Acute/short-term effects of stretching


Stretching is a critical component of many regimens seen in clinical and fitness settings. Whether you’re a person who prefers to stretch before/after your routine, many people will attest to the physiological benefits of stretching. Proponents of stretching believe that it improves performance during exercise and prevents injuries and soreness. Some would go so far as to say that an individual may not be stretching enough when they repeatedly experience pain or injury after their workouts with no signs of improvement. Despite these enduring beliefs, the science behind the benefits of stretching is questionable. For the purposes of this blog post, we will focus on the acute, short-term effects of stretching on performance during exercise.

Three forms of stretching  used in exercise and rehabilitation settings include dynamic stretching, ballistic stretching, and static stretching. Dynamic stretching is a type of stretching which involve fluid-exaggerated movements. Ballistic stretching utilizes fast countermovements. Static stretching involves extending target muscles to a limit point, and maintaining that position for an interval between 10 and 30 seconds. In order to minimize injuries, static stretching is encouraged for non-athletes.

Numerous scientific studies have shown that have shown that static stretching results in an improved joint range of motion  (ROM) and greater flexibility in the muscles targeted by this technique. Conversely, research has also shown that stretching before exercises can result in a lower force output generated in the muscles that are targeted. Compliance is the lengthening of muscle fibers in response to an applied force. According to an article cited by the the National Institute of Health (Anderson, 2005), increased compliance (which occurs a result of stretching) has been linked to a decreased ability to absorb force at rest, whereas decreased compliance results in a muscle being able to withstand higher tension. This is significant because, when sarcomeres are stretched to the point that the actin and myosin filaments do not overlap, the force absorbed is transmitted to the muscle fiber cytoskeleton; resulting in fiber damage (regardless of a muscle’s joint ROM). Thus, compliance may result in decreased performance depending on the type of exercise performed. Another issue that arises related to the use of stretching before exercise is the type of stretching utilized. Science has shown that muscle fibers can experience tension when stretched as little as 20% of their total length1. Thus, it is difficult to establish a universal standard describing correct stretching techniques. In addition, improved joint ROM can be attributable to extraneous factors (such as increased pain tolerance); making the strength of its relationship to stretching highly questionable.

There are a plethora of studies conducted that attempt to quantify the effect of stretching on performance. One study, conducted by researchers at Sahmyook University in 20182 examined the effects of stretching on muscle strength, endurance, and endurance in a non-athletic sample of 13 active collegiate male students. These subjects were separated into three groups: those who did not perform any warm ups before exercise  (NWU), those who performed aerobic warm ups in the form of power walking for ten minutes (AWU) before exercise, and those who performed aerobic warm ups with static stretching for ten minutes (ASU). All three groups performed isokinetic muscle testing. The stretching used in the study consisted of straddling, seated calf stretching, and standing quadriceps stretching for the lower body. Two repetitions of each stretching motion were performed for 20 sec each and the entire stretching program took 5 min to perform. All subjects rested for 1 min after warming up and then underwent isokinetic muscle testing of the knee joints. The sequence of performance of each warm-up exercise was individually randomized. In the successive weeks, each group was tested according to the type of warm-up performed. The testing was conducted for 3 weeks, and all groups were allowed a week to rest in between tests.

In order to quantify the results in each group, a knee extension/flexion isokinetic  dynamometer was used. Participants were asked to extend and flex the knee by exerting their maximum strength as fast as possible while keeping their trunk up against the backrest during the test and to hold onto the handles. The subjects performed the maximal test of four repetitions. Each maximal test was conducted with an angular speed of 60°/sec to measure isokinetic muscle strength and an angular speed of 180°/sec to measure isokinetic muscle power. In addition, the muscle endurance test was conducted with an angular speed of 240°/sec. The exercise was conducted twice prior to testing to familiarize the subjects with the test, thereby achieving optimal results. The subjects were verbally encouraged and allowed to view their torque graphs during testing as a form of visual feedback to increase motivation.  To analyze muscle strength, power and endurance, measurements of the left and right knee joints were divided into each independent variable before data processing was performed. In addition, psychological evaluations in the form of questionnaires were administered to subjects before and after workouts for individuals in all three groups. These assessments utilized a 5-point Likert scale (1, very bad; 2, bad; 3, average; 4, good; 5, very good). The Kruskal–Wallis rank test were used to examine the differences of variables among groups and the Wilcoxon test was used to investigate psychological conditions before and after warm-ups within times in each group. A Mann–Whitney post hoc test was implemented to detect any significant differences in the Kruskal–Wallis test. The significance of all data was established at p ≤0.05. The results from the table have been included in figures attached to this post. The data is shown in the bottom of this point via a hyperlink. 

Based on the results of this experiment, the researchers concluded that there was no significant effect of the type of warm-up activity on performance in any of the tests performed in this study. Shown in Table 2, at 60°/sec (which is an angular speed for rating muscle strength), the NWU showed higher rates for both the extensor and flexor. However, the researchers determined that the difference was not statistically significant Shown in Table 3, at 180°/sec (an angular speed associated with rating muscle power), AWU and ASW groups attained higher rates for the flexor and extensor, respectively, although the difference was not statistically significant. The total work at 240°/sec (which reflects muscle endurance) was higher in ASW for both the flexor and extensor than NWU and AWU, though not statistically significantly. These results are shown in Table 4. In a similar manner to the trends seen when evaluating athletic performance, the individuals in the ASW group marked higher scores on their psychological assessments than the AWU and NWU groups. The results are shown in Table 5. However, the researchers determined that the result were not statistically significant.

Overall, while there appears to be some merit to the psychological benefits of stretching before exercising, its effect on athletic performance remains inconclusive. However, if you find that stretching helps improve your outlook/state-of-mind during the course of your workout, I would highly encourage you to continue your routine.


Questions to Consider

  1. Based on the experiment, do you believe that stretching before a workout provides any benefits/advantages towards performance?
  2. Does this post affect your views towards stretching?
  3. Would you encourage someone seeking to exercise more frequently to stretch before/after their exercises?



