# Reply to the letter: To consider the exercise density in the dose-response relationship: the idea is promising, the operationalization tricky!

Fabian Herold, Liye Zou, Paula Theobald, Patrick Manser, Ryan Falck, Qian Yu, Teresa Liu-Ambrose, Arthur F. Kramer, Kirk I. Erickson, Boris Cheval, et al.

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Fabian Herold, Liye Zou, Paula Theobald, Patrick Manser, Ryan Falck, et al.. Reply to the letter: To consider the exercise density in the dose-response relationship: the idea is promising, the operationalization tricky!. European Journal of Applied Physiology, 2025, 10.1007/s00421-025-06003-w. hal-05456660

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# Reply to the letter: To consider the exercise density in the dose-response relationship: the idea is promising, the operationalization tricky!

Fabian Herold¹, ∗ · Liye Zou² · Paula Theobald³ · Patrick Manser⁴ · Ryan S. Falck⁵,⁶,⁷,⁸ · Qian Yu² ·

Teresa Liu-Ambrose⁶,⁷,⁸ · Arthur F. Kramer⁹ · Kirk I. Erickson¹⁰,¹¹,¹² · Boris Cheval¹³,¹⁴ · Yanxia Chen² ·

Matthew Heath¹⁵,¹⁶,¹⁷ · Zhihao Zhang² · Toru Ishihara¹⁸ · Keita Kamijo¹⁹ · Soichi Ando²⁰ · Joseph T. Costello²¹ ·

Mats Hallgren²²,²³ · David Moreau²⁴ · Vahid Farrahi²⁵ · David A. Raichlen²⁶,²⁷ · Emmanuel Stamatakis²⁸,²⁹ ·

Michael J. Wheeler²³,³⁰ · Neville Owen³⁰,³¹ · Sebastian Ludyga³² · Henning Budde³³ · Thomas Gronwald³⁴,³⁵

Received: 13 September 2025 / Accepted: 19 September 2025

© The Author(s) 2025

**Keywords** Physical exercise · Sedentary behavior · Brain · Cognition · Dose

## Introduction

We thank Desgorces for taking the time to read our recent publication in the European Journal of Applied Physiology (Herold et al. 2025b) and providing an insightful commentary (Desgorces 2025). In his commentary, Desgorces (2025) supports our view that density is an important variable for analyzing and prescribing the dose and dosage of physical activity (PA) in the consideration of their effects on brain health. However, he also acknowledges that quantifying PA density is challenging, which is underlined by different perspectives on its definition, operationalization, and interpretation. In this context, we are pleased to have the opportunity for further clarification and for a constructive discussion by providing our perspective on the points raised by Desgorces (2025) in this reply. While we acknowledge the points raised in Desgorces’ commentary (2025), our response provides additional support for our understanding of PA density as conveyed in our initial review.

## Definition of density

Desgorces (2025) is accurate in noting that our definition of the term *density* differs from the International System of Units (i.e., Système International d’Unités; SI), which

is an established and globally used measurement standard based on the metric system (Gilbey and Wilson 2020). Specifically, SI broadly defines density as *mass divided by volume*. In contrast, we provide a PA-specific definition of density, particularly as the *timing of PA* (also referred to as *work bout[s]*) within a single PA bout as well as the *timing between successive PA bouts* within a specific time period (e.g., day, week, month, or year) by providing information on the temporal intervals (i.e., time spent resting; also referred to as rest, recovery, or relief bouts) within or between successive PA bouts (Herold et al. 2025a, b; Manci et al. 2024).

Interestingly, a comparable discourse has emerged concerning the term (*training* load (Impellizzeri et al. 2022a, b; Staunton et al. 2021, 2022). In this context, Impellizzeri and colleagues (2022a; b) assert that employing the SI to operationally describe and define a phenomenon in the broader field of exercise science (i.e., constructs such as *training load*, or exercise and training variables such as *density*) is not justified because the SI is neither an obligation nor a requirement for the purpose of scientific communication. Moreover, Desgorces’ (2025) narrow application for the definition of density does not acknowledge that the term *density* is often used in other scientific disciplines (e.g., psychology) to reflect the general principle relating to a quantity’s distribution (e.g., number of individuals; analogously number of PA and rest bouts) within a given space (e.g., per square mile; analogously total time spent on PA and timing of PA and rest bouts within this period) (https://dictionary.apa.org/density).

