Ixodidae Ticks of Bovine; Prevalence and Major Species Identification in Soddo Zuria Districts of Wolaita Zone, Ethiopia _Crimson publishers

 Ixodidae Ticks of Bovine; Prevalence and Major Species Identification in Soddo Zuria Districts of Wolaita Zone, Ethiopia by Biruk Alemu in Approaches in Poultry, Dairy & Veterinary Sciences_The Journal of Poultry Science

Abstract

The distribution and abundance of cattle tick species in Soddo Zuria woreda, Wolaita zone, was studied over a period from November 2016 to April 2017. Adult ticks were collected from seven main body regions of 501 cattle which were under an extensive management system. Out of the total of 501 cattle examined, 327 (65.27%) were found to be infested by one or more tick species. In this study, 3290 adult ticks were collected from the animal body parts and identified to genera and species level. Four tick species of three genera (Amblyomma, Boophilus, and Rhipicephalus) were identified. The relative prevalence of each species was Boophilus decolaratus (45%), Amblyomma varigatum (23%), A. cohaerence (17%), and Rhipicephalus evertsi-evertsi (13%). The risk factor like sex of cattle did not show significant association with the infestation rate but there was an association with age, breeds and body conditions. The prevalence of tick infestation in poor body condition (75%), medium body condition (61%) and good body condition (55%) were found to be statistically significant (p<0.05) among the three groups of body conditions.

The prevalence of tick infestation was found to be statistically significant (p<0.05) among the three breeds, with the highest prevalence in local breeds (70%) than both exotic (62%) and cross breeds (54%). The result indicated that the favorable predilection sites of Amblyomma species were ventral body and perineum. B. decolaratus preferred dewlap, udder/scrotum, belly, leg/tail, head, and perineum. R. evertsievertsi had strong predilection sites for perineum, dewlap, udder/scrotum, and ears. The sex ratio of all tick species identified during this study periods was skewed towards male except for B. decolaratus. Considering the economic importance of tick and tick-borne diseases (TBDs) in the Soddo Zuria district, also in the country, there should be country wide control strategy, taking into account acaricide residues in products.

keywords: Attachment site; Cattle; Ixodidae; Prevalence, Soddo zuria woreda; Tick burden

Introduction

Ticks are obligate, blood-feeding ectoparasites of vertebrates, particularly mammals and birds. It has been estimated that about 80% of the world population of cattle is infested with ticks. The lifecycle of ticks (both Ixodids and Argasids) undergo moulting stages in their development; eggs, 6-legged larva, 8-legged nymph and adult [1]. According to the numbers of hosts, Ixodids ticks are classified as one-host ticks, two-host ticks, three-host ticks and Argasids classified as multi-host ticks. In one-host ticks, all the parasitic stages (larva, nymph, and adult) are on the same hosts; in two- host ticks, larva attach to one host, feed and moult to nymphal stage and engorged, after which they detach and moult on the ground to adult; and in three-host ticks, the larva, nymph, and adult attach to different hosts and all detach from the host after engorging, and molt on the ground. In multi-host ticks (Argasids), a large number of hosts are involved, and it is common to have five molts, each completed after engorging and detaching from the hosts [2].

Ticks are most numerous, particularly in tropical and sub-tropical regions, and their impact on animal health and production is greatest in these regions [3]. Ticks are usually relatively large and long-lived, compared to mites, surviving for up to several years [4]. Ticks belong to the phylum Arthropod, class Arachnid, and order Acari. The families of ticks parasitizing livestock are categorized into two, the Ixodidae (hard ticks) and Argasidae (soft ticks). Though sharing certain basic prosperities, they differed in many structures, behavioral, physiological, feeding, and reproduction pattern [5]. Ticks that are considered to be most important to domestic animals’ health in Africa comprise about seven genera and forty species. Among these tick genera, the main ticks found in Ethiopia are Ambylomma (40%), Boophilus (21%), Heamaphysalis (0.5%), Haylomma (1.5%), and Rhipicephalus (37%) [1]. Among these, A. varigatum and B. decoloratus are the most important and widely distributed [6].

A. coherence, A. gemma, A. lepidium, Haylomma marginatum rufipes, H. truncatum, and R. evertsi are also commonly found in Ethiopia [7,8]. Even though there were a number of studies on ticks and tick-borne diseases (TBDs) in many parts of Ethiopia, in some location, there was no previous study on tick and TBDs. Therefore, the objectives of this study were to estimate the prevalence of tick infestation of cattle in Soddo Zuria district and to identify the common tick species in Soddo Zuria district.

Materials and Methods

Description of study area

The tick survey was conducted in South Nation Nationalities and Peoples Region, Wolaita zone particularly, in Soddo Zuria woreda from November 2016 to March 2017. The town is located 380 km Southwest of Addis Ababa on the way to Arbaminch town and it has a latitude and longitude of 6°54′N 37°45′E with an elevation between 1650 and 2980 meters above sea level. The town is bounded with Damot Gale Woreda to the North, Humbo Woreda to the South, Damot Woide Woreda to East and Damot Sore Woreda to the West. The annual rainfall of the area is 1000-1200mm. The dry season extends from September to February and the rain season stays from March to August. The livestock population of the area comprised about 1,097,710 cattle; 150,383 sheep; 185,250 goats; 60,055 equines and 734,924 poultry [9].

Study population

The cattle population found in Soddo Zuria woreda was considered as a study population. The study populations were constituted in all breeds that are known as local, cross and exotic breeds depending on their respective blood level. Therefore, local breeds have pure indigenous traits, cross breeds have both indigenous and exotic traits about less than 75% and exotic breeds are considered having more than 75% of the exotic trait.

Study methodology

The selected study animal was properly restrained, and all tick samples were collected from half the body regions. Ticks were removed carefully and gently in a horizontal pull to the body surface. The collected ticks were preserved in universal bottles containing 70% ethanol and labeled with respect to predilection site, age, sex and date of collection, then transported to Wolaita Sodo Regional Veterinary Laboratory for counting and identification. The ticks were counted and subsequently identified to genus and species level by using stereomicroscope, according to standard identification keys as given by [10].

Sampling design and technique

A cross-sectional study was conducted to determine the prevalence of ticks, and identification of species of ticks collected and labeled according to predilection site. All the animals selected as sampling unit were checked for any tick infestation based upon the numbers of ticks found on the animal and the study record period. Ticks were collected from ears, heads, dewlaps, belly/flunk, udder/scrotum, perineum and legs/tails in the separated sample bottles with 70% ethanol. In addition to the attachment site of tick in different body regions, the burden of ticks based on age, sex, body condition, and breeds of animals were determined.

Sampling methods and determination of sample size

The cattle to be examined were selected by simple random sampling method, and multistage sampling strategy was used to determine appropriate sample size. The sample size was determined by using the formula given by Thrustifield [11]. The expected prevalence of Ixodidae ticks of cattle in Soddo Zuria woreda was assumed as 50%. The parameters used were 95% confidence interval and 5% desired level of precision. By substituting these values in the formula, the sample size was calculated to be 384 as shown below but, 501 animals were included in the study to increase precision.