  1. Andersen JC. Stretching before and after exercise: effect on muscle soreness and injury risk. J Athl Train. 2005;40(3):218–220.
  2. Park HK, Jung MK, Park E, et al. The effect of warm-ups with stretching on the isokinetic moments of collegiate men. J Exerc Rehabil. 2018;14(1):78–82. Published 2018 Feb 26. doi:10.12965/jer.1835210.605


How It Works Problem Post: “Whole Body Air Displacement Plethysmographic “


In order for whole body air displacement plethysmographic machines such as the BodPod to function optimally (so that viable data can be collected), it is crucial that laminar flow is maintained throughout the machine’s ventilation system at all times. Imagine that you are an engineer (imagine that!)  tasked with manufacturing the tube components for the Bod Pod.

If the flow rates in the inlet and outlet tubes are equal, the volumetric  flow rate of air in the tubing system will be 0.25 cubic meters/second , and the BodPod functions in laminar/laminar-like conditions, what are the ideal dimensions for the diameters of the inlet and outlet tubes in the Bod Pod?



  • Flow rates are equal in the inlet and outlet tubes
  • The tubes are cylindrical  
  • Laminar flow is maintained at all times
  • Pressure changes are negligible
  • Air circulating inside the BodPod has similar thermodynamic/kinematic properties ambient air at room temperature
  • Temperature conditions of the device are identical to those at room-temperature

A link has been included to a power point presentation that contains diagrams that will aid readers in solving this problem:



Figure 1: Schematic of Adult-Sized Bod Pod and circuitry components that will be used as a reference for this problem.





According to the 4th page of the patent filed by the manufacturer, Life Instruments Inc., it is okay to assume laminar conditions inside the tubing ventilation due to the fact that flow rate inside the inlet and outlet tubes are always set to values of low magnitudes. Literature in courses such as Signals and Systems show that low flow rates result in low generation of acoustic noise by  air circulation systems.


I was unsuccessful in locating some sort of testing standard that establishes set values for the volumetric flow rates of air in laminar conditions. There appears to be any information pertaining to any testing protocols the manufacturer used for design verification purposes in the original 510(k) form filed with the FDA. To establish an appropriate flow rate value for this test question, I searched for similar problems online. In short, the values for the volumetric flow rate of air (Q) ranged from 0.1 to 0.8 cubic meters/second in my searches. I decided to use a value of 0.25 cubic meters/second in this problem. By assuming that the values for Q are equal for both tubes, it is possible to design both tubes with an equal diameter. Thus, along with other reasons that will be outlined later in this section, all the solver is required to do to calculate the correct value in this problem is to use one equation.

Normally, pressure fluctuations trigger changes in tubings and pipes create flow gradients in closed ventilation systems. Because of this, mathematical expressions such a Boyle’s Law and Bernoulli’s equations are used to solve changes in volume and volumetric flow when pressure fluctuations occur. According to page 4 of the patent filed for the Bod Pod, the authors state that the use of pressure transducers which are coupled to the inlet and outlet tubes helps monitor any pressure changes that occurs in the tubing; automatically adjusting the pressure settings in the tubes to more optimal levels through negative feedback. This is done in order to maintain a constant flow rate (and thus, laminar flow throughout the circulation system). Later on in section 4 of the patent,  the manufacturers also state that constant air flow can be maintained with the addition of rotary pumps to the circulation system (which are not actively displayed in any of the figures included).

The manufacturer’s statements in the patent confirm the presence of temperature-sensing circuitry in the inlet and outlet tubes that control the internal temperature of the environment inside the tubing and the pod itself. Thus, any temperature fluctuations that could create flow gradients in the device’s tubing are negligible since they are always corrected in  rapid fashion. This also eliminates the need for Fourier’s law to solve the value of Q in this problem.

Assuming that the tubing is cylindrical eliminates the need to solve for any hydrodynamic radius  values(which are used in equations associated with fluid flow in which tubes/pipes are any shape that is non-cylindrical).


By assuming that the air inside the device’s circulation system behaves in a similar fashion to ambient air, and that the conditions inside the circulation system are similar to those at room-temperature and that the device is used in STP conditions, it is possible to estimate the value of the kinematic viscosity of air (which is needed to solve the value for the diameter of the tubing using the Reynolds number equation along with the value of the flow rate given in the problem description and the upper-limit value of the Reynolds number associated with laminar flow).




In order to solve for the value of the tube diameter, the solver must utilize the following equation:

Re = QD/v ,

Re = reynolds number

Q = volumetric flow rate of air

D = pipe bore or tube diameter

v = kinematic viscosity

Reynolds number flow rate equation-16umdck  <— Click the link to view a more detailed image of the equation


NOTE: Pipe bore is equivalent to the diameter of the tube, and this equation is applicable to both pipe and duct installations.

First, the value of Q is already provided in the description. So the reader is already provided one unknown.

Second, the reader is told in the problem description and background section to assume laminar conditions in the circulation system. The Reynolds number value used in this problem is 2300, which is the established upper limit for laminar flow. All values at or below this number is considered laminar flow.

Third, since the reader is told to assume that the air circulating through the inlet and outlet tubes are similar in kinematic/thermodynamic behavior to ambient air at room temperature, the reader can assume that air inside the circulation system has the same kinematic viscosity as ambient air at room temperature. This value is 1.494 x 10-5 meters ^2/ second.

At this point, the only unknown that the reader is left with is the value of D, or the tube diameter. After plugging all the known values into the above-aforementioned equation and solving for the value of D algebraically, the reader should arrive at a diameter value of approximately  0.13708 meters.




[1] Dempster Phillip, Michael Homer, and Mark Lowe (2004). United States Patent 20040193074A1. Retrieved from


[2] Engineers Edge. “Kinematic Viscosity Table Chart of Liquids” (2019). Machinery’s Handbook, 29th edition.  Retrieved from


[3] Foster, Trevon. “Laboratory Flow Meters: Flow Measurements In the Lab” (2015). Titan Enterprises, Ltd. Retrieved from

One, Two Step

Wrist pedometers are used by many to count their steps, and notify users when they “reach their 10,000”. These wearable devices quantify step activity and give indiviudals an idea of exactly how much they are moving throughout the day.

Accelerometers are often used within these wearable devices to detect the force acting on the device. The force acting on the accelerometer is correlated to an analog voltage output, which must be processed through a series of op amps to turn a users movement into an electrical output that can be analyzed through signal processing, but what signal processing circuitry is needed following the accelerometer within a wrist pedometer to correlate force acting on the pedometer to steps taken by the user?

In this post we will solve at the following engineering problem associated with pedometers: what signal processing circuitry is needed to convert the analog voltage input from an accelerometer to a binary digital signal that can be correlated to steps taken by a user?