Thus, we believe that using the term *density*, when appropriately contextualized (e.g., as PA density), and

Communicated by Michalis G Nikolaidis.

Extended author information available on the last page of the article
as done by others (Bompa 2009; Hernández-Lougedo et al. 2021), is appropriate for scientific communication, although we acknowledge that others may prefer to use other terms, such as ‘interbout interval’ (Yin et al. 2025), to refer to this phenomenon.

## Operationalization of density

Desgorces' commentary (2025) questioned the operationalization of *density* through the quantification of the duration of the rest/recovery bout(s)/interval(s)/period(s), as he assumes '*that rest duration does not directly provide the value of density.'* This appraisal is inconsistent with the definition and operationalization of density in the broader exercise science literature (Bompa 2009; Hernández-Lougedo et al. 2021). In direct support of this view, Bompa (2009) states, '*The density of training can be thought of as a relationship that is expressed in units of time between working and recovery phases of training. Thus, the greater the density of training, the shorter the recovery time between working phases of training.*' Bompa's definition (2009) and operationalization of density directly support our position (i) that this variable can be quantified by the rest duration between two successive bouts of PA, and (ii) that a greater PA density is characterized by shorter rest durations, and, vice versa, a lower PA density is defined by longer ones (Herold et al. 2025a, b; Manci et al. 2024). Thus, the alternative interpretation of PA density proposed in Desgorces' commentary (2025), namely that '*a 3-min rest period should represent greater density than a 1-min period*', should be treated cautiously because it is neither consistent with the general interpretation of this term in other scientific disciplines, such as psychology (e.g., Would one attribute 'greater density' to a non-crowded environment with more physical space per individual [analogously to a 3-min rest period], or to a crowed environment with less physical space per individual [analogous to a 1-min rest period]?—[https://dicti onary.apa.org/density]), nor those provided in the broader exercise science literature (Bompa 2009).

Thus, and consistent with the broader exercise science literature concerning the definition and operationalization of density (Hernández-Lougedo et al. 2021; Bompa 2009), we maintain the opinion that (i) density can be quantified by the rest duration and timing of PA within a single PA bout as well as the timing between successive PA bouts within a specific time period, and (ii) a longer rest duration (e.g., more time between successive bouts of PA), which allows for a longer and tendentially more substantial recovery, reflects a *lower* instead of a *greater* density.

## Density in the context of physical activity dose and dosage

Desgorces (2025) states in his commentary that the manipulation of density would result in changes of the '*total exercise dose*' (i.e., '*...when the protocols promoted changes in the exercise density, this concomitantly led to alterations in the total exercise dose.'*), and suggested an alternative approach to incorporate density to quantify PA dose (i.e., '*...we propose that the maximal duration achieved in each exercise design (including rest bouts) can represent the maximal dose (Desgorces et al. 2020). The dose of an exercise would, thus, be defined as the percentage of this maximum.*'). Before discussing these points in more detail, it is imperative to clarify the terms *dose* and *dosage*, as a definition of '*total exercise dose*' and an explanation of how it differs from '*maximal dose*' are absent in Desgorces' commentary (2025).

## Definition of dose and dosage in the broader physical activity literature

Within the exercise science literature, the *dose* is typically defined as a product of exercise variables (e.g., exercise intensity, exercise duration, type of exercise), and training variables (e.g., frequency of training sessions) (Solomon 2018; Wasfy and Baggish 2016; Williams et al. 2019). Therefore, *dose* is synonymous with *training load* (Impellizzeri et al. 2023), which is a higher order, multidimensional, and latent construct commonly defined as *input variable(s) to elicit a change in a specific outcome of interest* (Impellizzeri et al. 2019, 2020, 2023; McLaren et al. 2022). In this context, a single ‘gold standard’ metric for operationalizing the *dose/dosage/training load* is unlikely to exist, as the validity and appropriateness of a metric depend on the particular aim and application scenario of the intervention (Herold et al. 2019; Impellizzeri et al. 2023; Lambert and Borresen 2010; McLaren et al. 2022). For clarification and in reference to the comment by Desgorces (2025), in our previous work on this topic, we added the discourse on *dose* by proposing that (i) it can be defined as specific indicators of internal load for which there is evidence that they are (causally) involved in the complex psychophysiological processes that drive the desired changes in outcomes of interest (Gronwald et al. 2020; Herold et al. 2019, 2020, 2025b), with internal load as the psychophysiological response to external load (i.e., work performed by an individual independent of individual characteristics) and further influencing factors (e.g., environmental and/or personal factors) (Bourdon et al. 2017; Impellizzeri et al. 2019; Wallace et al. 2009), and (ii) it should be differentiated from the term *dosage* (i.e., *dose*