Where,

n=Sample size;

Pexp=Expected prevalence;

d2=Expected precision which is usually 5% (0.05)

Data analysis

The data collected were entered and managed in Microsoftexcel. An intercooled SPSS 20 version software [12] statistical program was employed for the data analysis. The overall prevalence of tick was determined by dividing the number of positive animals by total sample size and was expressed as a percentage. Chi-square (X2) test was used to assess if there was a statistically significant association in tick infestation between ages, sex, breeds and body conditions.

Result

In the current survey, a total of 501 animals were included with breed distribution of local (n=308), cross (n=137), and exotic (n=56). Out of the 501 animals examined, ticks were found on 327 animals yielding an overall prevalence of 65.27%. The distribution of tick genera was identified and located in Table 1 below. The statistical analysis was done for the prevalence of tick infestation with hypothesized risk factors (age, sex, breed and body condition). There were statistically significant association with breeds (x2=11.9698, P=0.003), body conditions (x2=14.2337, P=0.001) and age (x2=9.8475, P=0.0) (Table 2). Higher tick infestation rate was seen on both poor body condition and local breeds. There were no statistical significances (P>0.05) associated with the sex of animals (Table 2). Of the total 3290 Ixodid ticks collected from seven body region of 327 cattle, four different species in three genera were identified. The tick species identified were B. decolaratus (45.47%), R. evertsi subspecies evertsi (13.98%), A. varigatum (23.04%) and A. cohaerence (17.5%) (Table 3). By considering the relative abundance of each tick species identified in the study area, B. decolaratus was the most abundant (45.47%) and R.eversi subspecies eversi were the least abundant (13.98%).

Table 1:Distribution of tick genera of cattle in the study area.

Table 2:Prevalence of tick in relation to body conditions breeds, sex and age of animals.

Table 3:Number of tick Species identified in half body region of cattle.

The observed proportion of tick species of Ambylomma identified during the study preferred udder/scrotum, dewlap/ brisket, perineum, belly/back, legs/tail, and head regions. The B. decolaratus preferred the attachment site such as dewlap/brisket, udder/scrotum, belly/back, legs/tail, perineum, ears, and heads regions. The Rhipicephalus species were encountered mainly in the perineum, dewlap, udder/scrotum, ears, belly/back, and head and legs/tail regions (Table 3). The numbers of ticks collected from the cattle dominated by males, but an exception was found in one host tick (B. decolaratus) in which females’ collection was higher than the males’ (Table 4).

Table 4:The distribution and sex ratio of adult tick species in the study area.

Discussion

The prevalence and distribution of the most common tick species infesting cattle are different from one area to another. In the present study, a detailed investigation was carried out to identify and determine the type of species and predilection site of ticks infesting cattle in Soddo Zuria district. Although there are different species of ticks, only four species of ticks, B. decolaratus, A. varigatum, A. coherence, and R. evertsi evertsi were identified. B. decolaratus were found to be the most abundant tick species in Soddo Zuria district with a rate of 45.47%. This finding was in agreement with the report of Sileshi et al. [13] who described that B. decolaratus was the commonest and most widespread tick in Ethiopia, collected in all administrative regions except in the Afar region.

The current finding was also in line with the report of Tamru [14] in Asela et al. [15] in Ethiopia, who reported the highest prevalence of B. decolaratus (80%) in the study areas. According to Shiferaw [16], B. decolaratus had the highest frequency in the observed area during dry seasons (January, February, and early March) in Wolaita zone. This result disagreed with the findings of Alekaw [17] at Metekel Ranch, Ethiopia showing the prevalence of 5.7%. This may be due to the geographical location and altitude factors which are 1,500 to 1,600m above sea level of Metekel Ranch. The females were abundant from September to April and transmitted Babesia bigemina to cattle, and a severe infestation can lead to tick worry, anorexia, and anemia [18]. The one-host ticks of the genus Boophilus that parasitize ruminants represent a hindrance to livestock farming in tropical and sub-tropical countries. They transmit the causative agents of Anaplasmosis (“Gall Sickness”) and Babesiosis (“Red Water”) in cattle [10].

A. varigatum was the second widespread tick species of the cattle in the current study area with a rate of 23.04%. This result disagreed with different reports done by other authors in different parts of Ethiopia such as Tessema & Gashaw [19] in Asela, Belew & Mekonnen [20] in Holeta, Seyoum [18], Mehair [21] in Awassa who as described A. varigatum as the first most abundant tick species in their study areas. The difference in result was due to the geographical location where A. varigatum was found in highest number in the highland and high rainfall, and also due to its being relatively active throughout the year in most part of Ethiopia.

A. varigatum is a widely distributed cattle tick in Ethiopia [22], and it is a potential vector of diseases caused by Cowdria ruminantium, Theleria mutan, T. velifera (“Benign Bovine Theileriosis”) and viral diseases, Nairobi sheep disease, and also aggravates the situation of bovine dermatophilosis (Dermtophilus congolence) [13]. The study conducted in Wolaita zone by Dessie & Getachew [23] agreed with this study that shows A. varigatum was the second abundant tick species at Highland and Midland, and the first abundant in the lowland during the wet period. This variation may be due to the change in environmental conditions, with the result of global warming that highly affects the ecology of ticks. Change in temperature and rainfall have been reported to affect the distribution of diseases of vectors and tick-borne diseases [2].

A. cohaerence was the third abundant tick species with a rate of 17.5% in the study area. Amblyomma coherence is the most prevalent and abundant tick on cattle [24]. According to [25], A. cohaerence was also the third abundant tick species in the Bench Maji zone with a prevalence of 4.2% in the area. The prevalence of A. cohaerence is alarmingly important as this tick has been reported as a vector for C. ruminantium which is the causative agent of cowdriosis (“Heartwater”) [13]. Moreover, Amblyomma coherence transmits Ehrlichiosis, but less important vector than A. varigatum. Another report indicated a spontaneous infection of Amblyomma coherence by Rickettsia conorii in Ethiopia [25,26].

R. evertsi-evertsi was found to be the least abundant with a rate of 13.98% tick species in this study area. The native distribution of R. evertsi-evertsi in Ethiopia seems to be connected with middle height dry Savannas and steppes, in association with zebra and ruminant and it is widely distributed throughout Ethiopia [20]. This tick species shows no apparent preference for particular altitude, rainfall zone or seasons [24]. According to Sileshi et al. [13], R. evertsi-evertsi was collected throughout their study period, with the peak of abundance in January coinciding with the beginning of the rainy season and they also described that the discovery of this tick in that area was in line with its widespread occurrence in most parts of the country. The occurrence of this species in and around the Wolaita zone was also reported by Dessie & Getachew [23]. R. evertsi-evertsi has short mouthparts with which to feed on a soft area. As a result, it is a possible vector of Babesia, Rickettsia, and Theleria [27].