Figure 1. Force acting on wrist pedometer during gait cycle[1].

The average person takes between 0 and 120 steps per a minute. Throughout each gait cycle, a wrist pedometer experiences forces relative to its position, as shown in Figure 1. While standing the force detected by the pedometer is 1G (one times the force of gravity). When a user is pushing against the ground to step forward the force detected by the pedometer can rise above 1G, and while the user is between steps the force detected by the pedometer can go below 1G. The pedometer can detect when a user takes a step by monitoring forces and determining when the 1G threshold is crossed. Many wrist pedometers use a threshold of at least +/- 0.2G to prevent noise and standing movements from being accounted for in step count. So a step count will be equal to crossing the 1.2G and -1.2G thresholds[1].


Figure 2. Voltage Output as a function of force for Analog Devices+/- 2g accelerometer [2]

Accelerometers are often used to relate the force acting on an object to an electrical signal. Analog Devices, a circuitry component manufacturer, produces an +/- 2g accelerometer that relates forces between -2g and +2g to a voltage output, as shown in Figure 2. A linear region exists between +/- 2g, which can be defined by the following simplified function V(g)=(.875*g)+2.5 [2].


In designing the signal processing circuitry necessary to convert an analog signal from an accelerometer to a binary digital signal, we will do the following:

1.Define the input signal in terms of force acting on a wrist pedometer, and the voltage output of an accelerometer

2.Determine the signal processing necessary to convert the analog signal into binary digital output

3.Select circuit components to complete desired signal processing, and appropriate values for integrated components

4.Use LTSpice to model desired circuitry, and confirm that designed circuit solves the defined engineering problem

Signal Input

It is known that the force acting on a wrist pedometer can be defined by a sine wave function fluctuating +/ 0.5g around 1g, with a frequency of 0-2Hz. Therefore we will define the force acting on the pedometer as F(t)= 0.5sin(t) + 1g. Given the voltage output of analog devices accelerometer is V(g)=(.875*g)+2.5, the voltage output of the accelerometer can be defined as V(t)=0.4105sin(t)+3.375.

Figure 3. Force acting on pedometer throughout gait cycle

Figure 4. Voltage signal generated by accelerometer from force input signal









Signal Processing

To generate a digital binary signal from an analog voltage input signal processing through circuitry is required.

Figure 5. Flow chart of signal processing of input analog signal from accelerometer to binary output signal

First, the input signal should be passed through a low pass filter, with a cutoff frequency of 2Hz to remove high frequency noise from the signal. The force acting on the pedometer, and voltage output of an accelerometer can be defined by sine wave functions. The baseline of accelerometer voltage output exists above zero volts, therefore a subtractor should be used to bring the baseline of this signal to 0V. A full wave rectifier will be used as an AC to DC converter, converting both polarities of the signal to a pulsating DC signal. A compactor will be used to produce a binary DC output that indicates whether the signal is above a given threshold, voltage relative to passing +/- 0.2g force threshold. This binary signal is the system output and can be used to count total steps taken by a user.

Circuit Components 

Circuit components were selected to complete necessary signal processing, and assumed to be ideal for simplification of solving this problem.

Low pass filter 

Figure 6. Low pass filter


With a cutoff frequency of 2Hz, a low pass filter with a Capacitor of 4.7 nF and resistor of 0.0169 Ohms can be used to filter out high frequency noise






Figure 7. Op amp acting as follower


Follower used to preserve signal and prevent current flow back to the user




Figure 8. Op amp acting as a subtractor


A subtractor can be used to reduce the baseline signal to zero. Given our voltage input is V(t)=0.4105sin(t)+3.375 V, and the Voltage output of this component is Vout = (R3/R1)*(Vin-Vs), we will set Vs=3.375V DC and R1=R2=R3=100 Ohm to bring the baseline signal down to 0V.





Full Wave Rectifier

Figure 9. Op amps acting as a full wave rectifier


A full wave rectifier will be used to convert all polarities of the input signal to the same polarities. If R1=R2=R3=R4=R5, then if Vin>0 Vout=Vin and Vin<0 Vout=-Vin. Therefore, we will set all the resistors equal to each other to achieve a rectified DC signal.





Figure 10. Op Amp acting as a comparator

A comparator will be used to convert the pulsating DC signal to a binary digital output. Op amps functioning as comparators follow the rule that if V+>V- Vout = Vc+ and V->V+ Vout=Vc-. In our ideal circuit, we aim our binary signal to be either 0 or 1.

V+ terminal will be our signal, and we look to determine if this signal represents crossing the 1.2g threshold. To find what the V- terminal should be we need to determine the voltage at this point in the circuit if it has crossed the threshold. Given, V(g)=(.875*g)+2.5, V(g=1.2)=3.52. The signal is brought through a subtractor where it is reduced by 3.375 and afterword is no longer amplified or modified, so the threshold voltage at this point is 0.1534 V. The negative input terminal will be set to be a DC voltage of 0.1534V.

To generate a binary output where 0V= not crossing the threshold and 1V= crossing threshold, the op amp terminals will be set to be Vc+ = 1V and Vc-=0V.

LTSpice Modeling and Verification 

Figure 11. LTSpice signal processing circuit following accelerometer to convert analog accelerometer signal input to binary output

LTSpice was used to model the designed circuit, as shown in figure 11. This circuit was simulated using LTSpice software and it’s ability to produce a binary digital output from an analog signal was verified as depicted in figure 12.

Figure 12. Voltage input, green, and output, blue, of signal processing circuit in figure 11


Our goal was to design signal processing circuitry is needed to convert the analog voltage input from an accelerometer to a binary digital signal that can be correlated to steps taken by a user.

Figure 13. Accelerometer analog output signaling processing circuit to produce binary digital output

A series of signal processing components were integrated within a circuit, depicted in figure 13, to convert an analog voltage signal from an accelerometer into a binary digital signal. This circuit removes high frequency signal noise, reduces the signal baseline, generates a pulsating DC signal, and generates a binary signal output, as shown in figure 14.

Figure 14. Binary digital output of accelerometer signal processing circuit

This binary digital output can be correlated to steps taken, as two square waves is equal to one step taken. These square waves can be counted by an integrated software and used to count user steps. Thus, turning the analog accelerometer voltage output into a binary digital signal.

This binary signal can be used to count steps and step frequency, and when integrated with GPS and other technologies can be used to determine step distance and user speed.

