Background <p>Mader’s mathematical model, widely employed for endurance performance prediction, aims to accurately represent metabolic response to exercise. However, it traditionally overlooks dynamic changes in metabolic processes at varying movement velocities.</p> Methods <p>This narrative review examined the effect of cycling cadence on its key input parameters, including oxygen demand per Watt (<InlineEquation ID="IEq1000"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="421_2024_5663_Article_IEq1000.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="48" /> </InlineMediaObject> <EquationSource Format="TEX">\(\text{CE}_{{\dot{\text{V}}}\text{O2}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mtext>CE</mtext> <mrow> <mover accent="true"> <mtext>V</mtext> <mo>˙</mo> </mover> <mtext>O2</mtext> </mrow> </msub> </math></EquationSource> </InlineEquation>), resting oxygen uptake (<InlineEquation ID="IEq1001"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="421_2024_5663_Article_IEq1001.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="56" /> </InlineMediaObject> <EquationSource Format="TEX">\({{\dot{\text{V}}}\text{O}_{\text{2Base}}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mover accent="true"> <mtext>V</mtext> <mo>˙</mo> </mover> <msub> <mtext>O</mtext> <mtext>2Base</mtext> </msub> </mrow> </math></EquationSource> </InlineEquation>), maximal oxygen uptake (<InlineEquation ID="IEq1002"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="421_2024_5663_Article_IEq1002.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="54" /> </InlineMediaObject> <EquationSource Format="TEX">\({{\dot{\text{V}}}\text{O}_{\text{2max}}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mover accent="true"> <mtext>V</mtext> <mo>˙</mo> </mover> <msub> <mtext>O</mtext> <mtext>2max</mtext> </msub> </mrow> </math></EquationSource> </InlineEquation>), and maximal blood lactate accumulation rate (<i>v</i>La<sub>max</sub>). These findings were integrated into the model to assess cadence-induced variations in predicted power output at maximal aerobic power (MAP), maximal lactate steady state (MLSS), and peak fat oxidation (FAT<sub>max</sub>).</p> Results <p>A U-shaped relationship was found between cadence and both <InlineEquation ID="IEq1004"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="421_2024_5663_Article_IEq1004.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="48" /> </InlineMediaObject> <EquationSource Format="TEX">\(\text{CE}_{{\dot{\text{V}}}\text{O2}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mtext>CE</mtext> <mrow> <mover accent="true"> <mtext>V</mtext> <mo>˙</mo> </mover> <mtext>O2</mtext> </mrow> </msub> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq1005"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="421_2024_5663_Article_IEq1005.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="56" /> </InlineMediaObject> <EquationSource Format="TEX">\({{\dot{\text{V}}}\text{O}_{\text{2Base}}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mover accent="true"> <mtext>V</mtext> <mo>˙</mo> </mover> <msub> <mtext>O</mtext> <mtext>2Base</mtext> </msub> </mrow> </math></EquationSource> </InlineEquation>, while <InlineEquation ID="IEq1006"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="421_2024_5663_Article_IEq1006.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="54" /> </InlineMediaObject> <EquationSource Format="TEX">\({{\dot{\text{V}}}\text{O}_{\text{2max}}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mover accent="true"> <mtext>V</mtext> <mo>˙</mo> </mover> <msub> <mtext>O</mtext> <mtext>2max</mtext> </msub> </mrow> </math></EquationSource> </InlineEquation> remained largely cadence-independent within typical cadences. <i>v</i>La<sub>max</sub> exhibited a polynomial increase with cadence, attributed to changes in lactate elimination, suggesting cadence-independent maximal glycolytic flux. Incorporating these findings into Mader’s model considering various scenarios revealed significant cadence-induced variations, with power output differences of up to &gt; 100 W. Using cadence-dependent <InlineEquation ID="IEq1007"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="421_2024_5663_Article_IEq1007.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="48" /> </InlineMediaObject> <EquationSource Format="TEX">\(\text{CE}_{{\dot{\text{V}}}\text{O2}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mtext>CE</mtext> <mrow> <mover accent="true"> <mtext>V</mtext> <mo>˙</mo> </mover> <mtext>O2</mtext> </mrow> </msub> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq1008"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="421_2024_5663_Article_IEq1008.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="56" /> </InlineMediaObject> <EquationSource Format="TEX">\({{\dot{\text{V}}}\text{O}_{\text{2Base}}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mover accent="true"> <mtext>V</mtext> <mo>˙</mo> </mover> <msub> <mtext>O</mtext> <mtext>2Base</mtext> </msub> </mrow> </math></EquationSource> </InlineEquation> while maintaining constant <InlineEquation ID="IEq1009"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="421_2024_5663_Article_IEq1009.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="54" /> </InlineMediaObject> <EquationSource Format="TEX">\({{\dot{\text{V}}}\text{O}_{\text{2max}}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mover accent="true"> <mtext>V</mtext> <mo>˙</mo> </mover> <msub> <mtext>O</mtext> <mtext>2max</mtext> </msub> </mrow> </math></EquationSource> </InlineEquation> and <i>v</i>La<sub>max</sub> yielded polynomial power output-cadence relationships, with optimal cadences of 84&#xa0;rpm at MAP, 80&#xa0;rpm at MLSS, and 70&#xa0;rpm at FAT<sub>max</sub>. Incorporating cadence-dependent <i>v</i>La<sub>max</sub> produced implausible results, supporting cadence-independent maximal glycolytic flux. A hypothesized cadence-dependent <InlineEquation ID="IEq1010"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="421_2024_5663_Article_IEq1010.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="54" /> </InlineMediaObject> <EquationSource Format="TEX">\({{\dot{\text{V}}}\text{O}_{\text{2max}}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mover accent="true"> <mtext>V</mtext> <mo>˙</mo> </mover> <msub> <mtext>O</mtext> <mtext>2max</mtext> </msub> </mrow> </math></EquationSource> </InlineEquation> improved alignment between model predictions and empirical data.</p> Conclusion <p>Neglecting dynamic changes in metabolic processes across different movement velocities can lead to inaccurate modelling results. Incorporating cadence alongside established parameters enhances the precision of Mader’s metabolic model for cycling performance prediction.</p> Graphical abstract <p></p>

