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Design Prompts for Metric Illustrations

This document contains detailed prompts for claude.ai/design to generate explanatory graphics for dosemetrics metrics that are not yet covered by the slide visuals from the Joseph Weibel MSc Thesis Defense (University of Bern).

Visual Theme Reference

All graphics should match the aesthetic of the existing slide illustrations:

  • Background: white (#FFFFFF)
  • Primary accent: deep red (#CC0000 / University of Bern red)
  • Secondary fills: light red / pink (#FFCCCC or rgba(204,0,0,0.15))
  • Structure contours: solid black lines, 2 px
  • Prescription isodose contours: dashed red lines
  • Text labels: black for anatomy labels; dark red for formula annotations
  • Grid lines: light grey (#EEEEEE), subtle
  • Charts: axes in dark grey with tick marks; curve in solid red (target), dashed black (prediction/reference)
  • Formula style: serif math font (LaTeX-style), black, below the diagram
  • Layout: diagram on the left or centre, formula below or to the right; single title in bold sans-serif at top

Group 1 — DVH Point Metrics

1a. Volume at Dose (VX) — compute_volume_at_dose

Prompt:

Create a clean educational diagram explaining the "Volume at Dose" (VX) DVH metric for radiotherapy documentation.

Left panel — DVH diagram: Draw a smooth cumulative dose-volume histogram curve in solid red. X-axis labelled "DOSE (Gy)", Y-axis labelled "VOLUME (%)". Mark a vertical dashed line at a specific dose value "X Gy" on the x-axis. Draw a horizontal dashed line from the intersection of the DVH curve and the vertical line across to the y-axis, landing at a value labelled "VX (%)". Shade the area to the left of the vertical line under the DVH curve in light red. Add annotation arrows pointing to: the DVH curve labelled "cumulative DVH", the intersection point labelled "read-off point", and the y-axis landing point labelled "VX".

Right panel — formula: Display the formula: V_X = DVH(X Gy) = |{v ∈ V_structure : d_v ≥ X}| / |V_structure| Below the formula, add a one-line note: "VX is the fraction of the structure receiving at least X Gy."

Style: white background, red curve, University of Bern red (#CC0000), sans-serif axis labels, LaTeX-style formula. Title: "Volume at Dose (VX)".

1b. Dose at Volume (DX) — compute_dose_at_volume

Prompt:

Create a clean educational diagram explaining the "Dose at Volume" (DX) DVH metric for radiotherapy documentation.

Left panel — DVH diagram: Draw a smooth cumulative DVH curve in solid red. X-axis "DOSE (Gy)", Y-axis "VOLUME (%)". Mark a horizontal dashed line at a volume fraction "X %" on the y-axis. Draw a vertical dashed line from the intersection of the DVH curve and the horizontal line down to the x-axis, landing at a value labelled "DX (Gy)". Shade the region above the horizontal line (the top X% of the volume) in light red. Add annotation arrows: DVH curve labelled "cumulative DVH"; y-axis level labelled "X% of volume"; x-axis landing point labelled "DX".

Right panel — formula: DX = min{d : DVH(d) ≤ X/100} Below: "DX is the minimum dose received by at least X% of the structure volume." Add a small example table: | Metric | Volume fraction | Meaning | |--------|----------------|---------| | D95 | 95% | Near-minimum (coverage dose) | | D50 | 50% | Median dose | | D2 | 2% | Near-maximum dose |

Style: white background, University of Bern red (#CC0000). Title: "Dose at Volume (DX)".

Group 2 — Dose Summary Statistics

2a. Mean, Max, Min, Median Dose

Prompt:

Create a four-panel educational diagram showing four DVH-derived dose statistics (mean, max, min, median) for radiotherapy documentation.

Use a single representative cumulative DVH curve (smooth S-shape in red) shown in each panel. White background with light grey grid lines.

Panel 1 (Mean Dose, D̄): Shade the entire DVH area under the curve in light red. Mark the mean dose on the x-axis with a vertical dashed line labelled "D̄". Formula below: D̄ = (1/N) Σ dᵢ

Panel 2 (Max Dose, Dmax): Mark the rightmost non-zero point of the DVH curve (where volume approaches 0%) with a vertical dashed red line labelled "Dmax". Annotate: "D0 — dose at 0% volume".

Panel 3 (Min Dose, Dmin): Mark the leftmost point where the DVH drops below 100% with a vertical dashed red line labelled "Dmin". Annotate: "D100 — dose at 100% volume".

