Reference for PCSA values in regard of age and gender needed

[Lutz Fred. (Ph.D.)]

Dear Biomch-L Members,

We are looking for maximal muscle forces for lower body musculoskeletal simulations of a 57 year old woman and 55 year old man. Therefore we would use PCSA values of Brand et al. 1996 and Klein et al. 2007. To calculate the maximum muscle force we need the Force/PCSA relationship which is reported to be about 40-100N/cm² (Brand et al. 1996). Unfortunately, after literature review (Fick 1910 etc.) we cannot find clear recommendations regarding age and gender.

My estimation based on previous experiments in the lab, the woman would have about 50-60 and the man 60-70 N/cm² but of course for a publication we need references.

We would appreciate some recommendations from the community and thank you for your time.

Yours sincerely,

Lutz F. (Ph.D)

PS: Increasingly the search for PCSA values in the forum brings up 21 posts with only one answer regarding a textbook.

[Ton van den Bogert]

Re: Reference for PCSA values in regard of age and gender needed

Fred,

There have been several studies which measured PCSA from MRI, and maximal muscle force from maximal isometric contractions. "muscle specific tension" is a good search term.

For example, one study found specific tension values in the quadriceps of about 55 N/cm² and there was no difference between men and women [1].

However, I would be cautious about generalizing to other muscles. Similar studies on ankle muscles produced values that are far lower, for instance 13 N/cm² for the plantarflexors in young men and 9 Nm/cm² in older men [2]. I have seen other studies that confirm these low values for the plantarflexors.

The assumption that maximal force is proportional to PCSA is based on the idea that all muscle fibers act in parallel. In my opinion, this is an overly simple approximation of muscle architecture. In long pennate muscles, the proximal muscle fibers and the distal muscle fibers do not act perfectly in parallel. There is probably a significant amount of force transmission in series, from the distal end of the proximal fiber to the proximal end of the distal fiber. As soon as there is series force transmission, the effective (functional) fiber length is longer than the physical length of the fibers and therefore, there is effectively a lower PCSA. This will depend on the architecture of the muscle, and how the fibers are mechanically coupled to the aponeurosis, to each other, and to the fascia.

I first noticed this when looking at maximal isometric moment-angle curves. Human curves were much wider than the theoretical curves, especially in the plantarflexors [3]. This suggested that the effective fiber length was larger than the physical fiber length.

For modeling of submaximal activities, the Fmax is often not a critical parameter because errors can be compensated by changes in activation. If optimization is used to predict muscle load sharing in a model, those results may be affected, though.

Ton van den Bogert

References

[1] O'Brien et al., Exp Physiol 2009. DOI: 10.1113/expphysiol.2009.048967
[2] Morse et al., J Appl Physiol 2005. DOI: 10.1152/japplphysiol.01186.2004
[3] van den Bogert et al., J Electromyogr Kinesiol 1998. http://dx.doi.org/10.1016/S1050-6411(97)00028-X

[Allan Carman]

Re: Reference for PCSA values in regard of age and gender needed

Fred,

I have copy/pasted the following brief summary I did some time ago, could be helpful even though it could be out of date:

"Muscle specific tension reported in the literature varies considerably from 22.5 N/cm² (Hawkins and Hull, 1992), 30.0 N/cm² (Enoka, 1988), 40.0 N/cm² (Pierrynowski and Morrison, 1985), 70 N/cm2 (Kawakami et al., 1994) and 100 N/cm² (Brown et al., 1999; Li et al., 2006), or reported ranges between 16-30 N/cm² (Enoka, 1988; Fukunaga et al.,1996; Alexander 2002), 20-100 N/cm² (Winters and Stark, 1988; Bogert van den et al., 1998) and 35-137 N/cm² (Buchanan et al., 2004). Enoka (1988) suggests that the larger values (>30 N/cm²) result from a failure to correct for internal structure (adipose and other non-contractile elements) and muscle architecture (such as pennation). Overall, the specific tension of fast and slow twitch muscle fibers may be considered similar at 25.4 N/cm² and 23.8 N/cm² respectively (Lucus et al., 1987) or simplified to a constant 25 N/cm² and independent of fiber type. Alternatively, Out et.al (1996) viewed muscle specific tension as reported in the literature as too unreliable and simply used relative PCSA (also reported from the literature) and total isometric muscle force to predict individual muscle force."

Unfortunately I have nothing on age or gender on muscle specific tension.

