Nuclear Morphology

In histopathology and biomedical image analysis, morphological metrics provide valuable insights into the geometry and complexity of nuclei which can be used to evaluate, for example, nuclear pleomorphism (variation in the size, shape, and staining characteristics of cell nuclei within a population of cells). The histolytics library offers a comprehensive suite of tools to compute a wide range of shape metrics for nuclei and other segmented objects. In this workflow, we will demonstrate how to:

• Compute a comprehensive set of morphological shape metrics for each nucleus.
• Visualize spatial distributions of selected metrics

Let's start by loading example data.

In [16]:

# Install seaborn for visualizing the results.
# !pip install seaborn

# Install seaborn for visualizing the results. # !pip install seaborn

In [2]:

from histolytics.data import cervix_nuclei_crop

nuc = cervix_nuclei_crop()
nuc.plot(figsize=(10, 10), column="class_name", legend=True)
nuc

from histolytics.data import cervix_nuclei_crop nuc = cervix_nuclei_crop() nuc.plot(figsize=(10, 10), column="class_name", legend=True) nuc

Out[2]:

	geometry	class_name
uid
1	POLYGON ((29 485.005, 29 492.996, 31.998 497.9...	inflammatory
2	POLYGON ((19 516.996, 19.998 518.993, 25.651 5...	connective
3	POLYGON ((25 806.995, 27.995 809.99, 30.995 81...	inflammatory
4	POLYGON ((36 1576.995, 36.993 1577.988, 45.985...	connective
5	POLYGON ((32 1601.995, 33.993 1603.988, 37.574...	connective
...	...	...
13368	POLYGON ((10101 3552.005, 10101.162 3554.174, ...	neoplastic
13369	POLYGON ((10066 3584.005, 10066 3589.995, 1006...	neoplastic
13370	POLYGON ((11026 3052.004, 11026 3060.997, 1102...	neoplastic
13371	POLYGON ((11019 3102.005, 11019 3110.996, 1102...	neoplastic
13372	POLYGON ((11040 3073.989, 11053.985 3073.988, ...	neoplastic

13364 rows × 2 columns

Computing Morphological Metrics¶

We will compute all of the different shape morphological metrics that are available in histolytics and then visualize some of 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 histolytics.spatial_geom.shape_metrics 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",
    "shape_index",
    "fractal_dimension",
]

nuc = shape_metric(nuc, metrics=metrics, parallel=True, num_processes=4)

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

from histolytics.spatial_geom.shape_metrics 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", "shape_index", "fractal_dimension", ] nuc = shape_metric(nuc, metrics=metrics, parallel=True, num_processes=4) # compute perimeter metrics.append("perimeter") nuc["perimeter"] = nuc.length nuc

Out[3]:

	geometry	class_name	area	solidity	major_axis_len	major_axis_angle	minor_axis_len	minor_axis_angle	convexity	compactness	circularity	eccentricity	elongation	equivalent_rectangular_index	rectangularity	squareness	shape_index	fractal_dimension	perimeter
uid
1	POLYGON ((29 485.005, 29 492.996, 31.998 497.9...	inflammatory	294.472159	0.992279	21.976612	89.999545	16.976212	0.000455	0.999082	0.909061	0.910733	0.635055	0.772472	0.727584	0.789301	1.157453	0.815479	0.974280	63.801444
2	POLYGON ((19 516.996, 19.998 518.993, 25.651 5...	connective	704.808300	0.986220	40.988412	45.000643	21.908378	44.999357	0.997811	0.818837	0.822434	0.845167	0.885641	0.732458	0.784874	1.042576	0.720237	0.993642	104.001974
3	POLYGON ((25 806.995, 27.995 809.99, 30.995 81...	inflammatory	552.898221	0.950128	31.801183	47.276957	23.203572	42.723043	0.986643	0.837890	0.860730	0.683826	0.965478	0.716518	0.749285	1.066834	0.821957	0.989756	91.061351
4	POLYGON ((36 1576.995, 36.993 1577.988, 45.985...	connective	393.676413	0.984017	24.976512	89.999545	20.976179	0.000455	0.997444	0.828655	0.832907	0.542840	0.839849	0.728765	0.751417	1.055076	0.713557	0.991028	77.265890
5	POLYGON ((32 1601.995, 33.993 1603.988, 37.574...	connective	401.297157	0.984667	30.976312	0.000119	16.976206	89.999881	0.997073	0.821024	0.825851	0.836453	0.548040	0.713866	0.763125	1.045360	0.711818	0.992600	78.371836
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
13368	POLYGON ((10101 3552.005, 10101.162 3554.174, ...	neoplastic	502.084214	0.866430	43.310253	57.804266	17.411344	32.195734	0.983972	0.587113	0.606396	0.915633	0.941137	0.696524	0.665815	0.747536	0.575882	1.046790	103.665042
13369	POLYGON ((10066 3584.005, 10066 3589.995, 1006...	neoplastic	643.473940	0.985765	41.742560	11.888947	20.885481	78.111053	0.998321	0.773000	0.775602	0.865829	0.536340	0.701513	0.738087	0.984214	0.685636	1.002461	102.277653
13370	POLYGON ((11026 3052.004, 11026 3060.997, 1102...	neoplastic	1361.789550	0.995665	44.976705	0.000297	34.988345	89.999703	0.999011	0.897157	0.898934	0.628361	0.777926	0.803332	0.865364	1.142296	0.823241	0.981565	138.110197
13371	POLYGON ((11019 3102.005, 11019 3110.996, 1102...	neoplastic	1411.671604	0.947686	61.179662	1.636598	28.821395	88.363402	0.991724	0.745090	0.757578	0.882083	0.475204	0.767000	0.800593	0.948679	0.689294	1.007264	154.300483
13372	POLYGON ((11040 3073.989, 11053.985 3073.988, ...	neoplastic	1160.007601	0.996997	41.976293	89.998287	30.988188	0.001713	0.999357	0.878228	0.879359	0.674548	0.738225	0.833721	0.891786	1.118194	0.800407	0.984168	128.834387