With one two sqaure waves equaling a step, the designed integrated circuit turns user movement into step count, enabling the signal processing necessary to count those 10,000 steps everyone is so desperately trying to reach!


[1] Modi, Yash Rohit. (2014). United States Patent No. US20140074431A1. Retrieved from

[2] “Accelerometer Specifications – Quick Definitions.” Accelerometer Specifications – Quick Definitions | Analog Devices,

Engineering Concerns for a Portable NIRS Device

When designing a portable Near-Infrared Spectroscopy (NIRS) device for the measurement of muscle oxygenation, design engineers have plenty of factors to consider. They must think about battery life, portability, affordability, safety, and many other design criteria. Before considering many of these criteria, however, an engineer must design a working technology that is capable of actually measuring muscle oxygenation. Without this basic attribute, the device would be a complete failure. The basics for measurement of relative oxygenated and deoxygenated hemoglobin concentrations was introduced previously in the patent blog post, but the engineering design problem was mostly glossed over. This post will dive a little deeper into the quantitative nature of measurement of muscle oxygenation and what functions the design engineer must consider when designing a device that will operate properly and accurately. The main question to be answered is: how does an engineer use light to measure concentration of a particle in muscle?

Fig 1: Molecular Absorption Coefficient Profiles for Oxygenated and Deoxygenated Hemoglobin

As mentioned before, NIRS works by measuring the absorbance or attenuation of light as it passes through a sample to make a measurement of concentration of the absorbing analyte or particle. Also previously introduced were the benefits of using near-infrared light since it can pass through biological tissue and is primarily absorbed by hemoglobin. In an ideal world the absorbance is defined by the Beer-Lambert Law. According to this law, the absorbance of a particle is equal to the natural log of incident light over the detected light and this is further equal to the product of the molar absorbance coefficient, the concentration of the particle, and the mean path length of detected photons. In an ideal case this law works because it describes when light is shown through a glass cuvette with a solution with only one absorbance particle, but this is not helpful for a NIRS device for muscle oxygenation. Thus, for a NIRS device, the modified Beer-Lambert Law must be used, which is the same as the original equation but with an extra scattering term to account for photon scatter when passing through tissue like skin and muscle (Eqn. 1).

Here A is absorbance, I0 is incident (transmitted) light, I is detected light, ɛ is molar absorbance coefficient, c is concentration, L is mean path length, and G is the scattering term. This is great in theory because it appears that concentration can be calculated relatively easily, but there are further problems to solve. Start by considering the knowns and unknowns. The absorbance coefficient is a known value for any analyte given the wavelength of the laser used (Fig. 1), and the path length can easily be found from the distance between the light emitter and detector with some regards to the path shape which is known to be roughly banana shaped. This leaves two unknown terms: the unknown that to be measured, i.e. concentration, and the scatter term. The scatter term is unfortunately a problem. It varies by tissue and considering the device should be designed for consumers to use on different locations, different muscles, and different amounts of say fat that may lie in the way of the muscle, this G term will forever be changing. Thus, there needs to be a way to get rid of it. The easiest way to do this is to find change in absorbance so that G will be subtracted away. This uses the assumption that G is constant for a given location. The resulting equation will then give change in concentration as it is the only factor that changed between measurements 1 and 2 (usually an initial measurement and a second measure at a later time) (Eqn. 2). Notice that absorbance is now equal to the natural log of the first intensity detected divided by the second intensity measured based on the identity (log(x/y) = log(x)-log(y). Note that the need to get rid of G, because it cannot be calculated on every single consumer, leads to the fact that NIRS devices almost always measure change in concentration or relative concentration when measuring muscle oxygenation.

This equation looks great. So change in concentration as opposed to exact concentration is found, but so what, this is still a very helpful measure for oxygenation during exercise. BUT, this equation is not the whole story. NIRS works by measuring both oxygenated and deoxygenated hemoglobin (Hb). Both species of Hb contribute to absorbance in the near-infrared range. Thus the equation actually looks like this (Eqn. 3)

In this equation, subscript O is used for oxygenated Hb, and subscript Hb is used for deoxygenated Hb. Now there are two unknowns and only one equation. So what does a smart engineer do? They add more lights. By measuring multiple wavelengths, two changes in absorbance can be measured allowing both concentrations to be calculated by solving the system of equation (Eqn. 4-5).

In these equations, superscripts refer to the wavelengths of light 1 and 2. It must be remembered that absorbance coefficient, absorbance change, and path length will all vary based on wavelength. This clearly allows for the output of relative concentrations or total blood oxygen saturation percentage (oxyHb / [oxyHb + deoxyHb]). Here the assumption is that total Hb is equal to oxyHb plus deoxyHb. The last piece of the puzzle for an engineer is to decide on what wavelengths should be used for the lights. This is a very impactful decision in building the algorithm to calculate the outcome measures of the device since ɛ, A, and L all depend on wavelength. It should be noted based on Figure 1 that certain wavelengths will be better than others. For example, if 805 nm light is used, then the absorbance coefficients for both species of Hb will be the same. This leads to irrational answers for Equations 4 and 5, so this wavelength should be avoided. The best case is to pick a wavelength above and below this so that one is more sensitive to oxyHb and the other is more sensitive to deoxyHb. Thus, using 750 and 850nm could be viable options, and these are used in several current devices.

These results allow an engineer to design a device that will properly measure muscle oxygenation through the relative concentrations of oxygenated and deoxygenated Hb. A reminder that some of the assumptions that needed to be made were that the tissue was homogenous, that oxy and deoxy Hb are the only particles contributing to absorbance, that absorbance is constant in time when Hb concentrations do not change, that the scattering term remained constant, and that oxy + deoxy Hb is the total Hb. Realistically, tissue is not homogeneous, but this assumption causes smaller errors in the volumes being considered close to the skin surface. Unfortunately, Hb is not the only chromophore contributing to absorbance. Fat is a major problem because it shares a similar range of wavelengths for absorbance. Some devices take fat correction into account, but other do not, and papers have pointed this out. It is reasonable to assume that absorbance is constant in time when concentration is constant, but pulsatile flow can cause error here. The scattering term should remain constant if the position of the device is not changed, and it is also reasonable to assume that there are not Hb species besides oxy and deoxy in the muscle. Some of these do cause limitations to the design described here, and as already mentioned it will only measure change in concentration not the absolute value. In conclusion, two wavelengths of light are needed measure muscle oxygenation with NIRS.



