Quantifying Neoplastic Nuclear Morphology

Introduction¶

In histopathology and biomedical image analysis, morphological metrics provide valuable insights into the geometry and complexity of nuclei which can be used to evaluate nuclear pleomorphism (variation in the size, shape, and staining characteristics of cell nuclei within a population of cells). Histolytics offers a comprehensive suite of morphological metrics to compute for nuclei and other segmented objects. In this workflow, we will demonstrate how to compute these at WSI-scale and visualize the spatial distributions of some of these metrics.

We will use a WSI from that we segmented in the panoptic segmentation example as our input data. We will also be focusing solely on the neoplastic nuclei in this tutorial.

In [1]:

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

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

In [ ]:

import geopandas as gpd

nuc = gpd.read_parquet("/path/to/nuclei_seg.parquet")  # <- modify path
tis = gpd.read_parquet("/path/to/tissue_seg.parquet")  # <- modify path

ax = tis.plot(figsize=(10, 10), column="class_name", aspect=1, legend=True)
ax.set_axis_off()

import geopandas as gpd nuc = gpd.read_parquet("/path/to/nuclei_seg.parquet") # <- modify path tis = gpd.read_parquet("/path/to/tissue_seg.parquet") # <- modify path ax = tis.plot(figsize=(10, 10), column="class_name", aspect=1, legend=True) ax.set_axis_off()

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",
]

neo_nuc = nuc[nuc["class_name"] == "neoplastic"]
neo_nuc = shape_metric(neo_nuc, metrics=metrics, parallel=True, num_processes=8)
neo_nuc.head()

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", ] neo_nuc = nuc[nuc["class_name"] == "neoplastic"] neo_nuc = shape_metric(neo_nuc, metrics=metrics, parallel=True, num_processes=8) neo_nuc.head()

Out[3]:

	geometry	class_name	id	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
0	POLYGON ((23532.205 71012.364, 23534.206 71014...	neoplastic	NaN	303.179889	0.996454	21.122759	34.167292	18.632316	55.832708	0.998349	0.928748	0.931822	0.471068	0.896783	0.707009	0.770341	1.182519	0.876445	0.970662
1	POLYGON ((23538.205 71151.421, 23534.205 71159...	neoplastic	NaN	595.511364	0.998364	38.856234	80.484152	20.130217	9.515848	0.999083	0.816035	0.817533	0.855339	0.572616	0.708278	0.761344	1.039008	0.703120	0.994011
2	POLYGON ((23526.205 72039.579, 23527.205 72040...	neoplastic	NaN	1668.573991	0.942004	62.826251	70.665622	34.472251	19.334378	0.986742	0.783256	0.804446	0.836025	0.623408	0.738001	0.770433	0.997273	0.730779	1.000368
3	POLYGON ((23528.964 72615.761, 23528.225 72618...	neoplastic	NaN	687.394834	0.996001	35.221928	84.881615	24.344484	5.118385	0.999539	0.901900	0.902731	0.722688	0.687848	0.735519	0.801664	1.148335	0.796325	0.978828
4	POLYGON ((23525.205 72869.579, 23527.205 72871...	neoplastic	NaN	985.062835	0.994368	39.643076	38.579682	31.336595	51.420318	0.998415	0.960170	0.963221	0.612503	0.951165	0.712232	0.792948	1.222527	0.889037	0.970850

Visualizing the Metrics¶

Spatial Plots¶

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

In [4]:

import mapclassify
from histolytics.utils.plot import legendgram
from histolytics.utils.gdf import col_norm