Panel 4 (Median Dose, D50): Mark the horizontal line at 50% volume and drop a vertical dashed red line to the x-axis labelled "D50". This is identical to the DX diagram at X=50%.

Layout: 2×2 grid of panels. Each panel has the same axes ("DOSE (Gy)" / "VOLUME (%)"). Title above each panel: "Mean Dose", "Max Dose", "Min Dose", "Median Dose". Overall title: "DVH Dose Statistics". University of Bern red (#CC0000), sans-serif.

2b. Equivalent Uniform Dose (EUD) — compute_equivalent_uniform_dose

Prompt:

Create an educational diagram explaining Equivalent Uniform Dose (EUD) for radiotherapy documentation.

Left panel — concept illustration: Draw two stacked panels: - Top: A pixelated/voxelised cross-section of a target structure (circle or oval). Each pixel is shaded from light to dark red representing varying dose levels (heterogeneous distribution). Label individual pixel doses: some at 55 Gy, some at 65 Gy, some at 60 Gy. Label the structure "heterogeneous dose distribution". Add a small colour bar below labelled "DOSE (Gy)". - Bottom: The same target structure, but uniformly shaded in a single medium red. Label it "uniform EUD distribution". Add a label "EUD = equivalent uniform dose". Connect the two panels with a double-headed arrow labelled "biologically equivalent".

Right panel — formula: EUD = (1/N · Σ dᵢᵃ)^(1/a) Add a table: | Tissue type | Parameter a | Interpretation | |-------------|-------------|---------------| | Serial OAR | a >> 1 | Sensitive to hot spots | | Tumour | a < 0 | Sensitive to cold spots | | Parallel OAR| a ≈ 1 | Mean dose |

Style: white background, University of Bern red (#CC0000). Title: "Equivalent Uniform Dose (EUD)".

Group 3 — Conformity Variations

3a. ICRU Conformity Index — compute_conformity_index

Prompt:

Create an educational diagram explaining the ICRU Conformity Index (CI) for radiotherapy documentation.

Diagram: Draw two concentric shapes on a white background with light grey grid lines: - An irregular solid-black-outline shape labelled "Target (V_target)" — slightly oval. - Overlapping this, a dashed red boundary shape labelled "Prescription isodose (V_rx)" that is slightly offset and larger than the target on one side, smaller on another. - Shade the overlap region (intersection) in medium red and label it "V_target_rx (overlap)". - Shade the prescription isodose region outside the target in light red/pink and label it "dose outside target". - Shade the target region outside the prescription isodose in light grey and label it "underdosed target".

Formula below: CI_ICRU = V_target_rx / V_rx Add interpretation: "CI = 1.0: all irradiated tissue is inside the target (ideal). CI < 1.0: dose spills outside the target."

Style: white background, University of Bern red (#CC0000). Title: "ICRU Conformity Index (CI)".

3b. RTOG Conformity Index — compute_rtog_conformity_index

Prompt:

Create an educational diagram explaining the RTOG Conformity Index for radiotherapy documentation.

Diagram: Draw two concentric shapes on white background with grey grid: - Solid-black-outline oval labelled "Target (V_target)", size reference = 1. - Dashed red outline of a larger oval labelled "Prescription isodose (V_rx)". - Shade V_rx in light red. Shade V_target within it in medium red. - Add bidirectional arrows: one for the diameter of V_target, one for the diameter of V_rx. - Label the ratio: "RTOG CI = V_rx / V_target = 1.8" as an example.

Formula below: RTOG CI = V_rx / V_target Add RTOG interpretation table: | RTOG CI | Grade | |---------|-------| | 1.0–2.0 | Acceptable | | < 1.0 or 2.0–2.5 | Minor deviation | | > 2.5 | Major deviation |

Style: white background, University of Bern red (#CC0000). Title: "RTOG Conformity Index".

3c. Coverage and Spillage — compute_coverage / compute_spillage

Prompt:

Create a side-by-side educational diagram showing Coverage and Spillage for radiotherapy documentation.

Left panel — Coverage: Draw an irregular oval (target V_target, solid black outline). Inside the oval, shade 85% of the area in medium red and label it "covered (V_target_rx)". Leave a small white crescent along one edge labelled "underdosed (not reached by Rx isodose)". Below: Coverage = V_target_rx / V_target = 0.85

Right panel — Spillage: Draw the same target oval (solid black). Surround it with a larger dashed red outline (prescription isodose V_rx). Shade the area inside V_rx but outside V_target in pink, labelled "dose spill (V_rx − V_target_rx)". Shade the overlap in medium red, labelled "V_target_rx". Below: Spillage = (V_rx − V_target_rx) / V_rx Add note: "Coverage + Spillage complement each other. High coverage is desired; low spillage is desired."