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provided over a particular time; Gronwald et al. 2020, Her-
old et al. 2020, Herold et al. 2025b).

Density—an essential piece of the puzzle
to determine physical activity dose and dosage
with higher precision

Although a definition of ‘total exercise dose’ is absent in
the work of Desgorces (2025), it is plausible to assume that
manipulating one exercise or training variable, regardless
of whether this variable will be frequency, intensity, time
(duration), type, or density of the PA intervention, will alter
the dose and dosage of the intervention. Such an interpreta-
tion is well-supported by the scientific literature on this topic
(Buchheit and Laursen 2013a, b; Impellizzeri et al. 2019,
2020, 2023; Toigo and Boutellier 2006). Undoubtedly, alter-
ing the PA dose and dosage by purposefully manipulating
exposure to a particular exercise or training variable (i.e.,
density) is the key to isolating its effects on specific health-
related outcomes (e.g., brain health), and thus for gaining a
more comprehensive understanding of dose–response rela-
tionships that are often not well understood, especially in the
PA-brain health field (Erickson et al. 2019, 2022).

As discussed in our previous work (Herold et al. 2025a,
b; Manci et al. 2024), and reflected in relatively low report-
ing rates in empirical studies (see the systematic review
with meta-analysis of Manser and colleagues (2024) for an
example), PA density has been neglected in contemporary
PA research practice compared to other exercise and train-
ing variables (e.g., exercise intensity and training duration),
whose effects on health-related outcomes are frequently
studied (e.g., in meta-analyses investigating PA effects on
specific markers for brain health; Falck et al. 2019; Ludyga
et al. 2020; Mavilidi et al. 2025; Northey et al. 2018; Singh
et al. 2025). This is precisely why we call in our work for
future research on density, a qualitative, yet underrecognized
property of the PA dose and dosage, providing important
information on the timing and clustering of PA (Herold
et al. 2025a, b; Manci et al. 2024)—a view supported by
Desgorces (2025).

As pointed out in our original work (Herold et al. 2025b), it is worth highlighting that manipulating the *density* should not be equated with manipulating *frequency* (i.e., the number of PA bouts within a specific time period (Herold et al. 2025a, b; Manci et al. 2024)). Thus, when elucidating the effect of *density*, the total number of physical exercise sessions, as planned and structured forms of PA (Caspersen et al. 1985), within a specific time interval (i.e., frequency, such as three planned physical exercise sessions per week) should be kept comparable between groups exercising at different densities (e.g., the ‘low-density’ group exercises on Day 1, Day 3, and Day 5, whereas the ‘high-density’ group exercises on Day 1, Day 2, and Day 3; see also Fig. 1b in

our original work; Herold et al. 2025b). Considering a time
frame of 7 days provided in the example, it is unquestionable
that a PA intervention that rigorously controls for frequency
(i.e., with the same number of physical exercise bouts in
both intervention groups) and other relevant exercise and
training variables (e.g., intensity, type, duration) will result
in different ‘final’ rest durations. In particular, the ‘high-
density’ group will have a maximum of 4 days of rest after
the last exercise session in a period of 7 days (i.e., Day 4
to Day 7) compared to the ‘low-density’ group which will
have a maximum of 2 days of rest after the last exercise ses-
sion in the same period (i.e., Day 6 and Day 7). While the
pattern of the final rest durations between the two density
groups differs fundamentally within the example period of
7 days, studies must be designed with careful considera-
tion of the long-term periodization of the PA intervention
(e.g., Does the ‘high-density’ group’s longer final rest dura-
tion at the end of the 7 days lead into another high-density
exercise block in the next training period?). This inherently
longer final rest duration in the ‘high-density’ group, when
rigorously controlling for frequency, can be considered a
potential challenge when studying the effects of density,
depending on study aim and context, and is a consideration
specifically demonstrated in Fig. 1b in our original work
(Herold et al. 2025b).

Desgorces' commentary (2025) posed the question of whether '...density of exercise [would] remain unchanged when an exercise is performed at a higher intensity with an unchanged rest duration?'. Based on the definition of density in our previous work (Herold et al. 2025a, b; Manci et al. 2024) and those provided in the broader exercise science literature (Bompa 2009; Hernández-Lougedo et al. 2021), PA density will remain unchanged in this example because the rest duration, as its key feature, is not manipulated. From a practical perspective, one could argue that the rest duration, and thus the density, could be adjusted (e.g., extended) to account for the increase in exercise intensity. However, such a potential adjustment of density strongly depends on further variables in the PA prescription puzzle, considering the intervention aims and context.

Taking the broader exercise science literature on PA
dose and dosage (i.e., synonymous with training load) into
account, we believe that the assumptions and contextualiza-
tion of density in terms of the constructs provided in our
original proposal (Herold et al. 2025b) are entirely valid
and appropriate. However, as detailed in our previous work
(Herold et al. 2025b), we agree with Desgorces' position
(2025) that a precise determination of PA dose and dosage,
including the variable density, can indeed be 'tricky'. This
has been acknowledged in our previous work (Herold et al.
2025b) as follows: ‘...we wish to emphasize that the precise
characterization or prescription of a specific PA dosage will
remain a considerable challenge...’.
**Summary**

In conclusion, we are grateful for the insightful commentary of Desgorces (2025), highlighting different views on the definition, operationalization, and interpretation of PA density, and providing an important impetus to discuss challenges related to the accurate determination of PA dose and dosage, particularly for PA density as one variable, in more depth. We hope that this reply and related discussion will contribute to a critical, yet constructive scientific discourse that will enable the identification of suitable approaches to determine PA dose and dosage, including PA density, in specific application scenarios with high precision. Characterizing the PA dose and dosage with high precision is an important prerequisite for a better understanding of PA-related health effects, which, in turn, is an essential piece of information for optimizing health-related PA recommendations and interventions.

**Acknowledgements** The authors have nothing to acknowledge.

**Author contributions** F.H.: conceptualization, writing—original draft; L.Z., P.T., P.M., R.F., Q.Y., T.L.-A., A.F.K., K.E., B.C., Y.C., M.H., Z.Z., T.I., K.K., S.A., J.C., M.H., D.M., V.F., D.R., E.S., M.W., N.O., S.L., H.B.: writing—review and editing. T.G.: writing—review and editing, supervision. F.H. is responsible for the overall content as guarantor. All authors read and approved the final version of the manuscript.

**Funding** Open Access funding enabled and organized by Projekt DEAL. This research was not funded by a specific grant issued by a funding agency in the public, commercial, or not-for-profit sectors.

**Data availability** Data sharing does not apply to this article because no data were created or analyzed for this review article.

**Declarations**

**Conflict of interest** The authors declare no conflict of interest or competing interests.

**Generative AI and AI-assisted technologies in the writing process** During the preparation of this work, the author(s) did not use generative AI or AI-assisted technologies. The author(s) take(s) full responsibility for the content of the published article.

**Open Access** This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

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Authors and Affiliations

Fabian Herold¹,¹• · Liye Zou² · Paula Theobald³ · Patrick Manser⁴ · Ryan S. Falck⁵,⁶,⁷,⁸ · Qian Yu² ·

Teresa Liu-Ambrose⁶,⁷,⁸ · Arthur F. Kramer⁹ · Kirk I. Erickson¹⁰,¹¹,¹² · Boris Cheval¹³,¹⁴ · Yanxia Chen² ·

Matthew Heath¹⁵,¹⁶,¹⁷ · Zhihao Zhang² · Toru Ishihara¹⁸ · Keita Kamijo¹⁹ · Soichi Ando²⁰ · Joseph T. Costello²¹ ·

Mats Hallgren²²,²³ · David Moreau²⁴ · Vahid Farrahi²⁵ · David A. Raichlen²⁶,²⁷ · Emmanuel Stamatakis²⁸,²⁹ ·

