	0.768171	0.824336	0.977224	0.396189	0.674762	0.898108	88.082112
1355	Feature	POLYGON ((1944.005 1691.988, 1951.996 1691.988...	glandular_epithel	803.788422	0.993490	51.851271	153.435627	19.205898	63.435627	0.999133	...	0.705127	0.928871	0.595539	0.757277	0.807138	0.896240	0.344882	0.616768	0.928871	119.789518
1356	Feature	POLYGON ((1981.005 1723.988, 1985.996 1723.988...	glandular_epithel	603.424619	0.995804	46.700700	162.474799	17.039395	72.474799	0.999346	...	0.675694	0.931061	0.511644	0.724112	0.758308	0.859195	0.324170	0.589923	0.931061	106.004838
1357	Feature	POLYGON ((1962.007 1726.990, 1965.005 1728.988...	glandular_epithel	509.535284	1.000000	33.989143	0.026300	17.986912	90.026300	1.000000	...	0.829131	0.848500	0.529248	0.771767	0.833446	1.055682	0.466899	0.743267	0.848500	87.878070
1358	Feature	POLYGON ((1991.012 1739.997, 1992.011 1742.994...	glandular_epithel	163.492979	0.851175	33.228779	180.000000	8.988087	90.000000	0.990231	...	0.359102	0.962722	0.270491	0.669348	0.547416	0.448333	0.212360	0.424890	0.962722	76.385164

1359 rows × 21 columns

Plotting the Metrics¶

Let's start plotting these metrics if we can see some differences between the cell types present.

In [4]:

# !pip install seaborn

# !pip install seaborn

In [5]:

import seaborn

# Let's first define a quick function to plot the data distributions with seaborn
def plot_kde(tidy_data):
    seaborn.set_style("whitegrid")
    seaborn.set(font_scale=1.5)

    # Setup the facets
    facets = seaborn.FacetGrid(
        data=tidy_data,
        col="Attribute",
        hue="Cell Type",
        sharey=False,
        sharex=False,
        aspect=2,
        col_wrap=2,
    )

    # Build the plot from `sns.kdeplot`
    kde_ax = facets.map(seaborn.kdeplot, "Values", fill=True).add_legend()
    return kde_ax

import seaborn # Let's first define a quick function to plot the data distributions with seaborn def plot_kde(tidy_data): seaborn.set_style("whitegrid") seaborn.set(font_scale=1.5) # Setup the facets facets = seaborn.FacetGrid( data=tidy_data, col="Attribute", hue="Cell Type", sharey=False, sharex=False, aspect=2, col_wrap=2, ) # Build the plot from `sns.kdeplot` kde_ax = facets.map(seaborn.kdeplot, "Values", fill=True).add_legend() return kde_ax

Let's tidy up the data first

In [6]:

m = list(metrics)
tidy = gc.reset_index().set_index("class_name")
tidy = tidy[m]
tidy = tidy.stack()
tidy = tidy.reset_index()
tidy = tidy.rename(
    columns={"class_name": "Cell Type", "level_1": "Attribute", 0: "Values"}
)
tidy

m = list(metrics) tidy = gc.reset_index().set_index("class_name") tidy = tidy[m] tidy = tidy.stack() tidy = tidy.reset_index() tidy = tidy.rename( columns={"class_name": "Cell Type", "level_1": "Attribute", 0: "Values"} ) tidy

Out[6]:

	Cell Type	Attribute	Values
0	glandular_epithel	area	520.239144
1	glandular_epithel	solidity	0.966439
2	glandular_epithel	major_axis_len	42.279910
3	glandular_epithel	major_axis_angle	157.380527
4	glandular_epithel	minor_axis_len	15.206325
...	...	...	...
24457	glandular_epithel	squareness	0.448333
24458	glandular_epithel	sphericity	0.212360
24459	glandular_epithel	shape_index	0.424890
24460	glandular_epithel	fractal_dimension	0.962722
24461	glandular_epithel	perimeter	76.385164

24462 rows × 3 columns

In [7]:

plot_kde(tidy)

plot_kde(tidy)

Out[7]:

<seaborn.axisgrid.FacetGrid at 0x7ffb14f77cd0>

We can clearly see that the inflammatory cells differ from the stormal and glandular cells based on the distributions. They tend to be smaller, more circular, compact, spherical and have a lower major axis length, eccentricity and fractal dimension (fractal dimension measures the complexity of the boundary). This is in line with what we would expect from inflammatory cells, since they are a lot smaller and have less variance in their shapes than stromal or epithelial cells. On the other hand, the glandular epithelial cells and stromal/connective cells are much more similar in their shape distributions.

Spatial Distributions of Morphological Metrics¶

Let's now look at how the metrics distribute spatially.