Style: white background, University of Bern red (#CC0000). Overall title: "Coverage and Spillage".

Group 4 — Advanced Homogeneity

4a. Coefficient of Variation — compute_dose_homogeneity

Prompt:

Create an educational diagram explaining the Coefficient of Variation (CV) as a dose homogeneity metric for radiotherapy documentation.

Left panel — histogram: Draw a bell-curve histogram of voxel doses within a target, x-axis "DOSE (Gy)", y-axis "NUMBER OF VOXELS". Mark the mean dose (μ) with a vertical solid red line. Mark one standard deviation (σ) on each side with dashed red lines. Shade the σ band in light red. Label μ and σ explicitly.

Right panel — formula: CV = σ / μ where σ = standard deviation of dose in the structure, μ = mean dose. Add comparison table: | CV value | Interpretation | |----------|---------------| | < 0.03 | Highly homogeneous | | 0.03–0.10 | Acceptable | | > 0.10 | Inhomogeneous |

Style: white background, University of Bern red (#CC0000). Title: "Coefficient of Variation (Dose Homogeneity)".

4b. Uniformity Index — compute_uniformity_index

Prompt:

Create an educational diagram explaining the Uniformity Index (UI) for radiotherapy documentation.

Left panel — DVH diagram: Draw a steep cumulative DVH curve (near-ideal homogeneous plan) in solid red. Mark on the x-axis: Dmin (leftmost point at 100% volume), Dref (median, middle), and Dmax (rightmost point at 0% volume). Draw vertical dashed lines at Dmin and Dmax. Shade the range between Dmin and Dmax in light red along the x-axis. Label the span "(Dmax − Dmin)".

Right panel — formula: UI = 1 − (Dmax − Dmin) / Dref Add note: "UI = 1.0: perfectly uniform (Dmax = Dmin = Dref). UI < 1: dose spread within the target."

Style: white background, University of Bern red (#CC0000). Title: "Uniformity Index (UI)".

Group 5 — Geometric Overlap Metrics

5a. Dice Coefficient and Jaccard Index

Prompt:

Create a side-by-side educational diagram explaining the Dice Similarity Coefficient (DSC) and Jaccard Index (IoU) for radiotherapy structure comparison.

Shared diagram (centre, used for both): Draw two partially overlapping circles/ovals: - Left oval: solid black outline, labelled "Structure A (reference)", lightly shaded grey. - Right oval: dashed red outline, labelled "Structure B (predicted)", lightly shaded pink. - Overlap region: shaded in medium red, labelled "|A ∩ B|". - Add labels for the non-overlapping portions: "|A \ B|" (left) and "|B \ A|" (right). - Add total area labels "|A|" and "|B|".

Left formula panel: DSC = 2|A ∩ B| / (|A| + |B|) "Range: 0 (no overlap) to 1 (perfect match). Ideal: DSC = 1.0."

Right formula panel: Jaccard = |A ∩ B| / |A ∪ B| "Relation: Jaccard = DSC / (2 − DSC)."

Style: white background, University of Bern red (#CC0000). Title: "Dice Coefficient and Jaccard Index".

5b. Volume Difference and Volume Ratio

Prompt:

Create an educational diagram showing Volume Difference and Volume Ratio for structure comparison in radiotherapy.

Left panel — Volume Difference: Draw two structures (ovals) side by side, one larger (reference, solid black) labelled "V_ref = 120 cc" and one smaller (predicted, dashed red) labelled "V_pred = 95 cc". Below: ΔV = |V_ref − V_pred| = 25 cc.

Right panel — Volume Ratio: Draw the same two structures. Below: VR = V_pred / V_ref = 95/120 = 0.79. Add note: "VR = 1.0: same volume. VR < 1: under-segmentation. VR > 1: over-segmentation."

Style: white background, University of Bern red (#CC0000). Title: "Volume Difference and Volume Ratio".

Group 6 — Surface Distance Metrics

6a. Hausdorff Distance — compute_hausdorff_distance

Prompt:

Create an educational diagram explaining the Hausdorff Distance (HD) for surface-to-surface structure comparison in radiotherapy.