Ticks are known to be distributed in different parts of the host’s body. In this study, the main infestation site of ticks in the body of hosts was dewlap, udder/scrotum, perineum, and belly. A variety of factors such as host density, the interaction between tick species, time and season, and inaccessibility for grooming determined the attachment site of the ticks on the skins [28]. The predilection sites found in this study were in line with those reported by Seyoum [29] and Behailu [30] in their study conducted in North Wollo zone and Asela, respectively.

In the current study, different animal-related risk factors were studied to determine whether there was a significant variation in tick infestation between and among different groups of animals with suspected risk factors. The proportion of tick infestation was higher in adult animals as compared to young animals. As a result, there was a statistically significant association (p<0.05), and the higher proportion may be due to outdoor management and longdistance movement of adult animals to search for food and water compared to younger animals, so the chance of exposure was higher. This finding was also in agreement with the finding of Feseha [31], Tessema & Gashaw [19] and Belew & Mekonnen [20] who stated a higher proportion in adult cattle.

There was a statistically non-significant association (p>0.05) in the infestation rate among different sex groups, where the higher infestation was recorded in female animals compared to their counterparts. Higher infestation in the female might be due to seasonal variation in some hormones like prolactin and progesterone at a higher level and stressors of production (such as pregnancy and lactation) that make female animals more susceptible than male [32,33]. It may also found that immunecompromised animals acquire high tick infestation in more over the stress of production such as pregnancy and lactation make the females more susceptible to such infestation. This result disagreed with the previous work done by Hussen [34] in Bako.

The proportion of tick infestation was higher in poor body conditioned (75.7%) as compared to medium body conditioned (61.65%) and good body conditioned animals (55.93%). This was due to the fact that poor body conditioned animals having reduced immunity and are exposed to any kind of disease when grazing on the field. The result of the current study agrees with Okelly & Seifert [35] who reported that the dietary deficiencies that influence the breakdown of tick resistance. The observation indicates that poor body conditioned animals are less resistant to tick infestation and lack enough body potential to build resistance with age advancement. Several authors have reported that high infestation of tick results in poor body condition due to the consumption of the high amount of blood and fluids by those ticks [36].

According to Aerts & Neshem [37] who reported the British cattle breeds having the lowest body condition score under tropical conditions had the highest infestation of ticks. Seid [38], Southerest [36] and Bianchi et al. [39] reported that tick load on the animal might be affected by breed and nutritional stress. Ultimately, these factors affect general body condition, which in turn affects blood composition, respiratory rate, appetite and eventually leads to poorer body condition score. However, the well-fed animals were very resistant to any kind of diseases when they grazed in the field or are kept at home. The fact that more tick burden was recorded in both local and exotic breeds compared to cross cattle.

The current finding agrees with the report by Belew & Mekonnen [20] that revealed the presence of tick infestation in local breeds were very high with the prevalence of 44.96% (n=223), while in cross breeds and Jersey, the prevalence were 15.83% (n=57), and 8.50% (n=30) respectively. The significant variation in tick infestation of cattle of different breeds may be attributed to the different management system, lack of supplementary feeding for local breeds, or lack of control measures against tick on local breeds. Furthermore, it can be assumed that it might be due to the lack of interest of farmers for local breeds as well as taking more care to cross and exotic breeds than local breeds.

The male to female ratios of B. decolaratus, A. varigatum, R. evertsi-evertsi, and A. cohaer were similar to previous reports of Seyoum [29] and Solomon et al. [28]. Except for B. decolaratus, all other species tick’s males outnumbered females because males normally remain on the host longer than females. Fully engorged female tick drops off to the ground to lay eggs while males tend to remain on the host up to several months to continue feeding and mating with other females on the host before dropping off [28]. The females of B. decolaratus outnumbered males in this study might be probably due to the small size of the male which may not be seen during collection [19].

Conclusion and Recommendation

Variable information on tick species distribution and dynamics are very essential to assess the economic loss encountered due to tick infestation and also to identify the appropriate measure of tick control. Among ectoparasites, ticks cause the greatest economic loss in livestock population either by transmitting a wide variety of TBDs or by affecting the health of animals as well as the quality of hiding and skins. The important and abundant tick species investigated in the study area were B. decolaratus, A. varigatum A. cohaerence, and R. evertsi-evertsi. The study indicated that there was a high burden of ticks in the area. However, the attention given to controlling the infestation had not been sufficient.

The control methods necessary for tick and TBDs were a selection of tick resistance cattle, acaricides treatment, appropriate livestock management, evaluation and incorporation of traditional practices or remedies that appear to be of value. In general, the distribution of ticks are not fixed but are determined by a complex interaction of factors such as climate, host density, host susceptibility, grazing habits, and pasture-herd management. Therefore, an effective tick control program should be formulated and implemented based on the distribution pattern of ticks and factors responsible for their distribution.

In light of the above conclusion the following recommendations are forwarded:

A. Tick control program (Application of Acaricide) should be continued with an increasing frequency of application in wet months.

B. Detection of acaricide resistance tick species which are economically important since limited types of acaricide was used in the area.

C. More attention should be given to the selection of resistant cattle breeds and types, and good performance with regards to the production of local breeds.

Appropriate pasture management in communal grazing area is recommended.

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Global Workspace, Self, and Mathematical Intuition_Crimson publishers

 Global Workspace, Self, and Mathematical Intuition by Robert Skopec in Research in Medical & Engineering Sciences_Journal of Medical Sciences

Abstract

In human consciousness a world of separated objects is perceived by an inner observer as a feeling of One-self. A topological correlation of the Self to the world, by either emerging all separated objects into one or splitting the Self in as many disconnected Sub-selves as there are objects perceived. The Self is generated in a neural network by algorithmic compression of spatial and temporal information into a toponeuronal structure (TNS). A correlation of an inner observer to parts of a structure inevitably entails a correlation to the whole, serving of the Self. Molecular mechanisms for the generation of a TNS in a neural network will be discussed.

Introduction

Coding of reward probability and uncertainty by dopamine neurons

The brain continuously makes predictions and compares outcomes (or inputs) with those predictions. Predictions are fundamentally concerned with probability. Substantial evidence indicates that dopamine neurons of the primate ventral midbrain code errors in the prediction of reward. Dopamine neurons of ventral midbrain areas A8, A9, and A10 were identified solely on the basis of electrophysiological characteristics, particularly the long waveform of their impulses (1.5 to 5.0ms). The phasic activations varied monotonically with reward probability. Statistical analysis revealed a significant effect of uncertainty on the population response (P<0.005 in each of four data sets) indicating that the sustained activation codes uncertainty. The peak of sustained activation occurs at the time of potential reward, which corresponds to the moment of greatest uncertainty [1].

The uncertainty is signaled by dopamine neurons, and the common measures of uncertainty (variance, standard deviation, and entropy) are all maximal at P=0.5, having highly nonlinear relations to probability, being very sensitive to small changes in probability near the extremes (P = 0 or 1). By always coding prediction error over the full range of probabilities, dopamine neurons could provide a teaching signal in accord with the principles of learning. The goal of learning can be seen as finding accurate predictors for motivationally significant events.

As indicated by mathematical principles of Shannon information, only in the presence of uncertainty is it anticipated that there will be information available in the outcome. When the prediction of reward is uncertain, the outcome (reward or no reward) always contains information. The outcome at P=0.5 contains, on average, the maximal amount of information (one bit) of any probability. The responses of dopamine neurons multiplicatively combine the probability and magnitude of reward.

The error-likelihood model of global workspace

Such techniques as functional magnetic resonance imaging (fMRI) and electrical recordings from single neurons enable dissection of the brain activities that underlie mental operations. The new works illustrate that neurons in the frontal region of the brain (or neuronal ensembles, or brain areas) may dynamically and adaptively switch between multiple functions. During a dynamic decision-making task is involved the comparison of two quantities (two frequencies of vibration presented to a fingertip), separated by a delay [2].

The mental operations involved in this quantity-comparison task in frontal region included:

1. perceiving the first signal S₁, holding in working memory for several seconds,
2. perceiving the second signal S₂, and
3. Deciding whether it was of lower or higher quantity than the first.

Neurons in the secondary somatosensory cortex of monkey brain remained silent in the delay interval between S₁and S₂, their preferences remained invariant. Neurons in the prefrontal cortex, by contrast, showed differential preferences for the low versus high quantity also during the delay interval, during which they sustained their preferential firing patterns. In the decision phase, however, prefrontal cortex neurons no longer encoded information about high versus low quantities, but rather encoded information for “S₂1 “ or “S₂>S₁ “, respectively.

The firing rates of single neurons in the prefrontal cortex:

1. first encode the quantity of S₁,
2. then represent the active maintenance of that quantity in working memory, and
3. Finally reverse sign to encode the appropriate decision.

Machens et al., results clearly show that the networks of prefrontal cortex neurons can dynamically adapt and reconfigure the encoding functions represented in their firing patterns as the cognitive flow develops, without changing their connectivity [3].

Neurons know when to encode a particular activity:

1. A. cognitive control should be envisioned as emergent properties of the neural network configuration,
2. B. More elementary mechanistic processes being tailored to allow new functions to emerge.

Probabilistic coding applies:

1. within-trial changes in the firing patterns of prefrontal cortex neurons,
2. the emergence of cognitive control through learning,
3. the specialized higher order nature of process called performance-error monitoring
4. a new function that emerges,
5. from more basic neural mechanisms for conflict detection,
6. which usually reside in medial frontal cortex (MFC) neurones,
7. detecting the simultaneous activation of competing correct and incorrect responses.

Both error detection and conflict monitoring are part of the computational process in which activation of MFC neurons is proportional to the perceived likelihood of an error taking place [4,5]. The representations of the likelihood of error by the MFC develop through experience. Such representations build:

1. on reinforcement-learning processes,
2. Mediated by phasic decreases in midbrain dopamine projections to the MFC when ongoing events turn out worse than expected.

The MFC as Global Workspace (GW) determines:

1. which goals may not be achieved,
2. a rewards may not be obtained unless the level of cognitive control is subsequently increased.

This increase in cognitive control takes place:

1. when a response conflict indicates a reduced probability of obtaining a reward,
2. when errors signal the loss of an anticipated reward,
3. the context predicts the likelihood of imminent errors.

These patterns of neural firing confirm that the principal task of the MFC-GW is:

1. to monitor performance,
2. to compute and signal the likelihood of obtaining or losing rewards in response to particular actions [6],
3. Guides decisions about which actions are worth taking [7].

The probabilistic error-likelihood model of the GW in consciousness must incorporate transient disengagements of MFC activity that predict errors. Occasional lapses and other forms of variability are characteristics of all cognitive processes [8]:

1. the fMRI revealed greater activity in the MFC during the high-error change trials compared with low-error change trials,
2. MFC activity increased with practice, reflecting an improved ability to predict the likelihood of making an error.

The toponeural structure (TNS) can itself be divided into a subsystem that is open to energy and information flow, and the subsystem´s environment: larger dual topological complex (L-DTC). The whole combined system still obeys the second law of thermodynamics, but it is possible that the subsystem: smaller dual topological complex (S-DTC) can experience a decrease of entropy at the expense of environment [9].

The entropy increase in the „sub-system environment“ is guaranteed by the second law, to more than offset the entropy decrease in the smaller, but main dual topological complex (M-DTC). The subsystem can only be maintained away from equilibrium as long as there is usable energy in environment. When the environmental energy at maximum (no usable energy), the subsystem is guaranteed itself proceed to equilibrium [10].

Toponeuronal model of the MFC: The medial frontal cortex (MFC) is a comparator system, which is the basis of global workspace (GW) in the human brain. As it proposes B. Baars [11,12], the consciousness is the result of a GW and distributes information to the huge number of parallel modules-processors that form the rest of the brain. The GW can be seen as main dual toponeuronal complex (M-DTC), correlated through GM with other modules: smaller DTCs (S-DTCs). The large complex of GW is formed by M-DTC plus S-DTCs.

Self-similarity between contents of the GW, endomorphisms (E) (internal transformation reshaping itself) and their shapes is mapped (simulated, replicated) into working memory (WM), if lead to the Morita-I, II, III, equivalence, could form the Self (consciousness) online circuit. Conscious are all contents of GW which are in real time restriction mapping an online reentry to WM. Consciousness can be understand as a neural online simulation generated in the frontal cortex of the brain. The stimulus beyond the GW is unconscious.

Based upon the reciprocal connections of the cingulated cortex with the hypothalamus, papez proposed that the cingulated cortex is involved in the subjective experience of emotions (EQ). Now it is suggested the anterior cingulated cortex (ACC) is involved in detecting when strategic control is required and the lateral prefrontal cortex is involved in strategic control. Some current findings are supporting the role of the ACC as an autonomic regulator during a need to monitor the sympathetic system. During cognitive activity, ACC activity begins within the first 150ms of a task that takes ~1100ms. Although the heart rate does speed up during target processing, it also tends to slow down while waiting for targets [13].

It has been proposed that the ACC plays a prominent role in the executive control of cognition, and could also participate in processing information and subjective faithful states. We propose that implementing a comparator process, the ACC monitors competition between processes that conflict during task performance. Dipole modeling suggests that an error-related negativity (ERN) has a medial frontal generator, possibly the ACC. The role of ACC in higher level cognition include the hypothesis that it is involved with late selection as attention to action, and is also responsive to errors, and may by a candidate for main dual toponeuronal complex (M-DTC) [14,15].

The alternative leads to the idea of immediate interaction of Ψ-function of macro-state (let’s name it ⍵-function) with Ψ-function of micro-state. The notion of ⍵-function has the content only when this ⍵-function is marked in the macro-world. Otherwise ⍵=Ψ.

Therefore, by calculating statistical weight of such a state (its logarithm due to Boltzmann equation is equal to the entropy with the accuracy up to a constant) we must not sum up the probabilities of alternative microstates, but multiply conditional probabilities of all succession microstates, composing the “thickness” of present for the given living macrostate [10]. This multiplication results in the statistical weight value less than one and, hence, to the negative value of entropy. Such re-normalization is a constant outer interference (topological neighborhood function), namely, from macro-state side having its own plot, image into the natural dynamics of microstates. And in this case the element of “miracle”, i.e., discrepancy of the observed processes at the microlevel for the second law of thermodynamics, and uncertainty of future to past, is introduced into the natural dynamics. The measure of this element is anti-entropy [16] and ⍵=Ψ-interaction (re-normalization of probabilities) is the mechanism of anti-entropy origination. We note that most theories of conscious processing have failed to recognize the important role of spontaneous thalamocortical activity within a distinct set of GW neurons [17].

Self

Topology of the Self: Topographic means that a sensory receptor sheet receiving signals from the world connects to its recipient map in such a way that neighboring locations in the sensory sheet are also neighboring locations in the recipient map. The interaction of multiple restriction maps can be coordinated in the same way. Coupling the outputs of multiple maps reentrantly connected to the sensorymotor behavior is achieved through a higher-order structure of global restriction mapping (GM). GM is a dynamic structure containing multiple reentrant local maps (motor and sensory) able to interact with nonmapped parts of the brain (the hippocampus, the basal ganglia and the cerebellum).

The brain carries out a process of conceptual “selfcategorization”, by matching past perceptual categories with signals from value systems, carried out by cortical systems capable of conceptual functions. Perceptual experience arises from the correlation by a conceptual memory of a set of ongoing perceptual categorizations [18].

1. Self (the social selfhood): Internal systems arise from interactions between the limbic and the cortical systems (brain stem, hypothalamus, autonomic centers).
2. Nonself (other entities): Differing from the Self the outside-world systems are strictly cortical (primary and secondary cortex for sight, hearing, touch, etc.) Both have correlations (through reentrant mapping) in hippocampus, amygdala, septum, and special value-category memory in frontal, temporal and parietal cortex.

Suppose that the Self can be defined as a set S with only one member: S itself. S is introduced as a quality in order to have a variable. Now suppose there is a topological space X in which this information is distributed. We will define a group of spatially distributed sensations as subset A disjointed from the complement subset non A. Accordingly, the intersection of A and non A will form an empty set: A and non A=0. Depending on which information S is focused on it will also be embedded in the respective and in turn distinct subspace or it will be split into two disjointed subsets S₁or S₂.

This correlation encoding the entire structure perceived by the Self is a scale-invariant magnification of each part of it. A solution for equation with x=S and X is then given by the power law: f(x) = Cx ^(1-D)

where, C is a constant and D = lim(x to 0) [logN(x)/log(1/x)].

The tiling of the world in our mind

The primary goal is to develop a figurative but still completely abstract algorithm for the realization of spatial information perceived in our consciousness. The smallest fractal d{SX} could represent the elementary tile for the construction of space perceived in consciousness. The metric underlying the elementary tile d{SX} can be formed by a coordinate system with the principle axes xⁱ lying in the plane enclosed by the tile.

In order to describe the perception of space by an inner observer it is suggested that these vectors generate the three components Xⁱ, Yⁱ, Zⁱ for one point in a three-dimensional space perceived by the Self. The respective operation “lifts up” the spatial information given by the fractal in R2 to a point seen in R3. The eye representing the Self, as the inner observer of visual information, adopts a dual position in either R2 or R3, indicating a general consideration for any RN. The components of any point perceived in consciousness are subject to transformation to a coordinate system opposite to the position of the observer [19].

Each elementary tile behaves like a “point”, but forms a connected space with other tiles covering the entire coherent lattice. The size of adjacent fractals may vary depending on the actual coherence length. This does not violate the principle of selfsimilarity, but gives rise to points in R3 with different distance to R2 and may distribute them in a three-dimensional space as it is experienced in our mind. It should be emphasized that the space perceived in consciousness is not to be assigned to Euclidean space, but to Grothendieck topology in the brain.

Suppose that in a pre-coherent state t1=x_c-x₁ and dx₂=x₂-x_c with the probabilities p₁(dx₁) and p₂(dx₂). The distribution of the Self is then given by a Markov operation according to fractal image construction:

M(v)=p₁ v(S) w_-1(dx₁)+p₂ v(S) w_-1(dx₂)

with w(dx) = Hutchinson operator with w_-1 = pre-image on dx

v(S) = integral of {u(dx,t) dx}

u(dx,t) = distribution density of “S” on the pre-image.

An iteration of w(dx) leads to a fractal distribution of S on sequentially contracting intervals of dx. After sufficient downscaling iterations, S is driven to the attractor x_c+/-dx₁ which is equivalent to the point of coherence. The probabilities for the distribution of S onto dx derived from the Markov process are transformed into those for the description of coherence equilibrium. An autonomous organism must be capable of generating spontaneous representations and intentions (Self-activation). The [17] shows how spontaneous membrane oscillations and noisy synaptic transmission can be harnessed to generate a stream of highly organized states of Self-activation. This may play a role in the spontaneous generation of novel, flexible behavior. The strongly recurrent connectivity of cortical neurons in association areas collectively form a conscious workspace, an internal space buffered from outside world and within which mental hypotheses can be entertained and discarded at will.

Mathematical intuition

The neural basis of the logarithmic mental number line: In the early days of neurophysiology, a few neurons that encoded number were reported in the association cortex. Nieder & Miller [20] recorded in monkey prefrontal cortex the number neurons (Principal sulcus, Arcuate sulcus). It was recording also in parietal cortex, and also in prefrontal cortex, reported the observation of neurons whose firing rate was tuned to a specific numerosity. This was possible to examine the neural code for an abstract psychological continuum. There is often evidence that the stimulus compression occurs at a peripheral sensory level. Information is classically defined as reduction of the uncertainty, measured by the entropy function [9], which is the weighted sum of the logarithm of probability (p) of alternatives outcomes (i):

  . The neural code for number can be also described in better way by logarithmic than by a linear scale. The monkeys encode the numerosities on an approximate compressed scale confirms that this approximation is the natural way that number is encoded in a brain without language [21,22].

Neural coding of expected value (EV): Comparative theorists proposed that regions innervated by mesolimbic dopamine projections play a critical role in the computation of EV. Because fMRI studies also indicate that:

1. gain outcomes instead activate the mesial prefrontal cortex (MPFC),
2. the outcomes involve a collapse of probability,
3. increased gain probability (PRB) might increase MPFC activation, even during anticipation,
4. the ventral tegmental area midbrain dopamine neurons that project to the nucleus accumbens (NACC), and MPFC have also been implicated in the computation of EV.

The main effect of probability coding is correlated:

1. with activation foci in the bilateral MPFC,
2. the left parahipocampal gyrus,
3. the posterior cingulate.

The interaction MAG (gain magnitude) by PRB was only correlated with activation foci in the bilateral medial caudate and right putamen.

The bilateral MPFC showed activity consistent with representation of:

1. the probability,
2. the value terms of EV.

The bilateral anterior cingulate activation might relate to integration of these two terms: the value and probability terms of EV.

Investigation of the neural correlates of EV, mesolimbic regions (including the midbrain, NACC, and MPFC) showed activation correlated with a linear model of EV. Whereas NACC activity correlated only with anticipated MAG, MPFC activity also correlated with anticipated gain probability.

MPFC activation was associated with the perceived probability of obtaining large gains. These findings suggest that distinct mesolimbic regions play different roles in EV computation. The MPFC showed linear but not quadratic trends, supporting probabilistic rather than uncertainty-based interpretations. Intuition probability at microscopic level.

Probabilities of the mathematical intuition (MI) at the microscopic level are governed by interfering probability amplitudes rather than by additive probabilities. In accordance with the Bohr´s correspondence principle the quantum scalar product

, between two stationary states

and

can be visualized as the overlap between two states depicted in x − p oscillator phase space as occupied bands traversed in a clockwise direction. The total probability amplitude

, is the sum of contributions

exp

from the two zones. Here the phase

is area between the center lines of the two states. The area-of-overlap concept illustrates the interference in phase space [23].

Interfering areas of overlap in phase space as a measure of interfering transition probability amplitudes brings us to Wigner´s phase space function, which provides directly the probability

The overlap between the Wigner functions

and

when integrated over the total phase space, yields the probability

The Wigner function approach deals in terms of probabilities [24]. Interference effects must herefore originate from phase space domains where the Wigner function product

assumes also negative values. The jump probability

is the weighted overlap in phase space between the Wigner functions representing the two quantum states. The main effect of probability is negatively correlated: with activation foci in the left anterior cingulate, left insula, bilateral medial caudate, right put amen. Mathematical intuition (MI) is based on the inputs from number neurons, without Morita equivalence in circuit, mapped to the mesial prefrontal cortex (MPFC) in a process computed due the complex probability amplitudes. Intuition (I) than means mapping of number neurons to the nucleus accumbens (NACC), based on computations of added probability.

Conclusions

Despite widespread acceptance of the idea that perception involves inference, probabilistic models of inferences have only recently entered mainstream neuroscience and psychology. David Marr described the output of the system as a function of its input [15]. To make distinguishability clear, we should use linear probabilities (intuition-I), or the complex probability amplitudes (mathematical intuition-MI). The last represents not linearly related quantities that lie on a sector of a plane, but quadratically related quantities that lie on a sector of a sphere. But medial frontal cortex (MFC) functioning as global workspace (GW), and Self as a toponeuronal structure (TNS), are also a product of probabilistic coding in neurones

Dehaene [21] suggest that the exact arithmetic puts emphasis on language-specific representations based on a left inferior frontal circuit, and is also used for generating associations between words. Symbolic arithmetic is seen as a cultural invention specific to humans, and depended on the improvement of number computing systems. The other domains of mathematics, as calculus, may depend critically on the invention of an appropriate mathematical language. Simple calculations activate a distributed network involving the parietal, prefrontal and premotor cortices. The posterior parietal cortex and prefrontal cortex are functionally interconnected, information could be transferred to the prefrontal cortex, where amplified, may be able to gain control over behaviour.

We predict that at the biological (neuronal) level a complex phenomena as for instance the neuroplasticity is, will be not fully understandable due this physically defined term of information. The biological level needs a more stochastic, probabilistic definition of information. The coming definition must reflect that every new information as innovation, is changing the values of probabilities of the system, at least due microscopic changes in its correlations in a given topological space, or domain. These changes in probabilities are encoded due the global restriction mapping based on neuronal group selection. Information at the biological level must be defined through a more flexible, more “live” flow, than it is obviously done with Shannon-type definitions working at the level of physics. Also Prigogine [25] pointed that the existence of phase transitions shows we have to be careful when we adopt a reductionist attitude. This flexible, live flow can be approached by the variable topology, and Riemannian manifold.

By Gödel [26], predictions are like a perception of the objects of set theory. Prediction is a mode of MI, which in sense of perception induces building up theories of the future. The given underlying mathematics is closely related to the abstract elements contained in our empirical ideas. The brain seems to have internal theories about what the world is like. Between brain theories is internal perceptual rivalry in Darwinian sense. The world as a system can be described due the polar decomposition, as a whole system consisting from two subsystems (Self subset A, and Non-self subset non A), mutually observing one another.

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Wear of Ultra High Molecular Weight Polyethylene against Synthetic Sapphire as Bearing Coating for Total Joint Replacements_Crimson Publishers

 Wear of Ultra High Molecular Weight Polyethylene against Synthetic Sapphire as Bearing Coating for Total Joint Replacements by DML Meyer in Research & Development in Material Science_Journal of materials science and technology research

Abstract

Materials commonly found in hip replacements are a polymer paired with metals or alloys. Tribological behavior of polyethylene bearing surfaces against synthetic sapphire are compared against other bearing combinations to evaluate sapphire as a viable means to lower the incidence of revision surgery by mitigating production of wear debris. Sapphire disks against polyethylene plates were tested utilizing a tribometer. The polyethylene wear rate was found to be 22.6mm³ per year, less than the 40-80mm³ per year typically found in traditional hip replacements. A power law function is presented correlating a decreasing friction coefficient as polyethylene volume loss increases as V^0.88. These results show potential for synthetic sapphire as an alternative bearing surface in joint replacements

Keywords: Polymer; Wear; Abrasive

Introduction

Synthetic sapphires have a common use in jewel bearings such as those found in some mechanical watches and sensitive measuring instruments due to low friction and also for improving bearing life [1,2]. Sapphire has mechanical properties, specifically its hardness of 9Mohs scale, making it the third hardest known natural substance [3]. Due to its hardness, it has a high resistance to scratching and abrasion, making it applicable to other bearing surfaces. To test if synthetic sapphire is a feasible option in other bearing surfaces, wear experiment were conducted to analyze volumetric wear rates and coefficients of friction of the polymer ultra-high-molecular-weight polyethylene (UHMWPE) against synthetic sapphire.

The inspiration for this research came from the total hip replacement. The majority of total hip (and knee) replacements are performed on adults when patients are having some type of arthritis of the hip or deterioration due to trauma, and who are usually 40+ years old [4,5]. If a patient’s hip is deteriorated and other treatments have failed, a hip replacement is often an option. While a total hip replacement is generally a successful surgery, there is the potential of failure of the replacement over time.