[1]. Shimadzu Commercial Website

[2]. Kocsis, L., Herman, P., & Eke, A. (2006). The modified Beer-Lambert law revisited. Physics in Medicine and Biology, 51(5).

[3]. Len-Carrin, J., & Len-Domnguez, U. (2012). Functional Near-Infrared Spectroscopy (fNIRS): Principles and Neuroscientific Applications. Neuroimaging – Methods.

[4]. McManus, C. J., Collison, J., & Cooper, C. E. (2018). Performance comparison of the MOXY and PortaMon near-infrared spectroscopy muscle oximeters at rest and during exercise. Journal of Biomedical Optics, 23(01), 1.

How accurate is your Garmin’s VO2max estimate?

Traveling along the trails, sidewalks, and main streets of the towns they reside in, runners, cyclists, and endurance sports athletes everywhere all know a familiar sound. The delightfully gratifying chirp of a fitness tracker as you complete your next mile, achieve a new PR (personal record), or record a new VO2max.

Ever since I entered the world of endurance sports training eight years ago, I’ve heard athletes talking about their VO2 max, how to improve it, and how accurate (or not?) fitness trackers are at actually measuring these values.

I decided to explore the technology of Garmin fitness watches to understand how VO2max is calculated and do a baseline comparison of how these wearable technologies VO2max predictions compare to laboratory testing.

Firstbeat Technology’s Fitness Test is used by Garmin and other fitness companies to calculate VO2max for a variety of different activities. Described in patent US20110040193A1, this Fitness Test calculates users’ VO2 in the following steps:

1) The personal background info (at least age) is logged
2) The person starts to exercise with a device that measures heart rate and speed
3) The activity collected data is segmented to different heart rate ranges based off the persons background info and the reliability of different data segments is calculated(reliability is measured based off how continuous the activity is- uninterrupted segments are better than those where the user has to stop)
4) The most reliable data segments are used for estimating the person’s aerobic fitness level (VO2max) by utilizing the person’s heart rate and speed data

Speed data from reliable segments are used to calculate a VO2, oxygen consumption, during that segment. 20-30s bouts are used to calculate VO2 across segments using one of the following theoretical VO2 calculations:

Walking and Pole Walking: Theoretical VO2 (ml/kg/min)=1.78*speed*16.67[tan(inclination)+0.073]
Running on a Level Ground: Theoretical VO2 (ml/kg/min)=3.5 speed
Running in a Hilly Terrain: Theoretical VO2 (ml/kg/min)=3.33*speed+15*tan(inclination)*speed+3.5
Cycling: Theoretical VO2 (ml/kg/min)=(12.35*Power+300)/person’s weight
Rowing (Indoor): Theoretical  VO2 (ml/kg/min)=(14.72*Power+250.39)/person’s weight                                Unit of speed=kilometers per hour (km/h) 
Unit of inclination=degrees)(°) 
Unit of power=watts (W) 
Unit of weight=kilograms (kg)

From these calculated theoretical VO2 values, heart rate information is used to determine effort of segments. Heart rate zones based on user information are utilized to evaluate effort, and then effort is used to determine that VO2 as a %VO2max. VO2max estimates are made for each segment using %VO2max. These segment VO2max can be weighted based off heart beat derived parameters and performance parameters, and then used to calculate VO2max.[1]

An affordable mode of tracking your VO2max through measuring heart rate and speed data – pretty neat, right? But how accurate is this technology and how does it match up to laboratory testing?

Firstbeat conducted their own study to validate the technology and its effectiveness at estimating VO2max. They found that “[t]he accuracy of the method when applied for running is 95% (Mean absolute percentageerror, MAPE ~5%), based on a database of 2690 freely performed runs from 79 runners whose VO2max was tested four times during their 6-9 -month preparation period for a marathon”(4). Error in estimated VO2max was less 3.5ml/kg/min in most cases, which is fairly accurate considering most submaximal testing has an error of 10-15%. Method accuracy varied with respect to estimated maximum heart rate(HRmax). ” If the HRmax is estimated 15 beats/min too low, the error in the VO2max result is about 9%. Respectively, if the HRmax is estimated 15 beats/min too high, the error in VO2max result is 7%. If the person’s real HRmax is known, the VO2max assessment error falls to the 5% level”(5). This study suggests a high degree of accuracy for Firstbeat’s fitness test technology in predicting VO2max.[2]

A group of scientists at Southern Illinois University Edwardsville evaluated the wearable technology’s accuracy by conducting a laboratory VO2max test on male and female runners, then allowing participants to use the wearable technology to calculate VO2max in a 10 minute self guided run. They found that the Garmin Forerunner 230MAX and 235MAX measured VO2max within -0.3 ± 3.4 ml/kg/min, p=0.02 for the 230MAX and -1.1 ± 4.0 ml/kg/min, p=0.026 for the 235MAX for female runners, and -1.1 ± 3.4 ml/kg/min, p=0.149 for the 230MAX and -3.2 ± 4.2 ml/kg/min, p=0.002 for the 235MAX for male runners. There is a greater amount of variability in the male group; however, this could be due to miscalculations in HRmax and potential variations in levels of effort in participant during the 10 minute self guided run. Although there is greater variability within the male group, the devices still appear fairly accurate at predicting VO2max.[3]

Wearable conducted an evaluation of their own putting fitness watches to the test – assessing the accuracy of Garmin, Fitbit, and Jabra devices in measuring VO2max. They found that Garmin technology provided a VO2max estimation within 0.3 ml/kg/min of their study participant, which was the most accurate of all devices tested. The high degree of accuracy found in their study remains consistent with other larger scientific studies.[4]

Across the board, there appears to be a high degree of accuracy with Firstbeat’s Fitness Test in estimating VO2max. For endurance athletes everywhere, this is a huge sigh of relief. Rather than partaking in expensive, strenuous VO2max testing, we can monitor our progress utilizing the technology in the watches we wear everyday. In addition to watching our paces, heart rates, and overall progress, we can also monitor our cardiovascular health and athletic progress as we continue to train and push ourselves everyday.


[1]Seppanen, M., Pulkkenin, A., Kurunmaki, V., Saalasti, S., & Kettunen, J. (2016). U.S. Patent No. US20110040193A1. Washington, DC: U.S. Patent and Trademark Office

[2] Firstbeat Technology(2014). Automated Fitness Level (VO2max) Estimation with Heart Rate and Speed Data.

[3]Snyder, N. C. , Willoughby, C. A. & Smith, B. K. (2017). Accuracy of Garmin and Polar Smart Watches to Predict VO2max. Medicine & Science in Sports & Exercise, 49(5S), 761. doi: 10.1249/01.mss.0000519024.10358.0b.

[4]Stables, J., & Stables, J. (2016, December 21). The big ​VO2 Max test: Fitbit, Garmin and Jabra go head-to-head. Retrieved from


Using NIRS to non-invasively monitor muscle oxygenation during exercise

Skeletal muscles are the basis of all movement in the human body, and athletes work years to train their muscles to be powerful yet efficient. Even if a single muscle could allow a person to lift a car, it would not be very useful if the muscle could no longer create forceful contraction again for several hours. The muscle also must be efficient in the use of oxygen, ions, and other substrates that allow for contraction to be able to quickly recover and be prepared for repeated contraction. Muscle oxygenation is particularly important for both endurance and power of a muscle because it is necessary to produce ATP to power muscle cells to contract. Heart rate and blood oxygen delivery are helpful for getting an idea of an athlete’s efficiency, but they do not tell the whole story for the muscle. At the muscle, the balance between delivery and consumption of oxygen explains its efficiency [1]. To measure muscle oxygen saturation, a technique called near-infrared spectroscopy (NIRS) is used to get real time data to inform athletes of the state of their muscles during training. This is a powerful tool for maximizing athletic gains in muscles from training and to see the state of the muscle over time and after rest.

Early NIRS instrumentation was contained to the lab, but recently portable versions have become more common, which is very important for its use in both the medical and research fields. In medicine, NIR has been used for study of septic shock, free tissue transfer, real-time tissue perfusion during surgery, cancer nanotechnology, and peripheral arterial disease.  For this post, the use of NIR in exercise will be highlighted. In exercise, NIRS is a great tool because it is a non-invasive method that can be applied locally to muscles or tissues of interest and provide real time data during exercise. NIRS is highly sensitive to changes in muscle tissue oxygenation [2, 3, 4], and it reflects the balance between oxygen delivery and utilization, unlike measurements of arterial or venous blood samples which have been used previously and are minimally invasive [2]. NIRS works by measuring the percentage of oxygenated hemoglobin to total hemoglobin (oxygenated and deoxygenated hemoglobin) to give muscle oxygenation. Hemoglobin is the main oxygen carrying protein in the blood and can carry 4 oxygen molecules (O2). Oxygenated and deoxygenated hemoglobin scatter NIR light (600-1000 nm) differently, so their relative concentrations can be found from their molecular absorption coefficients. To do this, three to four different wave lengths of light will be used to determine the concentrations of each based on the change in molecular absorption coefficients at different wavelengths (Fig 1). NIR light must be used as it: 1) passes through skin, bone, and most biological tissue, and 2) is the appropriate wavelength where the small amount of absorption that occurs is predominately from hemoglobin (Fig 2) [5].  As the muscle performs work, the muscle oxygenation will decrease as a function of the work and the training of the muscle.

Fig. 1: Molecular Absorption Coefficient Profiles for Oxygenated and Deoxygenated Hemoglobin [5]

Fig 2: Light Absorption by Wavelength [5]











A patent on google patent claims to leverage this technology in a wearable article of clothing for athletes to be able to measure muscle oxygenation real-time (Fig 3) [6]. The patent claims to be a method and apparatus for assessing tissue oxygenation saturation through two main claims that summarize to: a portable apparatus that is a wearable article capable of measuring oxygenation saturation of at least one of a skin dermis layer, adipose layer, or muscular fascial layer of a user during physical activity using at least one near-infrared spectroscopy probe including at least one near-infrared light source and at least one photodetector. In short, the patent is a claim on a portable, wearable NIRS device for tissue oxygenation levels. NIRS has been a research method for decades, so the novel part of this patent lies in the incorporation of this technology into a wearable article of clothing.

Fig 3: Figure from patent illustrating wearable shirt, shorts, and socks using NIRS

Fig4: Figures from patent showing example data of muscle oxygenation average during constant rate running at different grades (top) and real time data from medial gastrocnemius muscle during weighted exercise and unweighted control (bottom)

This patent pertains primarily to the measurement of tissue during exercise (Fig 4). This could be of use for athletes during training to be able to compare what levels of exercise cause certain levels of muscle oxygen saturation loss. For example, highly trained athletes often train at high altitude to reduce oxygen in the air so that their body adapts to becoming more efficient with oxygen usage. This prompts higher performance when returning to normal oxygen levels. Using NIRS could allow them to find a training regime that caused the same hypoxia in muscle without traveling to higher altitude (they will still miss out on some of the pulmonary and cardio vascular advantages that training at altitude can produce). This may also be helpful in rehabilitation as the change in muscle oxygenation is an indicator that the muscle is being used and can inform physical therapists if the patient is engaging the correct muscles during rehab. Additionally, the device may also have merit in the medical realm for monitor muscle oxygenation in patients with chronic heart failure, peripheral vascular disease, chronic obstructive pulmonary disease, and varying muscle diseases [3, 4].

  1. Patent title: Method and apparatus for assessing tissue oxygenation saturation
  2. Patent number: US20170273609A1
  3. Patent filing date: 2017-03-22
  4. Patent issue date: Patent Pending
  5. How long it took for this patent to issue: TBD
  6. Inventor(s): Luke G. Gutwein, Clinton D. Bahler, Anthony S. Kaleth
  7. Assignee (if applicable): Indiana University Research and Technology Corp
  8. U.S. classification: A61B5/0075
  9. How many claims: 20

References and Further Reading

[1] BSX Athletics

[2] Bhambhani, Y. N. (2004). Muscle Oxygenation Trends During Dynamic Exercise Measured by Near Infrared Spectroscopy. Can. J. Appl. Physiol., 29(4), 504–523.

[3] Hamaoka, T., Mccully, K. K., Quarisma, V., Yamamoto, K., & Chance, B. (2007). Near-infrared spectroscopy / imaging for monitoring muscle oxygenation and oxidative metabolism. Jounal of Biomedical Optics, 12(6), 1–16.

[4] Boushel, R., & Piantadosi, C. A. (2000). Near-infrared spectroscopy for monitoring muscle oxygenation. Acta Physiol Scand, 168, 615–622.

[5] Shimadzu Commercial Website

[6] Patent

[7] Ferrari, M., Muthalib, Makii, & Quarisma, V. (2011). The use of near-infrared spectroscopy in understanding skeletal muscle physiology : Phil. Trans. R. Soc. A, 369, 4577–4590. 

[8] Artinis Commercial Site

How to Quantify “Getting Back in the Game”

Sports injuries are a major roadblock for athletes, keeping them from playing their best, or even at all. Even after an injury is healed, athletes have to build back up muscles that atrophied over recovery time.  During rehab time, patients undergo different exercise routines to build the muscle that was left unused while the injury was healing. But how do the trainers know when it is safe to allow the athlete back in the field?

One way to quantify the “readiness” of the player is by using an Isokinetic Dynamometer machine to determine how much power the questioned muscle can exert and how that compares to its counterpart.  For example, let’s say a female athlete tears her right ACL. Throughout her rehabilitation, her trainers will set her up on an Isokinetic Dynamometer machine (Figure 1) to determine the power exerted by the right quadricep and hamstring, which are muscles that commonly experience atrophy during ACL recovery, and compare it to the power of her left quadricep and hamstring. Based on the presettings of range of motion, force, and speed, the device can calculate the torque provided by the athlete and then multiply it by the constant speed (isokinetic part) to find the power exerted by those specific muscles. It is obvious that time is needed to heal, but every patient is unique and time could vary. It is important to find a quantitative way to determine when each patient is back to normal strength and this design does just that.

One patent of an isokinetic dynamometer is the “Exercise Physical Rehabilitation and Testing Method and Apparatus” (Patent number: 5,722,937), which was filed in April 17, 1996 and issued on March 3, 1998.  Invented by James F. Smith, it is still used by assignee Cybex International, Inc to this day.  U.S. classifications are as followed: 601/23; 601/24; 482/4; 482/137; 482/142; 482/908.

Figure 1: Set-up of limb to lever arm and dynamometer. The user pushes leg up and back and the dynamometer, comprised of the motor and cycloidal speed reducer, monitors and alerts the computer if the motor needs to slow down or speed up to keep a constant speed depending on the torque exerted by the user.

The main claims of a total 30 for this patent is to help athletes and patients in rehabilitation for muscle atrophy or decreased muscle strength by evaluating the strength of a targeted muscle by forcing the patient to keep a constant speed through resistance. This machine consists of a base with a track to allow adjustability of the chair to customize the fit for each user. There is also a lever arm, where the user will push against during exercises, connected to the chair and to the dynamometer. The dynamometer is comprised of a motor to change torque and a cycloidal speed reducer with a high and low speed shaft to keep a constant speed during exercise (Figure 1).  This machine helps build muscle fibers by forcing the patient/athlete to provide maximum force to move a lever arm while the machine provides resistance (or takes away) to keep the patient moving at a constant speed. Not only can this machine provide biofeedback on the power of the muscle to help physical therapists plan an exercise regimen to help patients, but it can also help athletes build their muscles and ensure their body is balanced to avoid straining and injury. This device has various protocols that subjects the muscles of the user to “concentric or eccentric motion in isotonic or isokinetic modes or continuous passive motion.”

Physical Therapists, Athletic Trainers and athletes will primarily use this machine.  It is very bulky and expensive, so only established facilities can afford this technology.  This product helps physical therapists and athletic trainers assess the muscle strength of their patients to determine what the state of the targeted muscle strength is and help them prepare an exercise routine to get their patients to where they need to be to be healthy and avoid further injury. Athletes can also use this technology to grow muscles due to the max force and full range of motion the lever and program provide.  This product is designed for determining when muscles have developed enough to start playing again after suffering from atrophy during rehabilitation.

Figure 2: Schematic of Isokinetic Concentric mode feedback loop depending on the performance of the user.  If threshold torque is too high, the motor will accelerate. If threshold torque is too low, motor will decelerate to zero speed.

Patients sit in an upright position and strapped at the waist and thigh to stabilize the body and to force the patient to only use the targeted muscle. Next, after setting up the machine with the desired weight and speed, the patient must push and pull a lever arm as hard as they can.  The lever arm, attached to a low speed shaft of a cycloidal speed reducer follows a negative feedback and the machine. For example, Isokinetic Concentric mode, the mode most commonly used for determining the power produced by the muscle, uses the dynamometer control board to determine the angle (boundaries of range of motion) of the lever arm and signals the dynamometer to slow down to a stop until the user pushes the lever arm in the other direction. The torque on the dynamometer control board, which is measured by strain gauges, is sampled every two milliseconds.  The computer monitors the the measured torque (force of the limb attached to the lever arm multiplied by the distance to the targeted muscle) and compares it to the threshold torque. If the measured is greater than the threshold, the motor will accelerate (less resistance) based on the magnitude of the torque and the direction of the measured torque to approach the isokinetic speed. If the measured torque is not sufficient, the motor will decelerate to zero speed until sufficient torque is met (Figure 2).

Compared to other designs, this patent is less costly, smaller in size, and has less parts. Also, the speed reducer incorporated in this design does not create a high pitch noise that is  disruptive in quiet clinical scenes, which was commonly found in previous designs. As for the infrastructure of the machine, this new design fixes a previous problem of slack resistance during start up, which creates a loose and not smooth feeling for patients (also known as backlash). The slack would allow for additional bending torque on the shafts, which creates that loose and unnatural feel. This design fixes this problem because the cycloidal speed reducer specific to this design has a higher torsional stiffness. The cycloidal speed reduces also has a longer life and will reduce the overall effect of backlash throughout time. This patent is still the primary patent for CSMi Medical Solution’s HumacNorm Testing and Rehabilitation System, so it is reasonable to assume these claims are valid and the design is reliable and effective!




Smith, J.F. (1998). U.S. Patent No. 5,722,937. Retrieved from


Can You Beet The Competition With Nitrate Supplements?