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Enhancing endurance performance predictions: the role of movement velocity in metabolic simulations demonstrated by cycling cadence

  • Anna Katharina Dunst,
  • Clemens Hesse,
  • Olaf Ueberschär

摘要

Background

Mader’s mathematical model, widely employed for endurance performance prediction, aims to accurately represent metabolic response to exercise. However, it traditionally overlooks dynamic changes in metabolic processes at varying movement velocities.

Methods

This narrative review examined the effect of cycling cadence on its key input parameters, including oxygen demand per Watt ( \(\text{CE}_{{\dot{\text{V}}}\text{O2}}\) CE V ˙ O2 ), resting oxygen uptake ( \({{\dot{\text{V}}}\text{O}_{\text{2Base}}}\) V ˙ O 2Base ), maximal oxygen uptake ( \({{\dot{\text{V}}}\text{O}_{\text{2max}}}\) V ˙ O 2max ), and maximal blood lactate accumulation rate (vLamax). These findings were integrated into the model to assess cadence-induced variations in predicted power output at maximal aerobic power (MAP), maximal lactate steady state (MLSS), and peak fat oxidation (FATmax).

Results

A U-shaped relationship was found between cadence and both \(\text{CE}_{{\dot{\text{V}}}\text{O2}}\) CE V ˙ O2 and \({{\dot{\text{V}}}\text{O}_{\text{2Base}}}\) V ˙ O 2Base , while \({{\dot{\text{V}}}\text{O}_{\text{2max}}}\) V ˙ O 2max remained largely cadence-independent within typical cadences. vLamax exhibited a polynomial increase with cadence, attributed to changes in lactate elimination, suggesting cadence-independent maximal glycolytic flux. Incorporating these findings into Mader’s model considering various scenarios revealed significant cadence-induced variations, with power output differences of up to > 100 W. Using cadence-dependent \(\text{CE}_{{\dot{\text{V}}}\text{O2}}\) CE V ˙ O2 and \({{\dot{\text{V}}}\text{O}_{\text{2Base}}}\) V ˙ O 2Base while maintaining constant \({{\dot{\text{V}}}\text{O}_{\text{2max}}}\) V ˙ O 2max and vLamax yielded polynomial power output-cadence relationships, with optimal cadences of 84 rpm at MAP, 80 rpm at MLSS, and 70 rpm at FATmax. Incorporating cadence-dependent vLamax produced implausible results, supporting cadence-independent maximal glycolytic flux. A hypothesized cadence-dependent \({{\dot{\text{V}}}\text{O}_{\text{2max}}}\) V ˙ O 2max improved alignment between model predictions and empirical data.

Conclusion

Neglecting dynamic changes in metabolic processes across different movement velocities can lead to inaccurate modelling results. Incorporating cadence alongside established parameters enhances the precision of Mader’s metabolic model for cycling performance prediction.

Graphical abstract