Utility of local capillary supply indices: Insights from computational image‐based modelling

Muscle oxygenation critically depends on capillary number and distribution within a tissue. Despite the development of numerous morphometric indices to quantify these attributes, many lack sensitivity or validation against local oxygen tension ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:msub><mml:mi>P</mml:mi> <mml:msub><mml:mi>O</mml:mi> <mml:mn>2</mml:mn></mml:msub> </mml:msub> <mml:annotation>${{P}_{{{{\mathrm{O}}}_2}}}$</mml:annotation></mml:semantics> </mml:math> ) in muscle fibres, leading to uncertainty about their physiological relevance and utility for gauging adaptive changes. We assessed six local supply indices to determine which best correlated with and predicted calculated fibre <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:msub><mml:mi>P</mml:mi> <mml:msub><mml:mi>O</mml:mi> <mml:mn>2</mml:mn></mml:msub> </mml:msub> <mml:annotation>${{P}_{{{{\mathrm{O}}}_2}}}$</mml:annotation></mml:semantics> </mml:math> , using high-throughput histological analysis and image-based computational modelling of oxygen transport on digitised rat tibialis anterior sections: capillary contacts (CC_i), individual capillary-to-fibre ratio (C:F_i), capillary-to-fibre perimeter exchange (CFPE_i), local capillary-to-fibre ratio (LCFR_i), local capillary density (LCD_i) and a novel index, D_max, _i, which averages the maximum diffusion distances from capillary domains that overlap a fibre. LCD_i and D_max, _i exhibited the strongest correlations with fibre <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:msub><mml:mi>P</mml:mi> <mml:msub><mml:mi>O</mml:mi> <mml:mn>2</mml:mn></mml:msub> </mml:msub> <mml:annotation>${{P}_{{{{\mathrm{O}}}_2}}}$</mml:annotation></mml:semantics> </mml:math> (linear correlation: 0.8874 and -0.9054, respectively; P < 0.0001). Distance-correlation analysis confirmed both indices as robust predictors of fibre oxygenation (distance correlation: 0.85 and 0.79, respectively; P < 0.0001), demonstrating their ability to capture a curvilinear relationship that plateaus as mean fibre <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:msub><mml:mi>P</mml:mi> <mml:msub><mml:mi>O</mml:mi> <mml:mn>2</mml:mn></mml:msub> </mml:msub> <mml:annotation>${{P}_{{{{\mathrm{O}}}_2}}}$</mml:annotation></mml:semantics> </mml:math> approaches the capillary source <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:msub><mml:mi>P</mml:mi> <mml:msub><mml:mi>O</mml:mi> <mml:mn>2</mml:mn></mml:msub> </mml:msub> <mml:annotation>${{P}_{{{{\mathrm{O}}}_2}}}$</mml:annotation></mml:semantics> </mml:math> (P < 0.0001). Partial least squares and tree-ensemble regressions further identified both indices as the most sensitive and critical predictors of fibre <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:msub><mml:mi>P</mml:mi> <mml:msub><mml:mi>O</mml:mi> <mml:mn>2</mml:mn></mml:msub> </mml:msub> <mml:annotation>${{P}_{{{{\mathrm{O}}}_2}}}$</mml:annotation></mml:semantics> </mml:math> (P < 0.001), suggesting they are less likely to miss early pathophysiological or adaptive responses. These findings support the use of theoretically validated morphometric indices in research and clinical applications, to enhance understanding of fundamental muscle physiology and improve the diagnosis and treatment of muscle-related pathology. KEY POINTS: Assessing muscle oxygenation is fundamental to understanding muscle function and its adaptive or pathological responses. Many indices are used to describe capillary O₂ supply in skeletal muscle, but their physiological relevance in assessing local oxygenation remains uncertain. Using computational modelling of oxygen transport and machine learning, we evaluated six supply indices for their sensitivity in predicting fibre <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:msub><mml:mi>P</mml:mi> <mml:msub><mml:mi>O</mml:mi> <mml:mn>2</mml:mn></mml:msub> </mml:msub> <mml:annotation>${{P}_{{{{\mathrm{O}}}_2}}}$</mml:annotation></mml:semantics> </mml:math> . Area-based indices (LCD_i and D_max, _i) were identified as the most robust predictors of oxygenation and therefore better descriptors of pathophysiological and adaptive responses. These findings are expected to improve both research and clinical assessments of muscle health, streamlining methodologies and enhancing the diagnostic potential for muscle-related pathologies.