In [8]:

# !pip install legendgram

# !pip install legendgram

In [9]:

import mapclassify
import geopandas as gpd
import matplotlib.pyplot as plt
import palettable as palet
from legendgram import legendgram


# helper function to replace legend items
def replace_legend_items(legend, mapping):
    for txt in legend.texts:
        for k, v in mapping.items():
            if txt.get_text() == str(k):
                txt.set_text(v)
    

# Helper function to plot cells with a feature value highlighted
def plot_cells(f, ax, cells: gpd.GeoDataFrame, col: str):
    # bin the values with the Fisher-Jenks method
    bins = mapclassify.FisherJenks(cells[col], k=5)
    cells["bin_vals"] = bins.yb

    ax = cells.plot(
        ax=ax,
        column="bin_vals",
        cmap="viridis",
        categorical=True,
        legend=True,
        legend_kwds={
            "fontsize": 8,
            "loc": "center left",
            "bbox_to_anchor": (1.0, 0.94),
        },
    )

    bin_legends = bins.get_legend_classes()
    mapping = dict([(i, s) for i, s in enumerate(bin_legends)])
    replace_legend_items(ax.get_legend(), mapping)
    ax.set_title(col)
    ax = legendgram(
        f,
        ax,
        cells[col],
        bins=30,
        breaks=bins.bins,
        pal=palet.matplotlib.Viridis_5,
        loc="lower left",
    )
    ax.set_axis_off()

    return ax

fig, ax = plt.subplots(9, 2, figsize=(13, 43))
ax = ax.flatten()
plot_cells(fig, ax[0], gc, "area")
plot_cells(fig, ax[1], gc, "solidity")
plot_cells(fig, ax[2], gc, "major_axis_len")
plot_cells(fig, ax[3], gc, "major_axis_angle")
plot_cells(fig, ax[4], gc, "minor_axis_len")
plot_cells(fig, ax[5], gc, "minor_axis_angle")
plot_cells(fig, ax[6], gc, "convexity")
plot_cells(fig, ax[7], gc, "compactness")
plot_cells(fig, ax[8], gc, "circularity")
plot_cells(fig, ax[9], gc, "eccentricity")
plot_cells(fig, ax[10], gc, "elongation")
plot_cells(fig, ax[11], gc, "equivalent_rectangular_index")
plot_cells(fig, ax[12], gc, "rectangularity")
plot_cells(fig, ax[13], gc, "squareness")
plot_cells(fig, ax[14], gc, "sphericity")
plot_cells(fig, ax[15], gc, "shape_index")
plot_cells(fig, ax[16], gc, "fractal_dimension")
plot_cells(fig, ax[17], gc, "perimeter")

import mapclassify import geopandas as gpd import matplotlib.pyplot as plt import palettable as palet from legendgram import legendgram # helper function to replace legend items def replace_legend_items(legend, mapping): for txt in legend.texts: for k, v in mapping.items(): if txt.get_text() == str(k): txt.set_text(v) # Helper function to plot cells with a feature value highlighted def plot_cells(f, ax, cells: gpd.GeoDataFrame, col: str): # bin the values with the Fisher-Jenks method bins = mapclassify.FisherJenks(cells[col], k=5) cells["bin_vals"] = bins.yb ax = cells.plot( ax=ax, column="bin_vals", cmap="viridis", categorical=True, legend=True, legend_kwds={ "fontsize": 8, "loc": "center left", "bbox_to_anchor": (1.0, 0.94), }, ) bin_legends = bins.get_legend_classes() mapping = dict([(i, s) for i, s in enumerate(bin_legends)]) replace_legend_items(ax.get_legend(), mapping) ax.set_title(col) ax = legendgram( f, ax, cells[col], bins=30, breaks=bins.bins, pal=palet.matplotlib.Viridis_5, loc="lower left", ) ax.set_axis_off() return ax fig, ax = plt.subplots(9, 2, figsize=(13, 43)) ax = ax.flatten() plot_cells(fig, ax[0], gc, "area") plot_cells(fig, ax[1], gc, "solidity") plot_cells(fig, ax[2], gc, "major_axis_len") plot_cells(fig, ax[3], gc, "major_axis_angle") plot_cells(fig, ax[4], gc, "minor_axis_len") plot_cells(fig, ax[5], gc, "minor_axis_angle") plot_cells(fig, ax[6], gc, "convexity") plot_cells(fig, ax[7], gc, "compactness") plot_cells(fig, ax[8], gc, "circularity") plot_cells(fig, ax[9], gc, "eccentricity") plot_cells(fig, ax[10], gc, "elongation") plot_cells(fig, ax[11], gc, "equivalent_rectangular_index") plot_cells(fig, ax[12], gc, "rectangularity") plot_cells(fig, ax[13], gc, "squareness") plot_cells(fig, ax[14], gc, "sphericity") plot_cells(fig, ax[15], gc, "shape_index") plot_cells(fig, ax[16], gc, "fractal_dimension") plot_cells(fig, ax[17], gc, "perimeter")

Out[9]:

<Axes: >

From the plot above, we can see some spatial patterns. For example, we can see that the high eccentricity and high fractal dimension cells are located in the upper glandular epithelium. We can also see that the largest cells are located in the center of the image in the stroma and the high sphericity cells seem to be mostly the immune cells in the stroma. All of the cells seem to be quite solid and non-convex meaning that there are little irregular boundaries among the cells. All of these results are expected and in line with what we would expect from the different cell types.

In [ ]: