The essay is not easy to write and likely won't be easy to understand if one is averse to facts. Ever since Sir Isaac got beaned by a golden delicious, the world became aware of Gravity. Gravity seems to be acting on everything and everyone on earth--except one Jeffrey Epstein, now allegedly deceased. Perhaps Mr. Epstein learned to overcome the laws of physics by consulting Stephen Hawking. For it seems to be almost a physical impossibility for Mr. E. to have broken several neck bones in his determined exitus from this mortal coil.

The following combines multiple issues:
1. Cervical spine anatomy
2. Autopsy evidence, more precisely the lack thereof
3. Material provided allowing said strangulation / hanging to occur
4. The anatomy of Special Holding Unit cells (the SHU)
5. Calculations of physical forces
...5 A. energy expenditure in free fall
...5 B. velocity at terminus of fall
...5 C. force generated by a fall
...5 D. force required to fracture cervical vertebrae

I will not concern myself with refuting or approving the "official story" as promulgated by Medical Examiner Sampson of NYC. She says it's suicide--and that's that. Would you question a doctor? I would and I do. But for the sake of this essay (and only for this essay) I agree to the following
1. The decedent is indeed one Jeffrey Epstein
2. He died of hanging, self-inflicted
3. Some fractures were noted in the neck on autopsy

But is this narrative believable? To address this, we must go back to basics. In this case, basics involve cervical spine anatomy, physics, SHU cell configuration.

Cervical Spine Anatomy

The cervical spine consists of 7 vertebrae, associated intervertebral discs, ligaments, blood vessels, and nerves. Not included are the hyoid bone or the trachea (the latter being both external to the spine and cartilaginous). The vertebrae are numbered from top down as C1 (first cervical vertebra = atlas vertebra), C2 (second cervical vertebra = axis vertebra) and five more, which resemble each other. The C1 and C2 vertebra are unique among the vertebrae, sharing features not present inferiorly (i.e., below them).

The upper image demonstrates the view seen on a lateral spine X-ray. The image below this is more detailed, showing multiplanar views plus labelling.

JE's hyoid bone was fractured. This bone is unique in that it is the only bone which does not attach to other bones--only to neck soft tissue. The incidence of hyoid fracture in one series was less than 25% in one study

Twenty male cases of suicidal hanging were reviewed. Fractures of the hyoid bone and/or thyroid cartilage were found in five cases (25%). Two cases ofthe hyoid bone fracture, two cases of thyroid cartilage fracture, and one case was both bone fractures. Mean age of all cases, non-fracture, and fracture cases were 42.40, 35.93, and 61.80 years, respectively The knot was at the back of the neck in most cases (12 cases, 60%) and at the left, front, and right in four, two, and two cases, respectively. However there was no relation between location ofthe knot at the neck and fractures of hyoid bone and thyroid cartilage (p=1). Incomplete and complete hanging were found in 11 and nine cases. Five cases with fractures of the hyoid bone and/or thyroid cartilage were incomplete hanging. The visual and palpatory examination did not detect the fracture of hyoid bone in all 20 cases but stereomicroscopy and stereomicroscopy with Toluidine blue stain detected fracture in three cases. For detecting thyroid cartilage fractures, all three methods had the same result.
CONCLUSION:
Fractures of the hyoid bone and thyroid cartilage in 25% of Thais who died of suicidal hanging were related with older ages and incomplete hanging but not related with location of the knot. The stereomicroscopic method is fast and effective in detecting fractures of the hyoid bone and thyroid cartilage.

The above quote means that of 20 self-inflicted hangings, only 3 had associated hyoid bone fractures on autopsy, aided by microscopic findings. That's 15% incidence.

I researched 20+ articles on duckduckgo and none told me any more than "the hyoid bone was fractured as were other vertebrae". Which vertebrae? How many? Show me the imaging, please. I am fully qualified to evaluate such by training and experience.

Here is a typical example of non-informative evidence:

Jeffrey Epstein, the convicted sex offender and financier to millionaires, sustained multiple breaks in his neck bones, The Washington Post is reporting that his autopsy reveals.