Michael J. Wheeler²³,³⁰ · Neville Owen³⁰,³¹ · Sebastian Ludyga³² · Henning Budde³³ · Thomas Gronwald³⁴,³⁵

☒ Fabian Herold
fabian.herold@hmu-erfurt.de

Thomas Gronwald
Thomas.Gronwald@medicalschool-hamburg.de

1 Department of Physiology, HMU Health and Medical University Erfurt, Erfurt, Thuringia, Germany

2 Body-Brain-Mind Laboratory, Shenzhen University, Shenzhen, China

3 Research Group Degenerative and Chronic Diseases, Movement, Faculty of Health Sciences Brandenburg, University of Potsdam, Potsdam, Germany

4 Division of Physiotherapy, Department of Neurobiology, Care Sciences and Society, Karolinska Institute, Stockholm, Sweden

5 School of Biomedical Engineering, The University of British Columbia, Vancouver, BC, Canada

6 Aging, Mobility, and Cognitive Health Laboratory, Department of Physical Therapy, The University of British Columbia, Vancouver, BC, Canada

7 Djavad Mowafaghian Centre for Brain Health, Vancouver Coastal Health Research Institute, Vancouver, BC, Canada

8 Centre for Aging Solutions for Mobility, Activity, Rehabilitation and Technology (SMART) at Vancouver Coastal Health, Vancouver Coastal Health Research Institute, Vancouver, BC, Canada

9 Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana, IL, USA

¹⁰ Department of Neuroscience, AdventHealth Research Institute, AdventHealth, Orlando, FL, USA

11 Department of Psychology, University of Pittsburgh, Pittsburgh, PA, USA

12 Center for the Neural Basis of Cognition, University of Pittsburgh, Pittsburgh, PA, USA

13 Department of Sport Sciences and Physical Education, Ecole Normale Supérieure Rennes, Bruz, France

14 Laboratory VIPS2, University of Rennes, Rennes, France

15 School of Kinesiology, Faculty of Health Sciences, University of Western Ontario, London, ON N6A 3K7, Canada

16 Canadian Centre for Activity and Aging, University of Western Ontario, London, ON N6A 3K7, Canada

17 Graduate Program in Neuroscience, University of Western Ontario, London, ON N6A 3K7, Canada

¹⁸ Graduate School of Human Development and Environment, Kobe University, Kobe, Japan

19 Faculty of Liberal Arts and Sciences, Chukyo University, Nagoya, Japan

20 Graduate School of Informatics and Engineering, The University of Electro-Communications, Tokyo, Japan

21 Extreme Environments Laboratory, School of Psychology, Sport and Health Sciences, University of Portsmouth, Portsmouth, UK

22 Epidemiology of Psychiatric Conditions, Substance Use and Social Environment (EPiCSS), Department of Public Health Sciences, Karolinska Institute, Solna, Sweden

23 Institute for Physical Activity and Nutrition (IPAN), School of Exercise and Nutrition Sciences, Deakin University, Geelong, Australia

24 School of Psychology and Centre for Brain Research, University of Auckland, Auckland, New Zealand

25 Institute for Sport and Sport Science, TU Dortmund University, Dortmund, Germany

26 Human and Evolutionary Biology Section, Department of Biological Sciences, University of Southern California, Los Angeles, CA 90089, USA

27 Department of Anthropology, University of Southern California, Los Angeles, CA 90089, USA

28 Mackenzie Wearables Research Hub, Charles Perkins Centre, University of Sydney, Sydney, NSW, Australia

29 School of Health Sciences, Faculty of Medicine and Health, University of Sydney, Sydney, NSW, Australia

30 Physical Activity Laboratory, Baker Heart & Diabetes Institute, Melbourne, VIC, Australia

31 Centre for Urban Transitions, Swinburne University of Technology, Melbourne, VIC, Australia

32 Department of Sport, Exercise and Health, University of Basel, Basel, Switzerland

33 Institute for Systems Medicine (ISM), MSH Medical School Hamburg University of Applied Sciences and Medical University Hamburg, Hamburg, Germany

34 Institute of Interdisciplinary Exercise Science and Sports Medicine, MSH Medical School Hamburg, Am Kaiserkai 1, 20457 Hamburg, Germany

35 G-Lab, Faculty of Applied Sport Sciences and Personality, BSP Business and Law School, Berlin, Germany