Diagram: Draw two irregular closed contours on a white background with grid lines: - Solid black contour: "Reference structure". - Dashed red contour: "Predicted structure" — slightly offset, with one protrusion that extends further from the reference. - Draw multiple arrows from points on the reference contour to the nearest point on the predicted contour (and vice versa). Show the arrows as thin grey. - Highlight the single longest such minimum-distance arrow in solid red and bold, labelled "Hausdorff Distance (HD) = max of all nearest-neighbour distances".

Formula below: HD(A, B) = max(sup_{a∈A} inf_{b∈B} d(a,b), sup_{b∈B} inf_{a∈A} d(a,b)) Add note: "HD is determined by the single worst-case surface mismatch. Sensitive to outliers."

Style: white background, University of Bern red (#CC0000). Title: "Hausdorff Distance".

6b. Mean Surface Distance — compute_mean_surface_distance

Prompt:

Create an educational diagram explaining Mean Surface Distance (MSD) for structure comparison in radiotherapy.

Diagram: Draw two irregular close contours on white background with grid: - Solid black contour: "Reference". - Dashed red contour: "Predicted" — slightly offset uniformly. - Draw multiple evenly spaced arrows from points on the reference contour to the nearest point on the predicted contour. Label a few arrow lengths: "d₁ = 1.2 mm", "d₂ = 0.8 mm", "d₃ = 1.5 mm", etc. All arrows thin grey, equal weight (contrast with HD where one is highlighted). - Shade the gap between the two contours in light red.

Formula below: MSD = (1/|∂A|) Σ_{a∈∂A} inf_{b∈∂B} d(a,b) Add note: "MSD averages all surface distances — robust to small outliers. Lower is better."

Style: white background, University of Bern red (#CC0000). Title: "Mean Surface Distance (MSD)".

Group 7 — Sensitivity and Specificity

7a. Sensitivity and Specificity — compute_sensitivity / compute_specificity

Prompt:

Create an educational diagram explaining Sensitivity and Specificity in the context of binary structure segmentation for radiotherapy.

Left panel — 2×2 confusion matrix: Draw a 2×2 grid: - Columns: "Reference: Positive (in structure)" | "Reference: Negative (outside)" - Rows: "Predicted: Positive" | "Predicted: Negative" - Fill cells: TP (medium red, top-left), FP (light pink, top-right), FN (light grey, bottom-left), TN (white, bottom-right). - Label each cell: "TP (true positive)", "FP (false positive)", "FN (false negative)", "TN (true negative)".

Right panel — formulas: Sensitivity (Recall) = TP / (TP + FN) Specificity = TN / (TN + FP) Add interpretation: "Sensitivity = fraction of reference structure voxels correctly identified. Specificity = fraction of non-structure voxels correctly excluded."

Style: white background, University of Bern red (#CC0000). Title: "Sensitivity and Specificity".

Group 8 — Gamma Analysis Variants

8a. Gamma Passing Rate — compute_gamma_passing_rate

Prompt:

Create an educational diagram explaining the Gamma Passing Rate for dose distribution comparison in radiotherapy.

Left panel — gamma map: Draw a circular "body mask" cross-section filled with a 2D heatmap of gamma index values. Voxels with γ < 1.0 should be shaded white-to-light-red (passing). Voxels with γ ≥ 1.0 (failing) should be shaded in dark solid red. Show ~10% of voxels in dark red as failing. Add a colour bar labelled "γ value": light = 0, dark = ≥ 1.

Right panel — formula: Pass Rate = (1/N) Σᵢ 1[γ(vᵢ) ≤ 1] × 100% Add note: "A voxel passes if its gamma index γ ≤ 1.0. The passing rate is the percentage of all evaluated voxels that pass." Add a typical clinical threshold: "Clinical criterion: Pass Rate ≥ 95% for 3%/3mm".

Style: white background, University of Bern red (#CC0000). Title: "Gamma Passing Rate".

8b. 2D Gamma — compute_2d_gamma

Prompt:

Create an educational diagram explaining 2D Gamma Index analysis for per-slice dose QA in radiotherapy.

Left panel — 2D slice view: Draw a 2D cross-section grid (10×10 cells). Fill each cell with a colour from white (low dose) to medium red (high dose) representing a dose distribution. Overlay thin black circles at each cell centre representing the "distance-to-agreement" search radius for a specific voxel. Highlight one central voxel in bold red outline, with a larger dashed red circle showing the DTA search radius Δd. Label: "centre voxel v" and "search radius Δd".