Reports show that Epstein’s hyoid bone near his Adam’s apple was severed, The Post reported through sources. Such broken bones can occur when a person hangs themselves, but more commonly occur when there is strangulation involved in homicide cases, according to the newspaper, a point backed up by multiple research studies.

https://heavy.com/news/2019/08/jeffrey-epstein-neck-bones-broken-autopsy/

Most often the cervical vertebra fractured is the axis, C2.

The Mechanism of Hanging

https://lateralscience.blogspot.com/2015/09/the-mechanics-of-hanging-popular.html

Professor Hoffmann,[3] of Vienna, says that, "in hanging, the noose does not press directly on the larynx and the trachea, but almost always slips between the larynx and. the chin. In these cases the basis of the tongue is pushed upward, and pressed against the posterior wall of the pharynx, completely closing it. The most important agent, however, in this kind of death is the compression of the larger vessels and the cervical portion of the vagus nerve, the upper portion of the carotid being pressed against the transverse processes of the cervical vertebræ before it branches off into the external and internal carotids, and the inner coat of the vessel being ruptured. The jugular veins are compressed at the same time, and the brain can neither receive any more blood nor allow that which it contains already to flow away; its irritability is therefore extinct. The very important part which both the vagus and the vessels take in causing death by hanging is clearly shown through the following observations: 1. Loss of consciousness following immediately the compression caused by the rope at the moment when the noose is drawn tight by the weight of the body. The truth of this assertion is proved by the fact that no person who commits suicide by hanging ever attempts to rid himself of the rope which throttles him, although he might do so easily by standing upright, as the body is not always suspended above the surface of the ground. 2. The rapidity with which death ensues and the beating of the heart stops. The few struggling respirations which generally occur in asphyxia shortly before death have not been observed in persons who have been hung. It is also well known how difficult it is to restore such patients to life. Death by hanging is, then, complex. It results from the occlusion of the respiratory tubes, from the sudden interruption of the passage of blood into the brain, and possibly from arrest of the circulation determined by the compression of the vagi nerves." These observations of Professor Hoffmann obviously refer to cases of constriction of the neck without dislocation of the vertebræ, and show how death should take place rather than how it does in cases of the short drop. The constriction of the neck is not usually so complete as he has assumed; the carotids are not completely obliterated, as shown by the pulse in the temporal artery, and by the gradual increasing congestion of the head—owing to the obstruction to the venous return—until at last the tongue is protruded out of the mouth; nor is the vagus much pressed upon, as evidenced by the long continuance of the heart's beats in manv cases. It shows rather a paucity of reasoning to infer immediate loss of consciousness because no suicide "ever attempts to rid himself of the rope which throttles him." A suicide is a very unlikely individual to change his purpose during the short period which elapses between suspension and loss of consciousness.

JE is purported to evidence petechial (small, capillary rupture) hemorrhages in his eyes, presumably both retinal and conjunctival. His eyes were at least initially protruding, a sign of increased intracranial venous pressure which occurs during sudden occlusions of one or both jugular veins. These two signs do not prove either hanging from manual strangulation, because either method may produce the same findings.

The Hanging article continues:

The shock to the nervous system produces an immediate loss of consciousness, with complete paralysis of all the voluntary muscles. It takes a body moving under the influence of gravity three quarters of a second to fall through the space of nine feet; and, owing to the velocity acquired, according to the law of uniformly accelerated motion, the time occupied in the last seven inches during—which the stretching and tightening of the rope occurs—is only •0225 of a second.

Continuing the calculations:

if the drop be long enough, the vertebræ are certain to be dislocated, no matter what be the position of the ring or thickness of the rope. The vis viva in any case is equivalent to half the mass multiplied by the square of the terminal velocity. Let W represent the weight of the criminal, and S the length of the drop, then the formula will be:
1/2 X MV2 =1 W / G2 X 2 G S = WS

or the weight of the criminal multiplied by the length of the drop expresses in foot-pounds the amount of work expended on the neck of the criminal.

Now is such a thing possible in a Special Housing Unit (SHU)?

From the Bureau of Prisons comes information about Special Housing Units

Note mention of inmate clothing and bedding--these are not the paper issues for inmates on suicide watch. Inmates can only have such clothing in SHUs for maximum 6 days. Then they are issued regular prison bedding and clothing.

inmates for dispute resolutions, intelligence gathering, or security threat group/disruptive group meetings. This also applies to removing inmates from a secure housing unit to meet with inmates in general population. Institution staff must rely on trained investigative techniques, link analysis, and other means of gathering information without allowing inmates into a secure housing setting to conduct face-to-face meetings with one another....

A multidisciplinary team that includes, at a minimum, institution executive staff, Correctional Services, unit staff, Health Services, and psychology staff reviews the inmate’s initial and ongoing placement in SHU. This committee meets on a regular basis, ordinarily weekly. ...

The Warden’s written approval is required prior to placing an inmate on alternate clothing/linen status. The Warden or Acting Warden may not delegate the authority to place an inmate in alternate clothing/linen (e.g., paper). The memorandum must include, at a minimum, the signature of the Warden, Health Services Administrator, and a psychologist. A written explanation of the reason(s) for alternate clothing/linen status must be included in the Warden’s authorization. This status will be reviewed every 3 days. Inmates will not be authorized to remain in alternate clothing/linen for more than 6 days. After 6 days, the inmate is removed from the alternate clothing/linen status, or, if necessary, a new authorization is generated. Inmates must be offered a change of clothing daily and the clothing must be adequate to the temperature in the SHU.

Alternate clothing/linen is authorized when an inmate alters, destroys, or uses a clothing/linen issued article in a manner that poses a threat to safety, security, or good order of the SHU or to herself/himself, other inmates, or staff.

Unfortunately cell dimensions are not mentioned but I include 3 illustrations of SHU cells fitted with bunk beds. None are from NY's Medical Correctional Center, however.

SHU with bunk bed, example 1

SHU with bunk bed, example 2

SHU with bunk bed, example 3

Note the low ceilings, usually no more than 9 feet. Also note absence of ceiling light fixtures.

Physics

For you number crunchers and other interested types, we go back to basics:

Force = Mass x acceleration

The units involved = foot-pounds per second. This is convertible to Newtons per second as follows:

Conversion of foot-pounds to Newton-meters

One foot-pound is the work done by a force of one pound acting through a distance of one foot in the direction of force.

Terminal velocity calculation: https://www.gigacalculator.com/calculators/terminal-velocity-calculator.php

The entries selected include body weight 200 pounds, vertical descent 415 feet, which would yield the maximum terminal velocity obtainable. Falls from heights of 6 feet are substantially slower.

Kinetic energy produced by a fall

In this instance, the calculations of kinetic energy assumes that JE jumped to his death from the top of the MCC to achieve true terminal velocity. How about from 9 feet, which is a generous estimate of vertical descent.

Free fall energy and velocity:

For this calculation I estimated the maximum vertical descent JE could have experienced if his ceiling was 12 feet high--which is a 33% over-estimation of ceiling height presumed.

Using a vertical descent of 11.5 feet, the force produced would be 2300 foot-pound force, which equals 3118 Newton-meters, clearly enough to fracture C2--if the fall occurred from a height of 11.5 feet.

Spinal Pathophysiology

Back to anatomy. The hanging article indicates that C2 is the vertebra most commonly injured in hanging. Many other articles, modern, confirm this. This is not new information. The odontoid process, sometimes called the odontoid peg, is the usual site of fracture from hanging. Sometimes hanging fractures result from C2-C3 dislocation, which occurs at the next lower vertebral level. But this fracture is a minority.

There are 3 types of odontoid fracture, naturally called types I, II, and III. Pictorially, they look like this:

Type 1 is almost never unstable. Type 2 is almost never stable. Type 3 is often stable. Stability means propensity to dislocate.

Experimental studies of cervical spine failure load and fracture patterns have been performed.