13364 rows × 19 columns

Visualizing the Metrics¶

Spatial Plots¶

We will visualize some of the shape metrics of the neoplastic cells. First: Area (in pixels)

In [ ]:

import mapclassify
import matplotlib.pyplot as plt


# 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)


def plot_neoplastic(neoplastic_nuc, col: str = "area", k: int = 5):
    bins = mapclassify.FisherJenks(neoplastic_nuc[col], k=k)
    neoplastic_nuc = neoplastic_nuc.assign(bin_vals=bins.yb)

    fig, ax = plt.subplots(figsize=(10, 10))
    ax = nuc.plot(ax=ax, column="class_name", legend=False)
    ax = neoplastic_nuc.plot(
        ax=ax, column="bin_vals", legend=True, cmap="viridis", categorical=True
    )

    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_axis_off()

    return ax


neo = nuc[nuc["class_name"] == "neoplastic"]
plot_neoplastic(neo, col="area", k=5)

import mapclassify import matplotlib.pyplot as plt # 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) def plot_neoplastic(neoplastic_nuc, col: str = "area", k: int = 5): bins = mapclassify.FisherJenks(neoplastic_nuc[col], k=k) neoplastic_nuc = neoplastic_nuc.assign(bin_vals=bins.yb) fig, ax = plt.subplots(figsize=(10, 10)) ax = nuc.plot(ax=ax, column="class_name", legend=False) ax = neoplastic_nuc.plot( ax=ax, column="bin_vals", legend=True, cmap="viridis", categorical=True ) 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_axis_off() return ax neo = nuc[nuc["class_name"] == "neoplastic"] plot_neoplastic(neo, col="area", k=5)

Out[ ]:

<Axes: >

Eccentricity

In [14]:

plot_neoplastic(neo, col="eccentricity", k=5)

plot_neoplastic(neo, col="eccentricity", k=5)

Out[14]:

<Axes: >

Fractal Dimension

In [15]:

plot_neoplastic(neo, col="fractal_dimension", k=3)

plot_neoplastic(neo, col="fractal_dimension", k=3)

Out[15]:

<Axes: >

Kernel Density Estimation (KDE) Plots¶

Let's plot all the metrics with KDE with cell type grouping.

In [ ]:

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_theme(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_theme(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 [ ]:

m = list(metrics)
tidy = nuc.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 = nuc.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[ ]:

	Cell Type	Attribute	Values
0	inflammatory	area	294.472159
1	inflammatory	solidity	0.992279
2	inflammatory	major_axis_len	21.976612
3	inflammatory	major_axis_angle	89.999545
4	inflammatory	minor_axis_len	16.976212
...	...	...	...
227183	neoplastic	rectangularity	0.891786
227184	neoplastic	squareness	1.118194
227185	neoplastic	shape_index	0.800407
227186	neoplastic	fractal_dimension	0.984168
227187	neoplastic	perimeter	128.834387

227188 rows × 3 columns

In [ ]:

plot_kde(tidy)

plot_kde(tidy)

Out[ ]:

<seaborn.axisgrid.FacetGrid at 0x71b27cf09340>

Here. it is clear that the inflammatory and neoplastic nuclei differ from the the rest based on the distributions. Inflammatory nuclei 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). In contrast, the neoplastic tend to be larger in size than the rest of the nuclei. This is in line with what we would expect.

Conclusion¶

In this workflow tutorial we have demonstrated how to compute a wide range of morphological shape metrics for nuclei and how to visualize the spatial distributions of selected metrics. This type of analysis can be used to quantify nuclear size and morphology and can be used to evaluate, for example, nuclear pleomorphism.