# 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):
    vals = col_norm(neoplastic_nuc[col], "minmax")
    bins = mapclassify.Quantiles(vals, k=k)
    neoplastic_nuc = neoplastic_nuc.assign(bin_vals=bins.yb)
    neoplastic_nuc[f"{col}_minmax"] = vals

    ax = tis.plot(
        figsize=(10, 10), column="class_name", aspect=1, legend=True, alpha=0.1
    )
    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()

    ax.set_axis_off()

    ax = legendgram(
        gdf=neoplastic_nuc,
        column=f"{col}_minmax",
        n_bins=50,
        breaks=bins.bins,
        cmap="viridis",
        ax=ax,
        loc="lower right",
    )

    return ax


plot_neoplastic(neo_nuc, col="area", k=5)

import mapclassify from histolytics.utils.plot import legendgram from histolytics.utils.gdf import col_norm # 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): vals = col_norm(neoplastic_nuc[col], "minmax") bins = mapclassify.Quantiles(vals, k=k) neoplastic_nuc = neoplastic_nuc.assign(bin_vals=bins.yb) neoplastic_nuc[f"{col}_minmax"] = vals ax = tis.plot( figsize=(10, 10), column="class_name", aspect=1, legend=True, alpha=0.1 ) 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() ax.set_axis_off() ax = legendgram( gdf=neoplastic_nuc, column=f"{col}_minmax", n_bins=50, breaks=bins.bins, cmap="viridis", ax=ax, loc="lower right", ) return ax plot_neoplastic(neo_nuc, col="area", k=5)

Out[4]:

<AxesHostAxes: xlabel='Area_Minmax'>

We can tell that the smaller neoplastic nuclei tend to localize at the border regions of the tumor masses.

Eccentricity

In [5]:

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

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

Out[5]:

<AxesHostAxes: xlabel='Eccentricity_Minmax'>

Fractal Dimension

In [6]:

plot_neoplastic(neo_nuc, col="fractal_dimension", k=5)

plot_neoplastic(neo_nuc, col="fractal_dimension", k=5)

Out[6]:

<AxesHostAxes: xlabel='Fractal_Dimension_Minmax'>

Kernel Density Estimation (KDE) Plots¶

Next, we will look at how the distributions of the different attributes look like when we group the nuclei based on their area bins. Larger nuclei should to have different distributions compared to smaller nuclei, and this can be visualized using KDE plots.

In [7]:

import seaborn


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

    # Setup the facets
    facets = seaborn.FacetGrid(
        data=tidy_data,
        col="Attribute",
        hue=hue_col,
        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, hue_col): seaborn.set_style("whitegrid") seaborn.set_theme(font_scale=1.5) # Setup the facets facets = seaborn.FacetGrid( data=tidy_data, col="Attribute", hue=hue_col, 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 [8]:

m = list(metrics)

vals = col_norm(neo_nuc["area"], "minmax")
bins = mapclassify.Quantiles(vals, k=5)
neo_nuc = neo_nuc.assign(bin_vals=bins.yb)


tidy = neo_nuc.reset_index().set_index("bin_vals")
tidy = tidy[m]
tidy = tidy.stack()
tidy = tidy.reset_index()
tidy = tidy.rename(
    columns={"bin_vals": "Area Bin", "level_1": "Attribute", 0: "Values"}
)
tidy.head()

m = list(metrics) vals = col_norm(neo_nuc["area"], "minmax") bins = mapclassify.Quantiles(vals, k=5) neo_nuc = neo_nuc.assign(bin_vals=bins.yb) tidy = neo_nuc.reset_index().set_index("bin_vals") tidy = tidy[m] tidy = tidy.stack() tidy = tidy.reset_index() tidy = tidy.rename( columns={"bin_vals": "Area Bin", "level_1": "Attribute", 0: "Values"} ) tidy.head()

Out[8]:

	Area Bin	Attribute	Values
0	1	area	303.179889
1	1	solidity	0.996454
2	1	major_axis_len	21.122759
3	1	major_axis_angle	34.167292
4	1	minor_axis_len	18.632316

In [9]:

plot_kde(tidy, hue_col="Area Bin")

plot_kde(tidy, hue_col="Area Bin")

Out[9]:

<seaborn.axisgrid.FacetGrid at 0x713627c37bc0>

It looks like smaller nuclei tend to have higher eccentricity and lower circularity overall among the neoplastic nuclei which is an interesting finding. This indicates that the smaller neoplastic nuclei are more elongated and less circular in shape compared to larger neoplastic nuclei.

Conclusion¶

In this workflow tutorial we have demonstrated how to compute a wide range of morphological shape metrics for neoplastic 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 nuclear shape pleomorphism at WSI-scale.