Nitric Oxide (NO) is a supplement currently used by many athletes because it is a known vasodilator, which can increase blood flow, mitochondrial efficiency, and contractility of muscles. While there are a few different kinds of nitrate supplements, the most common comes in the form of beetroot juice. When ingested, the nitric oxide is easily broken down into nitrate, which can be used by the body to help increase efficiency of exercise. Multiple studies have been done regarding the effect of beetroot juice supplementation in both trained and untrained athletes; as well as by acute or long term dosing. Due to the nature of NO in exercise, it is generally used to supplement endurance activities, with only a few studies looking at shorter length, or strength exercise. Currently, there is data to suggest that beetroot juice has a more noticeable effect in untrained individuals than in trained athletes, which is not surprising. The trend normally seen in these studies is that acute doses of beetroot juice will lower VO2 during submaximal exercise, allowing individuals to exercise more efficiently. Another effect of nitrate is the increase in mitochondrial efficiency. This effect was tested through long term studies regarding beetroot juice supplementation. In low-moderately trained athletes it was also found that VO2 decreased at submaximal exercise, similar to acute dosing. Additionally, exercise tolerance was also increased by up to 16% after one week of supplementation. While this may be due to the effects of training it was a significant difference. In highly trained athletes, it was found that beetroot juice increased workload and reduced energy cost at exercise intensity. However, the variability in performance could have been the cause of this as noted by the authors of the study. Overall, while there is some evidence to support the use of beetroot juice as an ergonomic aid, there is also a large amount of data to suggest that it has very little to no effect of athletic performance.

Table of studies done to research the effects of acute nitrate supplementation in elite athletes

This topic relates to class in that it aims to determine what affect different training methods/supplements have on athletic performance. It seems that there are potential benefits to using beetroot juice or other nitrate supplements as a training tool in both acute and long-term doses. One of the issues seems to be in determining the proper dosage of beetroot juice. There were multiple studies where no benefit was seen with small doses and significant benefits were seen with a higher dose. Determining this value will be important in future studies to ensure that possible benefits are not being overlooked. Additionally, larger studies should be conducted as only one study referenced in the article had more than 20 subjects. This could be a potential major limitation given the large amount of variability in and between different athletes and sports. NO supplements also would seem to be more beneficial to endurance athletes than it would be to strength athletes during training. While there is only a small amount of evidence to support the claim that beetroot juice will improve athletic performance, there is no data to suggest that taking this supplement will have negative effects on performance so trying it in your next training cycle may be worth it.



References                                                                                                                         Andreas Zafeiridis. The Effects of Dietary Nitrate (Beetroot Juice) Supplementation on Exercise Performance: A Review. American Journal of Sports Science. Vol. 2, No. 4, 2014, pp. 97-110. doi: 10.11648/j.ajss.20140204.15

Muscle Stretch Shortening in Upper Extremity Explosiveness

After talking briefly about muscle stretch shortening in class, I thought this was an interesting topic and looked into some literature to better understand what is going on. I found a study that focused on upper-body explosive movements, and how load and stretch shortening cycles (SSC) affect the kinematics, kinetics, and muscle activation that occur. This was an interesting study because they looked at maximal effort bench throws, where much of the previous research focused only on lower-extremity exercises. Each subject performed an SSC throw and concentric only throws, comparing displacement, velocity, acceleration, force, power output and EMG from the pectoralis major, anterior deltoid, and triceps brachii. SSCs are usually performed before explosive movements (e.g. throwing, jumping) which lengthen the muscle preparing to contract to ensure maximal velocity is reached during the movement. When the muscle lengthens, elastic energy is stored which can then be released during the movement, however, if the time between lengthening and contracting is too long, the energy dissipates, leading to a slower contraction with less power.

As expected, the average velocity was lower for the concentric only throws when compared to the SSC throws, however, there was no difference in throw height between the two groups. Average and peak force and power output were both higher for the SSC through compared to the concentric only throw. The findings from this study agree with findings from previous studies focusing on vertical jump, showing that similar muscle kinetics are at play. Muscle kinetics are an extremely interesting area of study, and even though we only briefly discussed muscle length-tension, force-velocity, and power relationships in class, this is a huge field of study. Some groups choose to look at specific muscle groups, while others look at more complex movements that require multiple groups of muscles to be activated. This area of research has led to improvements in stretching suggestions for athletes; stretching before performing explosive movements is not actually as beneficial as we once thought. Stretching the muscle allows for elastic energy dissipation, instead of storing the energy for immediate release. However, stretching is still extremely beneficial after workouts, helping to prevent muscle soreness and excess inflammation. Additionally, there are some chronic adaptations to stretching including increasing flexibility for a wider range of motion during typical daily activities as well as athletic endeavors.


  1. Newton, R. U., Murphy, A. J., Humphries, B. J., Wilson, G. J., Kraemer, W. J., & Häkkinen, K. (1997). Influence of load and stretch shortening cycle on the kinematics, kinetics and muscle activation that occurs during explosive upper-body movements. European Journal of Applied Physiology and Occupational Physiology, 75(4), 333–342.
  2. Bosco, Carmelo, and Paavo V. Komi. (1979) Mechanical characteristics and fiber composition of human leg extensor muscles. European journal of applied physiology and occupational physiology4 (1979): 275-284.

Different ways to measure VO2max

After recently observed a VO2max test in class, I began wondering more about this type of measurement of maximal oxygen uptake. Is there a better, less exhausting way to measure metabolic limits and aerobic power? How do you measure VO2max in patients with paralysis? Is VO2max even useful to measure in impaired patients? I started looking into different ways to measure VO2max and found an interesting paper from 1980 (Epstein et al, A comparison of various methods for the determination of VO2max, Eur J Appl Physiol Occup Physiol). Although this paper is relatively old, it is still being cited today and remains relevant. In this study, four different methods were used to determine VO2max including direct measurements using uphill treadmill running, cycling on an ergometer, and a step test, and indirect measurements using the Astrand-Rhyming procedure of predicting VO2max. The subjects were non-professional sportsmen, so the conclusions of this study can be applied to non-professional athletes, unlike a lot of the previous articles we have discussed in class that only applied to college-level or professional athletes.

Looking at Table 2, we can see that VO2max was highest when measured using the uphill treadmill test, in agreement with previous results. Interestingly, this method did not have a significantly higher heart rate, indicating that it may not be the most strenuous method. Additionally, the O2 pulse, a measure of cardiac performance, was consistent across the three direct measurement methods. These discrepancies have been attributed to differences in subject motivation or involvement of a varying volume of muscles necessary to perform each method. Even so, the methods in this study did not generate significantly different measures of VO2max, so we can conclude that any of the four methods tested here will adequately determine VO2max.