Ton touches on an important concept when modeling whole muscle effects by a phenomenological Hill type muscle model. In that there is a discrepancy between in vivo muscle model parameters used to describe isolated muscle fibers and the larger changes seen in muscle-belly length over functional joint ranges of motion. Where in vivo optimal fiber lengths may be too short to describe changes in muscle belly length and consequently overestimate changes in fiber length (Hoy et al., 1990; Delp and Zajac, 1992; Legreneur et al., 1996; Bogert van den et al., 1998) and pennation angle (Maganaris et al., 1998). This leads to predicted fiber lengths beyond the limits of the length-tension curve (producing zero or negative force) and unrealistic pennation angles (>45 degrees). To model whole muscle effects Bogert et al. (1998) suggests the use of a functional or effective fiber lengths due to complex internal fiber architecture. This intern gives rise to muscle model parameter optimization to the isomeric muscle force-torque profile (Gardner and Pandy 2003). Considering that in functional ranges of motion in vivo muscle fibers appear to operate in the ascending and plateau regions of the classical length-tension curve of the isolated muscle fiber (Hawkins and Bey, 1997; Chleboun et al., 2001; Maganaris and Sargeant, 2001). The optimal fiber length (width of the length-tension relationship) may be optimized to fit functional changes in muscle belly length and the expected operating range of fibers on the length-tension curve. This would produce a Soleus effective optimal fiber length about 1.4 times the in vivo optimal fiber length of the isolated fiber. Although speculative it would suggest an in series arrangement of fibers producing more sarcomeres in series than predicted by isolated muscle fibers. The relationship to intra-fascicular muscle fiber terminations, fibers that do not run the entire length of the fascicle (Lieber and Friden, 2000; Young et al., 2000; Purslow, 2002) is also speculative. However from a practical perspective defining an effective optimal fiber length is necessary to model muscle-tendon elements and whole muscle effects with a Hill type muscle model.

[Ross Miller]

Re: Reference for PCSA values in regard of age and gender needed

I've always figured that values of specific tension for human muscle in vivo are an underestimate because humans are maybe not so good at truly fully activating our muscles under lab conditions (along with issues with antagonism). But maybe this gets into a chicken-egg argument of if the "maximum" isometric force should be the maximum voluntary force or the maximum absolute force (regardless of whether a human would/could actually produce it).

Related to Allen's point about adjusting muscle model parameters to track joint-level data, Anderson et al. (2007) has some nice data for producing "group-average" joint torque-angle-velocity profiles for young men/women and older men/women:

https://www.ncbi.nlm.nih.gov/pubmed/17485097

Ross

[Ton van den Bogert]

Re: Reference for PCSA values in regard of age and gender needed

Ross,

That is a very good point. Isometric and isokinetic dynamometer tests are rather unnatural tasks because the motion is fuly controlled by the machine. High activation is "rewarded" with pain, rather than a change in position or velocity as in functional tasks.

Some of the studies I saw used electrical stimulation, or at least twitch interpolation, to try to eliminate this concern.

Thanks for the Anderson reference, that looks like a very good study (although it was voluntary activation).

Ton

[Jack Winters]

Re: Reference for PCSA values in regard of age and gender needed

I agree with all that's been said, and am just adding a bit. While the lit survey an old paper of mine had a range of 20-100 in these units (I used MPa), some of that was just related to N Alexander's insightful comments related to cadaver data being off because low water content affected PCSA measurement data. I'd normally assumed the range of 20-50, once adjusted for this, and felt it depended more on muscle quality within this range. In the 1990 appendix to the Multiple Muscle Systems book, Gary Yamaguchi and students and I tried to assemble the available muscle anthro-data (a lot), and tried to note that context mattered.

Recently I've gotten interested in the relation between muscle tissue protein content/mRNA transcriptome data and Hill parameters (especially this one), and want to especially note the effect of fatty muscle (the kind we usually eat since we "gamey/healthy creatures are too chewy). While Gene Chip/Transcriptome data is limited in sample (e.g., usually 1 muscle/person, usually vastus lateralis), it is quite interesting and the heavily expressed values are remarkably consistent with known muscle physiology.

There is a myofibrillar structural "quality" component: Muscle cross-sectional images illustrate large differences in "quality" - from near-perfectly organized lattice formation (e.g., athletes) to disorganized assembly of content (quite common).
There is a relative volume component: Over 30% of tissue content can be non-myofibrillar (e.g., mitochondria and nuclear volume, fatty and glycogen content, fatty adipose columns within the tissue). A carbo-loaded pre-lace triathlete can easily have over 30% being non-myofibrillar, as can a person who never exercises, but have very different quality.
There is a cell/tissue content component: rMRA content changes dramatically and correlates well with protein composition, and not just the slow-fast isoforms but many other subfamilies. Dysfunctional tissue is remarkably obvious from mRNA up/down-regulation transcription data. Muscle biopsies from persons who are obese or with Type 2 diabetes or ALS express content that is why off what is "healthy" norm. Finally, the range of lifting capacity in a weight room does not depend just on size - not even close. I notice this especially nowadays, the actual weights lifted by many students who seem a bit "meaty/buffed" (but not really that fit) are often not very high. As Enoka and others have shown with ever-increasing evidence, age only plays a minor role for this parameter - "use history" matters the most, and unfortunately this often implies strength loss over time (power capacity seems more age-dependent).

So here are some heuristic rules of thumb, for purpose of discussion:
Fit athletic types who excel at high-intensity but moderate duration activities, thus moderate mitochondria and more room for myo-packing - about 25-50, depending on body location
Fit endurance types with more mitochondria volume - about 15-45 (depends a lot on which muscle)
Everyday Americans who are mildly overweight (or caged lab animals) - about 15-25 (range for much of the animal lit), perhaps higher for some anti-gravity muscles
Creatures we tend to like to eat - about 10-20 (fatty even when it says "lean" - and consistent with meat research lit)
Obese muscle - about 5 -15 (perhaps 15 for antigravity muscles, but can be below 5 for muscles such as in the shoulder girdle that have limited contractile capacity). An issue is measuring PCSA for such muscles.

With regard to the 57 year old female and 55 year old male, my guess is that these values are on the high end. Perhaps the estimated PCSA are too low? (Maybe check their weight room strength for a few tasks?)

Jack

[Ross Miller]

Re: Reference for PCSA values in regard of age and gender needed

Related to Jack's comments, here is a recent study on specific tension of single muscle fibers (vastus lateralis biopsies) from bodybuilders, "power athletes" ("American football players, track and field athletes, and weight lifters"), and untrained controls:

https://www.ncbi.nlm.nih.gov/pubmed/26388513

The controls and power athletes had similar specific tension, and bodybuilders had lower specific tension. No endurance-trained group unfortunately.

[Lutz Fred. (Ph.D.)]

Re: Reference for PCSA values in regard of age and gender needed

Dear Ton van den Bogert,

Thank you for the advice and publication references. The publication of O´Brien with the value about 55N/cm² looks appalling because it involves men in women.
Regarding the maximal possible specific muscle force tension, publications would be interesting in which PCSA values are calculated based on eccentric muscle contraction like during multiple one legged hopping. This would include the energy saving capacity which e.g. is done during the hopping shortly before landing and should lead to higher PCSA then the one from isometric tasks.

Lutz Fred.

[Lutz Fred. (Ph.D.)]

Re: Reference for PCSA values in regard of age and gender needed

Dear Jack Winterns,

And of course all others who replayed, thanks a lot!
Following the advice of calculating N/PCSA values based on some tasks, here are some values. Measurements where conducted in a gait lab, forces calculated by mechanical models (see attachment) partly with reconstructed MRI data for subject specific data. Subjects where “normal” people in regard of BMI, health and no athletes.

First task OLS = one-legged hopping (forces of the triceps surae)
Veilleux et al. 2010

Second task KJF = Knee joint force (forces of the quadriceps)
Measuring isometric force in sitting position. Tibia and thigh having 90° angle, antagonist forces are not considered.

PCSA values for males are taken from Brand et al. 1986 (subject 1) with triceps surae 251.6 cm² and quadriceps 256.2cm². Since I have no good PCSA values for females I reduced the values (male) of 30% because this is about the PCSA quadriceps gender difference in the publication of O-Brien et al 2010. Hence, female PSCA triceps surae 176.1cm² quadriceps 179.3cm².

My personal conclusion about calculated N/PCSA values (see diagram in attachment). I would have expected to see in higher values of N/PCSA and bigger differences regarding age, gender and the locomotor task (OLJ vs KCF). Mr. Winters statement “Everyday Americans who are mildly overweight (or caged lab animals) - about 15-25 (range for much of the animal lit), perhaps higher for some anti-gravity muscles Creatures we tend to like to eat - about 10-20 (fatty even when it says "lean" - and consistent with meat research lit)” expanded to everyday normal Caucasian = 15-20 N/PCSA.

One final question to interested people in the PCSA topic is in regard to available publications with PCSA values from muscles (especially lower extremities and comprehensive data collection).
Following publications are known:
Wickiewikcz et al 1983, Brand et al. 1986, Pierrynowski 1982, Klein Horsman et al. 2007, Ward et al 2009.
Are there other good once which would be recommendable to read and use? I like e.g. the quality of Ward et al because he offers a lot of additional material online some older publication are not so accurate with the description of subjects.

Best regards,

Fred. L
OLJ and KJF.pdf

[Ross Miller]

Re: Reference for PCSA values in regard of age and gender needed

Fred, in addition to those references, you might take a look at these two:

Yamaguchi GT et al. (1990). A survey of human musculotendon actuator parameters. In: Winters JM, Woo SLY (eds.), Multiple Muscle Systems, 717-773. Berlin: Springer.

Van der Helm FCT, Yamaguchi GT (2000). Morphological data for the development of musculoskeletal models: an update. In: Winters JM (ed.), Biomechanics & Neural Control of Posture & Movement, 645-658. Berlin: Springer.

They will not have the most recent data but they are both comprehensive summaries of muscle parameters for Hill-type modeling from many sources. They are both textbooks so you are probably unlikely to find them free online. Multiple Muscle Systems was recently printed again and is a great text:

http://www.springer.com/us/book/9781461390329

https://www.amazon.com/Multiple-Muscle-Systems-Biomechanics-Organization/dp/146139032X/

Ross

[Ross Miller]

Re: Reference for PCSA values in regard of age and gender needed

A related question here for those who study muscle architecture:

There seems to be some inconsistency in the literature for how muscle fiber lengths are reported. Some studies simply report a measured fiber length, while others report a "normalized" fiber length:

L_fiber_norm = L_fiber_meas * L_sarc_opt / L_sarc_meas

where L_fiber_meas is the measured fiber length, L_sarc_opt is the "optimal" sarcomere length (using 2.2 microns in reference to Gordon et al. (1966) is common), and L_sarc_meas is the measured sarcomere length.

What is the purpose of normalizing the measured fiber lengths in this way? Wickiewicz et al. (1983) said that this was done to "enable intermuscle comparisons" but I did not follow why normalization would be needed before doing that. Is it because the fibers may be at different locations on their force-length curves during the measurement?

Thanks,
Ross

[Steve Brown]

Re: Reference for PCSA values in regard of age and gender needed

Hi Ross,

Yes, muscles may be at different lengths, relative to optimal, when they are fixed. Normalizing to optimal length thus accounts for this discrepancy when calculating PCSA like this (important as fiber length appears in the denominator of the equation).

Note that optimal sarcomere length will differ amongst species, mainly due to differences in actin filament lengths; Gordon et el. (1966) studied frog muscle, optimal length for human muscle is longer (approx. 2.7 microns (e.g. Burkholder & Lieber, 2001)).

Steve

[Ton van den Bogert]

Re: Reference for PCSA values in regard of age and gender needed

I had not seen that before, but it makes sense as an attempt to obtain the optimal fiber length which is needed as a muscle model parameter. When a fiber length is measured in a cadaver specimen, the fibers will likely not be at optimal length.

The ratio Lfiber_meas/Lsarc_meas is the number of sarcomeres in series in the fiber, which will stay the same during a fiber length change, so this result does not depend on what the fiber length was when the cadaver was preserved. This is then multiplied by the 2.2 microns optimal sarcomere length, to obtain an estimate of the optimal fiber length.

Gordon et al measured the force-length relationship in frog muscle. For mammalian muscle, Huijing uses 2.4 microns [1]. I am not a muscle physiologist and I don't know what the consensus is on this.

If the physiological cross section area is calculated for the purpose of predicting the maximal isometric force, it would make sense to use the optimal fiber length in the PCSA calculation: PCSA = volume/optimal_fiber_length, rather than whatever the fiber length was during the measurement [1].

Ton van den Bogert

[1] Huijing PA, Maas H. Adaptation of physiological cross-sectional area and serial number of sarcomeres after tendon transfer of rat muscle. Scand J Med Sci Sports. 2016 Mar;26(3):244-55. doi: 10.1111/sms.12431.

[Ross Miller]

Re: Reference for PCSA values in regard of age and gender needed

Thanks Steve and Ton.

I found two references on human muscle that report an optimal sarcomere length of about 2.7 microns:

• Walker & Schroedt (1974): 2.64-2.81 microns (data from extensor digitorum longus, gastrocnemius, soleus, and sartorius, although it is not clear in the figure which muscle(s) the data are from)
• Lieber et al. (1994): 2.6-2.8 microns (data from extensor carpi radialis brevis)

I'm somewhat motivated now to put together a summary of these parameters (PCSA, fiber length, etc.). The most recent one is now 16 years old and there have been some major studies since then (e.g. Klein Horsman et al., 2007; Ward et al., 2009).

Ross

[Ross Miller]

Re: Reference for PCSA values in regard of age and gender needed

This is a work in progress, but I recently put together a summary of five parameters for muscle modeling here:

http://biorxiv.org/content/early/2016/12/03/090944

It includes data from 28 studies on PCSA, optimal fiber length, fiber type, pennation angle, and/or unloaded tendon length. Where possible I recalculated PCSA and optimal fiber length using the same definition (PCSA = V/Lo, Lo normalized to 2.7 microns) if the original study did something else.

In general the fiber length data are remarkably consistent between studies, the PCSA and pennation angle data are highly variable, and the tendon and fiber type data are rather sparse. The data are included as an electronic supplement.

I don't think I will try to publish this since it's not really "research" per se, but hopefully it will be a useful resource. Any feedback would be appreciated, in particular if there are any major studies I missed or if anyone has access to a copy of Weber (1846). I think bioRxiv lets you leave anonymous comments on the site.

Ross