Introduction

In descriptions of the fight-or-flight response,1–5 the actual decision-making process is rarely addressed, and to our knowledge never quantified. We have recently proposed that one of the major criteria in the decision-making process is the level of tissue damage, which is signaled by the level of pain perception.6 The body’s mechanism for detecting and transmitting the information about damage is pain.7,8 Here, we propose that the decision whether to fight or flee should be informed by two important measures of damage: acute damage (acute pain), and cumulative damage (cumulative pain). Cumulative pain refers to the experience of pain that gradually accumulates over time due to the contribution of multiple sources or episodes of damage (eg, multiple animal bites). Unlike acute pain, which is typically a response to an immediate injury or threat, cumulative pain arises from the repetitive or multiplicative nature of pain stimuli.

The body’s pain signaling systems play a key role in how cumulative pain is perceived. Nociceptors, sensory receptors responsible for detecting harmful stimuli, transmit signals to the central nervous system when tissues are damaged or under stress.7,9,10 In cases of cumulative pain, these signals may become more pronounced as the body experiences repeated or chronic stressors. Neuroplasticity – the brain’s ability to adapt and reorganize its neural connections11 – also contributes to the perception of cumulative pain. In some instances, the brain may “sensitize” to persistent pain signals, increasing sensitivity to pain, thereby making previously minor discomforts feel more intense.12–14 Adaptation to pain can also occur. In the following, we illustrate positive cumulation.

Ultimately, the perception of cumulative pain reflects the interaction between the body’s physiological responses, an individual’s emotional and cognitive state, and the broader social environment in which the pain is experienced. This multi-input interaction informs whether the appropriate decision to a pain-generating situation is to fight or to flee.

In a recent publication we proposed the concepts of pain as a part of the fight-or-flight response,6 postulated the existence of a “nocistat”,15 and introduced the mathematical framework of a coupled feedback control loop, using Lotka-Volterra dynamics – originally conceived for so-called predator–prey interaction models,16–20 the dynamics of which are conceptually similar to the postulated relationship between ascending and descending pain pathways – to model the choreographed interaction between “ascending pathways” and “descending pathways” in pain processing.21 This model is based on the realization that the ascending and descending pathways, rather than acting independently, should be connected in a coordinated, coupled, and well-controlled feedback loop. We have shown in another publication (submitted for publication) that our model exhibits an initial indication of the magnitude of the immediate injury by a spike in pain perception, followed by a saturation at a lower pain perception (ie, damping) for the remainder of the pain inflicting signal due to modulation. This current work explores and demonstrates the capabilities of our model when the individual is exposed to consecutive and/or multiple superimposed pain-inflicting events.

Methods

To simulate a cumulative pain experience, a sequence and/or superposition of rapid-onset and short-duration bite or swipe of a paw events inducing acute pain was modeled. Hereby, the sensory input (ie, pain stimulus) of each bite or swipe of a paw event was modeled as a rectangular function with a sudden onset of pain, where, in the absence of modulation M(t), pain perception P(t) rises rapidly in response to the constant pain stimulus S(t) through the ascending pain-transmitting pathways, then returns back to baseline once the pain stimulus has stopped. We add M(t) to include the influence of the descending pain-modulating (attenuating) pathways on the pain perception P(t). The underlying model equations, derived in detail in Fink and Raffa,21 were numerically solved/integrated using the standard Runge-Kutta-4 method with constant time steps,22 and are as follows:

Modulation Change over time (rate): , and

Pain Perception Change over time (rate) with Lotka-Volterra-style coupling (last term) to modulation:

, where

Sensory Input: for t < tonset; S(t) = Smax for tonset ≤ t ≤ toff; 0 for t > toff.

Given the above model equations we were interested in simulating a variety of scenarios of cumulative pain experiences as follows:

Pain perception of a singular bite or swipe of a paw event as a baseline for comparison to the following scenarios; Pain perception of two immediately consecutive bite or swipe of a paw events of the same magnitude; Pain perception of two consecutive bite or swipe of a paw events of the same magnitude with increasing temporal spacing between the first and the second pain signal event; Pain perception of three immediately consecutive bite or swipe of a paw events with differing respective magnitudes, which can be equivalently interpreted as a pain signal that momentarily intensifies/weakens to return back to its original initial level; Pain perception of two immediately consecutive bite or swipe of a paw events with differing respective magnitudes, which can be equivalently interpreted as a pain signal that intensifies/weakens before it vanishes altogether; Pain perception of three immediately consecutive bite or swipe of a paw events with monotonically increasing/decreasing respective magnitudes, which can be equivalently interpreted as a pain signal that intensifies/weakens in two subsequent stages (pain crescendo or decrescendo/diminuendo) before it vanishes altogether.Results

Given the above equations from Fink and Raffa,21Figures 1–6 show the simulation results of the time development of pain perception P(t) and modulation M(t) given a sequence of consecutive pain stimuli S(t) or partially overlapping pain stimuli, where each pain stimulus S(t) is modeled using the above equations, but with varying pain input characteristics.

Figure 1 The pain perception P(t) (middle tracing) and the pain modulation M(t) (bottom tracing) with Lotka-Volterra coupling in response to the pain stimulus time profile S(t) (top tracing), where the sensory input = 1 AU.

Notes: The underlying parameter values for the simulation are: for stimulation event S1(t): tonset = 10 and toff = 50, both in arbitrary time units (eg, seconds, minutes, hours, etc.), Smax= 1 AU. For all other simulation times t: S(t) = 0 AU. For all other model parameters: , , , , and .

Figure 2 The pain perception P(t) (middle tracing) and the pain modulation M(t) (bottom tracing) with Lotka-Volterra coupling in response to two consecutive pain stimuli time profiles S1(t) and S2(t) of same amplitude (top tracing) without time spacing, thereby essentially doubling the duration of the pain signal, where the sensory input = 1 AU for each pain stimulus.

Notes: The underlying parameter values for the simulation are: for stimulation event S1(t): tonset = 10 and toff = 50, and for S2(t): tonset = 50 and toff = 90 – all in arbitrary time units (eg, seconds, minutes, hours, etc). For both S1(t) and S2(t): Smax= 1 AU. For all other simulation times t: S(t) = 0 AU. For all other model parameters: , , , , and .

Figure 3 The pain perception P(t) (middle tracing) and the pain modulation M(t) (bottom tracing) with Lotka-Volterra coupling in response to two consecutive pain stimuli time profiles S1(t) and S2(t) of same amplitude (top tracing) with increasing time spacing (T and B), where the sensory input = 1 AU for each pain stimulus.

Notes: The underlying parameter values for the simulation are: (T) For stimulation event S1(t): tonset = 10 and toff = 50, and for S2(t): tonset = 60 and toff = 100 – all in arbitrary time units (eg, seconds, minutes, hours, etc.). For both S1(t) and S2(t): Smax= 1 AU. (B) For stimulation event S1(t): tonset = 10 and toff = 50, and for S2(t): tonset = 100 and toff = 140 – all in arbitrary time units (eg, seconds, minutes, hours, etc.). For both S1(t) and S2(t): Smax = 1 AU. For all other simulation times t: S(t) = 0 AU. For all other model parameters for (T) and (B): , , , , and .

Figure 4 The pain perception P(t) (middle tracing) and the pain modulation M(t) (bottom tracing) with Lotka-Volterra coupling in response to three consecutive (without time spacing) pain stimuli time profiles S1(t), S2(t), and S3(t) (top tracing), where the sensory input = 1 AU for the first and last pain stimulus and sensory input = 2 AU for the second pain stimulus (T); and the sensory input = 2 AU for the first and last pain stimulus and sensory input = 1 AU for the second pain stimulus (B).

Notes: The underlying parameter values for the simulation are: for stimulation event S1(t): tonset = 10 and toff = 30, for S2(t): tonset = 30 and toff = 50, and for S3(t): tonset = 50 and toff = 70 – all in arbitrary time units (eg, seconds, minutes, hours, etc). (T): for S1(t) and S3(t): Smax= 1 AU, and for S2(t): Smax= 2 AU. (B): for S1(t) and S3(t): Smax= 2 AU, and for S2(t): Smax = 1 AU. For all other simulation times t: S(t) = 0 AU. For all other model parameters for (T) and (B): , , , , and .

Figure 5 The pain perception P(t) (middle tracing) and the pain modulation M(t) (bottom tracing) with Lotka-Volterra coupling in response to two consecutive pain stimuli time profiles S1(t) and S2(t) of different amplitude (top tracing) without time spacing, thereby essentially doubling the duration of the pain signal, where the sensory input = 1 AU for the first and sensory input = 2 AU for the second pain stimulus (TL); sensory input = 1 AU for the first and sensory input = 6 AU for the second pain stimulus (TR); sensory input = 2 AU for the first and sensory input = 1 AU for the second pain stimulus (BL); and sensory input = 6 AU for the first and sensory input = 1 AU for the second pain stimulus (BR).

Notes: The underlying parameter values for the simulation are: for stimulation event S1(t): tonset = 10 and toff = 30, and for S2(t): tonset = 30 and toff = 50 – all in arbitrary time units (eg, seconds, minutes, hours, etc). (TL): for S1(t): Smax = 1 AU, and for S2(t): Smax= 2 AU. (TR): for S1(t): Smax = 1 AU, and for S2(t): Smax = 6 AU. (BL): for S1(t): Smax= 2 AU, and for S2(t): Smax = 1 AU. (BR): for S1(t): Smax= 6 AU, and for S2(t): Smax = 1 AU. For all other simulation times t: S(t) = 0 AU. For all other model parameters for (TL), (TR), (BL), and (BR): , , , , and .

Figure 6 The pain perception P(t) (middle tracing) and the pain modulation M(t) (bottom tracing) with Lotka-Volterra coupling in response to three consecutive pain stimuli time profiles S1(t), S2(t), and S3(t) of different amplitude (top tracing) without time spacing, thereby essentially tripling the duration of the pain signal, where the sensory input = 1 AU for the first, sensory input = 2 AU for the second, and sensory input = 3 AU for the third pain stimulus (T); and sensory input = 3 AU for the first, sensory input = 2 AU for the second, and sensory input = 1 AU for the third pain stimulus (B).

Notes: The underlying parameter values for the simulation are: for stimulation event S1(t): tonset = 10 and toff = 30, for S2(t): tonset = 30 and toff = 50, and for S3(t): tonset = 50 and toff = 70 – all in arbitrary time units (eg, seconds, minutes, hours, etc). (T): for S1(t): Smax = 1 AU, S2(t): Smax = 2 AU, and for S3(t): Smax = 3 AU. (B): for S1(t): Smax = 3 AU, S2(t): Smax = 2 AU, and for S3(t): Smax = 1 AU. For all other simulation times t: S(t) = 0 AU. For all other model parameters for (T) and (B): , , , , and .

For each pain stimulus event, as a net result of an increasing pain perception magnitude and an increasing inhibitory pain modulation, pain perception rises rapidly as a function of stimulus intensity, then begins to decline. However it does not return to zero. Instead, it saturates/plateaus at some value that is intermediately between zero and maximum perception, ie, at a level that is related to the stimulus intensity. Depending on the inter-pain-signal period, a new pain signal is registered as another spike or goes unnoticed if it follows immediately. A new pain signal is also registered, regardless of inter-pain-signal period, if its magnitude differs from the preceding pain signal. This registration manifests either as a momentary spike or dent.

An example of a single acute pain input of rapid onset and rapid offset (a “step” function) is demonstrated in Figure 1. Because of the modulation M(t), the pain perception P(t) registers as a brief spike, then saturates/plateaus at a lower level.

An example of two consecutive pain stimuli of the same amplitude without time spacing between them, thereby essentially doubling the duration of the pain signal, is demonstrated in Figure 2. Because of the modulation M(t), the pain perception P(t) registers as a brief spike, then saturates/plateaus at a lower level across the remainder of the first pain signal and all of the second pain signal.

An example of two consecutive pain stimuli time profiles of the same amplitude with increasing time spacing is demonstrated in Figure 3. Because of the modulation M(t), the pain perception P(t) registers as a brief spike, then saturates/plateaus at a lower level during the first pain signal and the second pain signal, respectively. Of particular interest, the second spike in pain perception P(t) is lower than the first one in the scenario on the top with shorter quiescence time between the two pain stimuli, because the modulation M(t) has not fully returned to baseline yet when the second pain signal occurs. This could be interpreted as a temporary numbing or attenuating effect. This is in contrast to the second scenario (bottom), which results in two identical pain episodes because the inter-pain time period is sufficient for the modulation M(t) to return to baseline before being triggered again by the second pain signal, resulting in the same original pain perception spike.

An example of three consecutive pain stimuli without time spacing and 1 AU (arbitrary units) sensory input for the first and last pain stimulus and double for the second pain stimulus is demonstrated in Figure 4 (top). In the scenario on the top of this Figure, because of the modulation M(t), the pain perception P(t) registers as a brief spike after the onset of the first pain stimulus, then saturates/plateaus at a lower level. It rises again momentarily upon the onset of the second pain stimulus, then saturates/plateaus at a lower but overall higher level than before. At the end of the second pain stimulus, the sensory input returns to the level of the first pain stimulus, which leads to a momentary modulation-mediated pain perception “hyperpolarization”, ie, an inverse “peak” or dent, then saturates/plateaus at a higher level than the dent, which corresponds to the plateau reached during the first pain stimulus. In the scenario on the bottom of Figure 4, because of the modulation M(t), the pain perception P(t) registers as a brief spike after the onset of the first pain stimulus (2 AU), then saturates/plateaus at a lower level. A momentary modulation-mediated pain perception “hyperpolarization”, ie, an inverse “peak” or dent, occurs upon the onset of the second pain stimulus (1 AU), then saturates/plateaus at a higher but overall lower level than before. At the end of the second pain stimulus, the sensory input returns to the level of the first pain stimulus (2 AU), which leads to a brief spike in pain perception, then saturates/plateaus at a lower level than the spike, which corresponds to the plateau reached during the first pain stimulus.

A more complex example of two consecutive pain stimuli of different amplitude without time spacing between them (essentially doubling the duration of the pain signal), with different combinations of input magnitudes, is demonstrated in Figure 5. Under one scenario (top left and right portion of the Figure), because of the modulation M(t), the pain perception P(t) registers as a brief spike, then saturates/plateaus at a lower level of increasing magnitude for both pain stimuli. Depending on the magnitude of the second pain stimulus, the second spike in pain perception P(t) is either lower or higher than the first spike, respectively. Under another scenario (bottom left and right portion of the Figure), because of the modulation M(t), the pain perception P(t) registers as a brief spike, then saturates/plateaus at a lower level for the first pain stimulus, followed by a brief dent with subsequent saturation at a higher (compared to the dent) level. Note, the larger the drop in magnitude of the second pain stimulus, the larger the depth of the dent in pain perception P(t).

A final example, of three consecutive pain stimuli time profiles of different amplitude without time spacing between them (thereby essentially tripling the duration of the pain signal) is demonstrated in Figure 6. Under one scenario (top portion of the Figure), because of the modulation M(t), the pain perception P(t) registers as a brief spike, then saturates/plateaus at a lower level of increasing magnitude, respectively. Even though the increase in magnitude of the second and third pain stimulus is the same, the magnitude change of the second spike in pain perception P(t) is slightly larger than the magnitude change of the third one (even though the absolute magnitude of the third spike is larger than the second one). This is due to the lower level of modulation during the second spike. This also explains why the second and third spike in pain perception are significantly smaller than the first spike even though the respective pain stimuli are increasingly larger than the first one. Under another scenario (bottom portion of the Figure), because of the modulation M(t), the pain perception P(t) registers as a brief spike, then saturates/plateaus at a lower level for the first pain stimulus, followed by two brief dents with subsequent saturation at a higher (compared to the dent) level, but overall decreasing magnitude.

Discussion

The simulation results (Figures 1–6) suggest that our model can be applied to cumulative pain. It can register, monitor, and discern individual consecutive pain signals:

If the inter-pain-signal time is larger than a certain threshold between two consecutive pain signal events during which the model is unable to register another pain event due to elevated modulation from the preceding pain event. This is akin to the notion of a “dead time” of a Geiger-Müller detector,23 ie, the period of time following a radiation detection event where the detector is unable to register another event/count. If the respective magnitude of immediate consecutive pain signals differs, ie, consecutive pain signals have different magnitudes. If during superposition of (partially) concurrent pain signals the magnitude of the resulting superimposed pain signal changes during an ongoing pain signal event. For example, if the subject is bitten by a wild animal, and during that time suffers another bite by another animal.

Moreover, while a consecutive higher magnitude pain stimulus is registered as a momentary spike in pain perception, a consecutive lower magnitude pain stimulus is registered as a momentary “dent” in pain perception akin to hyperpolarization in cells. One might call it a modulation-mediated pain perception hyperpolarization.

It should be noted that the original “fight-or-flight” concept has been expanded to the “predatory imminence continuum theory”.24–26 This model categorizes three stages: pre-encounter, post-encounter, and circa-strike, each activated by different levels of fear. Our formulation models what occurs during the third stage.

We recognize that the decision to fight or flee in response to a given magnitude of pain (tissue damage) is based on more than the contemporary level of pain. Other influences and contributing factors include: past experiences, training, pre-encounter anxiety level, age, a disability that inhibits the ability to flee, genetic sensitivity to pain, environmental factors, physiologic drivers (eg, degree of hunger of the predator), pre-encounter assessment of the threat, whether or not others are present (ie, alone or in a pack), focus (distractions present), other damage-assessment modalities (eg, visual cues), and cognitive interpretation of events.

It recently has been proposed that the brain computes fear by integrating space and time to guide survival behavior.27 Defensive responses are envisioned as organized along neural circuits that scale with threat imminence, shifting from higher cortical regions involved in planning and prediction to subcortical circuits that support rapid, reflexive action. Spatial distance, temporal proximity, and uncertainty shape fear-related decision-making and behavior. Fear is framed as an adaptive computational process that dynamically selects defensive strategies to maximize survival.

Conclusion

The modulation of pain, for example by the diffuse noxious inhibitory control (DNIC) pathways and mechanisms,28 appears to provide an organism a quantifiable mechanism to monitor cumulative injury (ie, multiple pain signals), since as P(t) declines after a single stimulus, it does not return to zero (or baseline). Instead it settles at a lower plateau level that is maintained essentially for the duration of the stimulus input. With each subsequent stimulus, the effect on the plateau can be cumulative, as a sort of pain memory “trace”. Therefore, in addition to a measure of the damage of an individual event (eg, claw swipe), a measure of the cumulative damage would be monitored (eg, multiple claw strikes). This would allow for time and intensity discrimination helpful for deciding whether to fight or to flee.

Funding

This research was supported in part by the Edward & Maria Keonjian Endowment in the College of Engineering at the University of Arizona.

Disclosure

The authors have no conflicts of interest to declare for this work.

References

1. Cannon WB. Bodily Changes in Pain, Hunger, Fear and Rage: An Account of Recent Researches Into the Function of Emotional Excitement. New York: D. Appleton; 1915.

2. Fanselow MS, Lester LS. A functional behavioristic approach to aversely motivated behavior: predatory imminence as a determinant of the topography of defensive behavior. In: Bolles RC, Beecher MD, editors. Evolution and Learning. Erlbaum; 1988:185–211.

3. Hashemi MM, Gladwin TE, de Valk NM, et al. Neural dynamics of shooting decisions and the switch from freeze to fight. Sci Rep. 2019;9(1):4240. doi:10.1038/s41598-019-40917-8

4. Kozlowska K, Walker P, McLean L, Carrive P. Fear and the defense cascade: clinical implications and management. Harv Rev Psychiatry. 2015;23(4):263–287. doi:10.1097/HRP.0000000000000065

5. Mobbs D, Petrovic P, Marchant JL, et al. When fear is near: threat imminence elicits prefrontal-periaqueductal gray shifts in humans. Science. 2007;317(5841):1079–1083. doi:10.1126/science.1144298

6. Raffa RB, Fink W, Tripathi AD. On including pain as an integral part of the fight-or-flight response. J Pain Res. 2024;17:3667–3668. doi:10.2147/JPR.S500847

7. Bourne S, Machado AG, Nagel SJ. Basic anatomy and physiology of pain pathways. Neurosurg Clin N Am. 2014;25(4):629–638. doi:10.1016/j.nec.2014.06.001

8. Middleton SJ, Barry AM, Comini M, et al. Studying human nociceptors: from fundamentals to clinic. Brain. 2021;144(5):1312–1335. doi:10.1093/brain/awab048

9. Garland EL. Pain processing in the human nervous system: a selective review of nociceptive and biobehavioral pathways. Prim Care. 2012;39(3):561–571. doi:10.1016/j.pop.2012.06.013

10. Gonzalez-Hermosillo DC, Gonzalez-Hermosillo LM, Villasenor-Almaraz M, et al. Current concepts of pain pathways: a brief review of anatomy, physiology, and medical imaging. Curr Med Imaging. 2023. doi:10.2174/1573405620666230519144112

11. Gazerani P. The neuroplastic brain: current breakthroughs and emerging frontiers. Brain Res. 2025;1858:149643. doi:10.1016/j.brainres.2025.149643

12. Nijs J, George SZ, Clauw DJ, et al. Central sensitisation in chronic pain conditions: latest discoveries and their potential for precision medicine. Lancet Rheumatol. 2021;3(5):e383–e392. doi:10.1016/S2665-9913(21)00032-1

13. Afridi B, Khan H, Akkol EK, Aschner M. Pain perception and management: where do we stand? Curr Mol Pharmacol. 2021;14(5):678–688. doi:10.2174/1874467213666200611142438

14. Latremoliere A, Woolf CJ. Central sensitization: a generator of pain hypersensitivity by central neural plasticity. J Pain. 2009;10(9):895–926. doi:10.1016/j.jpain.2009.06.012

15. Raffa RB, Fink W, Tripathi AD. Postulate of the existence of a ‘Nocistat’: rationale and implications for novel analgesics. J Pain Res. 2025;18:1945–1947. doi:10.2147/JPR.S524175

16. Lotka AJ. Contribution to the theory of periodic reaction. J Phys Chem. 1910;14(3):271–274. doi:10.1021/j150111a004

17. Lotka AJ. Analytical note on certain rhythmic relations in organic systems. Proc Natl Acad Sci U S A. 1920;6(7):410–415. doi:10.1073/pnas.6.7.410

18. Lotka AJ. Elements of Physical Biology. Baltimore: Williams & Wilkins; 1925:495.

19. Volterra V. Variations and fluctuations of the number of individuals in animal species living together. In: Chapman RN, editor. Animal Ecology. 1st ed. McGraw-Hill; 1931:409–448.

20. Goel NS, Maitra SC, Montroll EW. On the volterra and other nonlinear models of interacting populations. In: Reviews of Modern Physics Monographs. New York: Academic Press; 1971.

21. Fink W, Raffa RB. A pluripotent progression of the gate control system theory of pain – modeling ascending & descending pain pathways as a Lotka-Volterra coupled control & feedback loop. J Pain Res. 2025;18:4373–4385. doi:10.2147/JPR.S525449

22. Press WH, Flannery BP, Teukolsky SA, Vetterling WT. Numerical Recipes in C, the Art of Scientific Computing. 2nd ed. Cambridge: Cambridge University Press; 1992.

23. Costrell L. Accurate determination of the deadtime and recovery characteristics of Geiger-Muller counters. J Res Natl Bur Stand. 1949;42(3):241–249. doi:10.6028/jres.042.020

24. Bolles RC, Fanselow MS. A perceptual-defensive-recuperative model of fear and pain. Behav Brain Sci. 1980;3(2):291–301. doi:10.1017/S0140525X0000491X

25. Bouton ME, Mineka S, Barlow DH. A modern learning theory perspective on the etiology of panic disorder. Psychol Rev. 2001;108(1):4–32. doi:10.1037/0033-295x.108.1.4

26. Fanselow MS, Lester LS. A functional behavioristic approach to aversively motivated behavior: predatory imminence as a determinant of the topography of defensive behavior. In: Beecher MD, editor. Evolution and Learning. Erlbaum; 1988.

27. Mobbs D, Headley DB, Ding W, Dayan P. Space, Time, and Fear: survival computations along defensive circuits. Trends Cognit Sci. 2020;24(3):228–241. doi:10.1016/j.tics.2019.12.016

28. Bannister K, Kucharczyk MW, Graven-Nielsen T, Porreca F. Introducing descending control of nociception: a measure of diffuse noxious inhibitory controls in conscious animals. Pain. 2021;162(7):1957–1959. doi:10.1097/j.pain.0000000000002203