The type of failure evaluated in this research was weargenerated UHMWPE debris which initiates the destructive process of periprosthetic osteolysis and loosening of the implant. The polymer wear debris is created in part by abrasion between the femoral head and the UHMWPE acetabular liner. The debris particles can then migrate into regions contiguous with the femoral stem and femur bone, and initiate a bodily rejection [6,7]. However, these wear particles are resistant to the cellular response, which results in prolonged duration of inflammation and leads to progressive osteolysis [8], eventually causing loosening of the implant due to bone adsorption, and the requirement of a revision surgery.

The acetabular insert of a total hip replacement wears through its thickness at an average rate of 0.1mm/year, and in the case of one of the surfaces being polymer, it is estimated that 51billion polymer particles are produced each year from its surface [9]. The hip replacement is one of the most well-known implants, and a lot of research has been performed to analyze the implant material combinations and its wear characteristics. Previous work to mitigate the production of wear debris can be found in many articles, but for the current work [10-13] were used for comparative analysis, which included data for ultra-high-molecular-weight polyethylene-on-cobalt chromium (UHMWPE-on-CoCr), metalon- metal (MoM), ceramic-on-metal (CoM), ceramic-on-ceramic (CoC), and combinations of cross-linked and highly cross-linked polyethylene-on-cobalt chromium (CXPE and HXPE-on-CoCr) as well as HXPE-on-ceramic (Al2O3). A study using a flat sapphire disk against a flat UHMWPE disk [14], obtained friction coefficients of this material combination for a total of one hour of sliding, or the equivalent of 0.77% of one year of sliding of a total hip replacement. The short time period is insufficient to be able to use or compare the friction coefficients between the mating pair with other material combinations that typically have periods of sliding on the equivalent of one year or more. The same research group produced friction coefficients over a one hour period for sapphire-sapphire mating pairs [15].

The purpose of the current investigation was to determine the effectiveness of synthetic sapphire as a potential coating on the femoral head as a means to improve the durability of a total hip replacement, and potentially lower the incidence for revision surgery by mitigating the production of UHMWPE wear debris. The experiments utilized a pin-on-flat linear tribometer to simulate the sliding conditions of a hip replacement over the course of one year of use. The pin fixture in the experiment was replaced with an in-house fabricated one to hold a sapphire disk on its edge, and UHMWPE, a commonly used acetabular cup lining material, was used as the mating bearing surface against the sapphire in the form of a plate. Bovine serum was used as the lubricant to simulate synovial fluid found in human joints.

Due to some failures using UHMWPE inserts in hip replacements, the material combinations of ceramic-on-ceramic (CoC), ceramicon- metal (CoM), and metal-on-metal (MoM) hip replacements are now also being used in practice, each with their own complications involving wear. Metal implants can lead to conditions such as metallosis after wear debris is generated [16,17]. Ceramics have been shown to have lower wear rates. However, if they fail, the failure can be catastrophic [18]. To determine the effectiveness of synthetic sapphire against UHMWPE, volumetric wear rates of the materials used in current total hip replacements are compared to the UHMWPE volumetric wear rate for sapphire-on-UHMWPE.

Material and Methods

Dimensional analysis

With the inspiration of the hip replacement, the failure mode of this research is UHMWPE volumetric wear that exceeds that of conventional total hip replacement material combinations. The failure mode from a mechanics point of view is plastic deformation of the polyethylene surface due to abrasive plowing. Dimensional analysis allows for a description of which physical parameters to change during experiments based on the dependence of variables and guarantees that all of the variables are accounted for throughout experimentation, eliminating a “trial and error,” approach, and a tool to systematically design experiments.

The experimental parameters are combined using the Buckingham Pi Theorem into dimensionless Pi groups [19]. This process resulted in the four dimensionless groups of Equation (1),

Where, is the absolute viscosity of the lubricant, bovine serum in this case; F_f is the frictional force between contacting surfaces; V is the UHMWPE volume loss during sliding; U is sliding velocity; T is time; L is sliding distance; F_n is normal load of the sapphire disk on the UHMWPE flat plate, and p is the contact pressure between the sapphire disk and UHMWPE plate. Note that the first pi group of Eq. (1), F_f/F_n=μ, is the friction coefficient between the sliding surfaces. Analysis of the experimental data using pi groups was considered and was found to reveal a correlation between and UHMWPE volume loss, as well as with time and friction force.

Tests were performed with a disk of synthetic sapphire-on- UHMWPE flat plate using bovine serum as the lubricant at room temperature. Sliding speeds were varied based on values found in the literature [10]. An average annual use of a hip joint correlates to 1million cycles, where a cycle is defined as the distance that the femoral head traverses the acetabular cup through a heelstrike, toe-off to the start of a heel-strike again. The average range for the annual distance varies between approximately 20E06mm to 50E06mm based on the radius of the femoral head. The total sliding distance of 23E06mm was used in the current work to simulate a year of hip motion [10-13]. For the first 9.99E06mm of sliding distance, the sliding velocity was 38.2mm/s, increasing to 67.2mm/s for the next 9.99E06mm of sliding distance, with a final sliding velocity of 93.4mm/s for the remainder of the test. A contact pressure of 6.5MPa is the typical average generated in hip replacements and was the average contact pressure for all of the literature comparisons. The contact area of the edge of the sapphire disk on the UHMWPE plate was measured using microscopy (Leica Model DMLB) and determined to be 0.45mm2. The lowest average contact pressure that was achievable with the linear tribometer and this contact area was 36.1MPa.

To make comparisons of the UHMWPE wear volume with wear volume values from the literature, the UHMWPE volume loss per distance traveled was normalized with the average contact pressure from the experiments. For instance, in the current work, the volume loss of UHMWPE at the first measurement was 12.9mm3 after traveling a distance of 3.33E06mm with an average contact pressure of 36.1MPa. Dividing the UHMWPE volume loss (12.9mm³) by the distance traveled (3.33E06mm) and dividing that value by the average contact pressure (36.1MPa), normalizes data for comparisons with literature values. The same process was repeated for volume loss per distance traveled using data from the literature and similarly normalized with the respective average contact pressure of 6.5MPa [10-13].

Experimental setup

A linear tribometer, as shown in Figure 1, was used for the wear and friction tests to simulate a year of hip replacement UHMWPE wear against a sapphire disk. A fixture specifically designed and fabricated to hold the sapphire disk motionless on its edge, was used with a flat plate of UHMWPE as the articulating surface. The disk had a diameter of 6.27mm and a thickness of 1.63mm, while the rectangular sheet of UHMWPE had dimensions of 102mm x 305mm x 6.35mm. Prior to experimentation the mass and surface roughness of each material component were measured and are listed in Table 1.

Figure 1: Tribometer and experimental setup.

1a: Sketch of sapphire disk and UHMWPE plate, where Fn is the normal load, r is the sapphire disk radius, and t is the sapphire disk thickness.

1b: The tribometer and its components.