The injury mechanism and magnitude of failure load of C2 fractures are important in the clinical treatment of its fixation. The magnitudes of the failure load of C2 and the mechanism of injury in vivo are uncertain. Accordingly, nine C2 vertebrae obtained from cadaver spines, ranging in age from 51 to 80 years, were used for the study. Special restraint conditions were applied to yield specific fracture of C2. With the posterior element potted postero-anteriorly up to one-quarter of the inferior facet, posterior shear force ranging from 840 to 1220N was required to cause fracture across the pars interarticularis. For odontoid fracture study, a special rig was fabricated to encapsulate the body of C2 in a cell using ISOPON, and a thin layer of ISOPON sandwiched between the inferior facets and two lateral plates. The assembled rig permits slight sagittal movement of C2 about the cup lateral pivot supports. Failure load of between 900 and 1500N was recorded for odontoid fracture. These values are in agreement with published data. The experiment carried out under these two different restraint conditions had specifically resulted in different fractures of C2. In reality, depending on factors such as the inclination of this force vector applied to the head, the precise posture at the time of trauma, the spinal geometry, and the physical properties, different types of fracture patterns of C2 may be produced. This additional data will be useful in the biomechanical study of C2 vertebra using analytical approaches, and in surgical anterior/posterior fixation using screws.

https://www.ncbi.nlm.nih.gov/pubmed/11448692

So, all this shows that JE could have fracture his odontoid, as well as the hyoid. Yes and no. Could JE have launched himself off the top of the bunk bed, violently jerking his neck to hyperextension and constricting vital circulation? Interesting--but no proof.

His fall was certainly from a lower height, probably not more than 6 feet, and likely only 4 feet or less, considering the height from knee joint to chin.

Here is a revised energy estimate from a four foot descent:

Conversion of Joules to newton-meters: https://www.metric-conversions.org/energy-and-power/joules-to-newton-met...

918 Joules = 918 Newton-meters.

But this is still in range of fracturing necks, though at the lower range--under ideal conditions: meaning slip knot slipped appropriately, sheets did not stretch, sheets did not tear and JE kept his knees bent at least 90˚ at the end of descent.

What about old folks--you know greater than 65 years? Aren't they more prone to neck fractures, particularly of the odontoid? That has been studied.

Studies in patients aged 65 years with a minimum follow-up of 12 months were selected. One-hundred twenty-six articles were reviewed. No class I study was identified. There were two class II studies and the remaining were class III. Significant variability was found in the literature regarding mortality and morbidity rates in patients treated with and without halo vest immobilisation.

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3030710/

But what about oldsters with osteoporosis? Are they more prone to odontoid fractures than those Osteoporotic odontoid fractures in the elderly

We conducted a prospective study from January 2016 to January 2017 in patients > 65 years old, hospitalized in Nice University hospital for low energy odontoid fracture. An evaluation of bone status was proposed within 3 months after fracture event. Evaluation included demographic data, clinical risk factors of osteoporosis, bone mineral density (BMD) at spine and hip and vertebral fracture assessment (VFA) by dual X-ray absorptiometry and serum analysis to detect secondary osteoporosis.

Results:

38 patients were hospitalized for odontoid fracture: 8 patients 27 odontoid fractures followed a low energy impact: 18 women and 9 men, mean age 83.8 y. (±10.7). 8 patients died before bone status assessment (5 men and 3 women), 6 died during hospitalization with a mean delay of 3.5 days (±1.87) and 2 after discharge (1 month and 5 month). 3 patients refused bone status evaluation, 5 were lost to follow-up and 1 is awaiting evaluation. Finally 10 patients had bone status evaluation, all women, mean age 84.2 y. (±8.9). None had parental history of hip fracture, 1 had an early menopause, 1 received aromatase inhibitors for breast cancer and 2 had a history of steroid therapy (> 3 months). 3 patients had previously received hormone replacement therapy, 1 received bisphosphonate for 5 years and 4 had calcium + vitamin D supplements. Lumbar spine mean T-score was -1.45 (±1.08), femoral neck: -2.37 (± .040) and total hip: -1.99 (±0.6). VFA analysis revealed 4 unknown vertebral fractures. The table summarizes population bone status: 8 patients out of 10 fulfilled diagnostic criteria of osteoporosis, including 6 with previous fractures. 2 patients with T-score > -1.DS didn’t have hip BMD assessment because of bilateral hip replacement but had previous major osteoporotic fractures. No secondary osteoporosis was detected.