Right panel — formula: γ₂D(v) = min_{v'} √( r²(v,v') / (Δd)² + δ²(v,v') / (ΔD)² ) ≤ 1 Note: "2D gamma is computed slice-by-slice. Faster than 3D gamma; appropriate for per-slice patient-specific QA."

Style: white background, University of Bern red (#CC0000). Title: "2D Gamma Index".

Group 9 — Voxel-Based Dose Comparison

9a. Mean Absolute Error (MAE) — compute_mae

Prompt:

Create an educational diagram explaining Mean Absolute Error (MAE) for 3D dose comparison in radiotherapy.

Left panel — heatmap: Draw a circular body-mask cross-section. Fill it with a 2D heatmap showing |D_pred − D_target| at each voxel — white where the two plans agree, dark red where they differ most. Add a colour bar: "0 Gy" (white) to "|ΔD| max" (dark red). Label the structure "body mask".

Right panel — formula: MAE = (1/N) Σᵢ |D_pred,i − D_target,i| Add comparison with MSE/RMSE: "MAE treats all errors equally (linear). RMSE penalises large errors more (quadratic). Both measure voxel-wise accuracy."

Style: white background, University of Bern red (#CC0000). Title: "Mean Absolute Error (MAE)".

9b. Structural Similarity Index (SSIM) — compute_ssim

Prompt:

Create an educational diagram explaining the Structural Similarity Index (SSIM) for dose distribution comparison in radiotherapy.

Left panel — side-by-side dose slices: Draw two small square dose maps (5×5 grid cells each): - Left: "Reference dose" — smooth gradient from light to dark red. - Right: "Predicted dose" — similar but with slight Gaussian blur/noise applied, making gradients slightly softer. - Label both with "DOSE (Gy)" colour bars.

Centre panel — component breakdown: Show three component bars: - Luminance similarity (l) = comparison of mean doses - Contrast similarity (c) = comparison of dose variance - Structure similarity (s) = cross-correlation of dose patterns Draw each as a horizontal bar from 0 to 1, shaded in red proportional to value. Label numerical examples: l=0.98, c=0.95, s=0.91.

Right panel — formula: SSIM(x, y) = l(x,y)^α · c(x,y)^β · s(x,y)^γ Range: [−1, 1]. SSIM = 1.0: identical distributions. Note: "SSIM captures perceptual similarity — two plans can have the same MAE but very different SSIM if dose gradients differ."

Style: white background, University of Bern red (#CC0000). Title: "Structural Similarity Index (SSIM)".

9c. Dose Difference Map — compute_dose_difference_map

Prompt:

Create an educational diagram explaining the Dose Difference Map for radiotherapy plan comparison.

Three-panel layout (left → right):

Panel 1 — Reference dose: A circular cross-section with smooth dose gradient, light to dark red. Title: "Target dose". Colour bar: "DOSE (Gy)".

Panel 2 — Predicted dose: Similar cross-section with slightly different pattern. Title: "Predicted dose". Colour bar: "DOSE (Gy)".

Panel 3 — Difference map: A diverging-colour cross-section (blue = predicted lower, white = equal, red = predicted higher). Title: "Difference (Pred − Target)". Colour bar from "−ΔD" to "+ΔD". Show some localised red hotspots and blue cold regions.

Formula below all three: ΔD(v) = D_pred(v) − D_target(v) for each voxel v

Style: white background; for difference map use blue-white-red diverging scale with University of Bern red (#CC0000) for positive values. Title: "Dose Difference Map".

9d. Variance of Laplacian — compute_variance_of_laplacian

Prompt:

Create an educational diagram explaining the Variance of Laplacian as a dose sharpness metric for radiotherapy.

Left panel — smooth dose plan: Draw a 2D cross-section with a smooth, gently varying dose gradient (IMRT-like). Overlay the computed Laplacian as a subtle contour map with few lines. Label: "low VoL — smooth gradients". Show a small numerical example: VoL = 0.002.

Right panel — complex dose plan: Draw a 2D cross-section with many sharp dose boundaries, steep falloff edges, and complex gradient patterns (VMAT with many fields). Overlay a denser Laplacian contour map with many lines. Label: "high VoL — complex gradients". Show: VoL = 0.018.

Formula below both: VoL = Var[∇²D] where ∇²D is the discrete 3D Laplacian of the dose array. Note: "Higher VoL = sharper, more complex dose gradients. Useful for comparing plan complexity or modality (3DCRT vs IMRT vs VMAT)."

Style: white background, University of Bern red (#CC0000). Title: "Variance of Laplacian (Plan Sharpness)".

Group 10 — Advanced DVH Statistical Metrics

10a. DVH Wasserstein Distance — compute_dvh_wasserstein_distance

Prompt:

Create an educational diagram explaining the Wasserstein (earth-mover's) Distance between two DVH curves for radiotherapy dose comparison.

Left panel — DVH diagram: Draw two smooth cumulative DVH curves on the same axes (X: "DOSE (Gy)", Y: "VOLUME (%)"): - Solid red: "Target DVH" - Dashed black: "Predicted DVH" - Shade the vertical gaps between the two curves at multiple dose points in light red. - Draw several horizontal arrows between the two curves at different volume levels, labelled "transport distance".

Right panel — analogy: Draw a simple illustration of two piles of dirt (representing the two DVH distributions), with an arrow and a small cartoon shovel between them. Label: "Wasserstein = minimum work to transform one distribution into the other".

Formula below: W(F, G) = ∫₀¹ |F⁻¹(p) − G⁻¹(p)| dp where F and G are the cumulative DVH functions.

Style: white background, University of Bern red (#CC0000). Title: "DVH Wasserstein Distance".

10b. DVH Confidence Interval — compute_dvh_confidence_interval

Prompt:

Create an educational diagram explaining DVH Confidence Intervals for dose distribution uncertainty quantification in radiotherapy.

Diagram: Draw a central solid red DVH curve (mean DVH) with a shaded band around it representing the 95% confidence interval in light red/pink. Add two additional dashed red curves bounding the band: "95% CI upper" and "95% CI lower". X-axis: "DOSE (Gy)", Y-axis: "VOLUME (%)". Add several thin translucent grey curves inside the band representing individual sample DVHs from a population. Label the band width at D50 with a bidirectional arrow: "CI width at D50".

Formula below: CI = [D̄_X − z·σ/√n, D̄_X + z·σ/√n] where D̄_X is the mean dose at volume fraction X, σ is the standard deviation, and n is the number of samples. Note: "Confidence intervals quantify how much DVH metrics vary across a patient cohort or across planning iterations."

Style: white background, University of Bern red (#CC0000). Title: "DVH Confidence Interval".

10c. Mutual Information — compute_mutual_information

Prompt:

Create an educational diagram explaining Mutual Information (MI) between two dose distributions in radiotherapy.

Left panel — joint histogram: Draw a 2D heatmap (scatter density plot) where the x-axis is "Reference dose (Gy)" and y-axis is "Predicted dose (Gy)". Points clustered tightly around the diagonal (y = x line) in dark red; scatter in lighter red. Draw the diagonal line in black. Label: "perfect agreement → points on diagonal → high MI".

Right panel — Venn-diagram of information: Draw two overlapping circles: - Left circle: H(X) = entropy of reference dose distribution - Right circle: H(Y) = entropy of predicted dose distribution - Overlap: I(X;Y) = mutual information, shaded in medium red. Label each region.

Formula below: I(X; Y) = H(X) + H(Y) − H(X, Y) = Σ_{x,y} p(x,y) log(p(x,y) / (p(x)p(y)))

Style: white background, University of Bern red (#CC0000). Title: "Mutual Information (MI)".

10d. KS Test and Chi-Square on DVH — compute_dvh_ks_test / compute_dvh_chi_square

Prompt:

Create a side-by-side educational diagram explaining the Kolmogorov-Smirnov test and Chi-Square test applied to DVH curves for radiotherapy.

Left panel — KS test: Draw two cumulative DVH curves (solid red = target, dashed black = predicted). Draw a vertical double-headed arrow at the dose point where the two curves are furthest apart, labelled "KS statistic D = max|F(x) − G(x)|". Shade this maximum gap in red. Below: "KS test detects any shape difference along the full DVH. p-value tests significance."

Right panel — Chi-square test: Draw the same two DVH curves, but now divide the x-axis into discrete dose bins (vertical grey lines). For each bin, show a small rectangle whose height represents the observed difference in frequency between target and predicted. Shade positive differences in red, negative in pink. Below: χ² = Σ (O − E)² / E, where O = predicted bin count, E = reference bin count.

Style: white background, University of Bern red (#CC0000). Overall title: "Statistical DVH Tests (KS and Chi-Square)".

Usage Notes