1c: The sapphire disk in the tribometer fixture.

1d: The fixture and sapphire disk in the tribometer with the UHMWPE plate mounted below the lubricant tray.

Table 1: Initial material properties of sapphire and UHMWPE.

In the tribometer experiments, the sapphire disk remained stationary while the UHMWPE plate track oscillated along the “x” axis shown in Figure 1a. Force and moment data were collected. One cycle on this tribometer was set to be 457mm (229 mm in each direction). Approximately 50mL of 50% bovine serum combined with distilled water, resulting in a 25% bovine serum mixture was used as the lubricant. The absolute viscosity of bovine serum at 25% is approximately 0.9mPa•s [22] (Figure 1a-1d).

To compare the current results to those found in the literature [10-13] and other hip simulator experiments, normalizing the experimental variables was performed. In [10], one cycle was a total sliding distance of 30mm and ran at a frequency of 2Hz, yielding a velocity of 60mm/s. Hip simulators are often used in testing and results of such experiments are found in the literature. The average sliding distance for one cycle in a hip simulator running at a frequency of 1Hz is 1.045D, where D is the diameter of the femoral head [23]. In [11], a hip simulator was used with femoral head diameters of 32mm and 44mm. This yields a sliding distance for the 32mm head of 33.44mm and speed of 33.44mm/s in one cycle, and the 44mm head had a sliding distance of 45.98mm and speed of 45.98mm/s in one cycle. In [12], a hip simulator was used with a femoral head diameter of 36mm. This yields a sliding distance of 37.62mm and speed of 37.62mm/s in one cycle. In [13], a hip simulator was used with a femoral head diameter of 28mm. This yields a sliding distance of 29.26mm and speed of 29.26mm/s in one cycle. In [11-13], the frequency and contact pressure were not explicitly stated. To extrapolate the normalization variables, a frequency of 1Hz and contact pressure of 6.5MPa were used to compare data. In the current experiment, to simulate the average hip movement in about one year, a distance of 23 × 10⁶mm was traveled. The experimental parameters and those found in the literature are summarized in Table 2.

The experiment was interrupted every 3.33E06mm of distance that the sapphire disk traveled against the UHMWPE plate, to obtain the mass of the sapphire disk and UHMWPE plate (Mettler Toledo xs403s digital scale), as well as each material’s surface roughness (Mahr Federal profilometer). The UHMWPE volumetric wear, coefficients of friction and resultant forces were calculated from the experimental data.

Calculation

UHMWPE wear rate and friction

Prior to experimentation the initial mass, mi, of the UHMWPE plate was measured and recorded, and again at each 3.33E06mm traveled until the final measurement, mf, resulting in the mass loss as in Equation (2),

Δm = m_i − m _f(2)

The UHMWPE wear volume range for a traditional metal-on- UHMWPE hip replacement is between 40 and 80mm3 per year [13,24]. A volumetric wear rate that exceeds these bounds is considered a failure mode for the current experiments. To calculate UHMWPE volumetric wear, V, the change in mass of the UHMWPE, Δm, was used with its known density, ρ, as in Equation (3),

The instantaneous coefficients of friction, μ , were calculated using the ratio of the measured friction forces, F_f, to the measured normal forces, F_n [25].

Results

Table 3: Uncertainty values.

All uncertainty values from the experimental measurements were calculated using equations from [25,26], and are listed in Table 3. To evaluate an uncertainty, the law of propagation of uncertainty is utilized to determine the combined uncertainty, which is a function of the standard uncertainty of each input measurement and associated sensitivity coefficients. The standard uncertainty of each input variable was determined from the standard deviation of the force measurements, F_f and F_n, and from the tolerances given by the manufacturers of the sapphire disk and the mass scale, respectively.

The gravimetric data collected was converted into a volumetric wear of UHMWPE using the density of Table 1 with Equation (3). Note that all comparative data from the literature has been estimated by transcribing data from graphs or tables presented.

To compare the different material combinations found in total hip replacements, the normalized data as described earlier, of sapphire-on-UHMWPE from the current experiments are plotted against the normalized data of UHMWPE-on-CoCr, CXPE-on-CoCr, HXPE-on-CoCr, pre-worn HXPE-on-CoCr, HXPE-on-Al₂O₃, MoM, CoM, and CoC, as in [10-13]. This normalization takes into account the different contact pressures generated, different sliding distances, and frequencies at which the experiments were performed. By normalizing these factors, different experiments can be directly compared. The interpolated averaged data from [10-13] is within confidence intervals presented in [9-13,29-34].

Figure 2: Ratio of UHMWPE volumetric wear to distancetraveled and contact pressure versus time of sapphire-on- UHMWPE, compared with material combinations found in the literature for UHMWPE-on-CoCr, CXPE-on-CoCr, HXPE-on-CoCr, pre-worn HXPE-on-CoCr, HXPE-on-Al₂O₃, MoM, CoM, and CoC [10-13].

Figure 2 shows the ratio of the normalized UHMWPE volumetric wear to distance traveled and contact pressure versus time. Figure 3 shows the ratio of volumetric wear to frequency and contact pressure versus time. Note that the literature wear data used for comparisons with the UHMWPE wear against sapphire, of the current work, compare UHMWPE wear data from [10,11], while the wear data comparisons from [12,13] are that of metal and ceramic, specifically CoCr and zirconia toughened alumina ceramic (ZTA).

Figure 3: Ratio of UHMWPE volumetric wear to frequency and contact pressure versus time of sapphire-on-UHMWPE, compared with material combinations found in the literature for UHMWPE-on-CoCr, CXPE-on-CoCr, HXPE-on-CoCr, pre-worn HXPE-on- CoCr, HXPE-on-Al₂O₃, MoM, CoM, and CoC [10-13].

Figure 4: Friction coefficient versus time, plotted as a rolling average of the original data with the uncertainty.

Equation (4) was used to calculate the friction coefficients, which are plotted versus time, as shown in Figure 4. A rolling average was used to determine a best fit of the original data. Notice that when the velocity is set to the highest setting, the data becomes very noisy. This is due to the vibration of the stepper motor on the tribometer which affects the force transducers while collecting data.

The UHMWPE surface roughness was measured along the wear track as well as across the wear track. The surface roughness of the sapphire disk was found to remain relatively constant, yielding an average roughness of 0.32μm. The surface roughness of the UHMWPE along the wear track is of interest. This surface roughness versus time is shown in Figure 5 and compared to surface roughness data shown in [11].

Figure 5: Comparative UHMWPE surface roughness versus time of sapphire-on-UHMWPE experiments and of surface roughness data of CXPE-on-CoCr, HXPE-on-CoCr, pre-worn HXPE-on-CoCr, and HXPE-on-Al₂O₃ [11].

Figure 6: Power law correlation of friction coefficient between the sapphire disk against the UHMWPE plate with time, friction force and UHMWPE volume loss.

Using the first two pi groups of Eq. (1), namely and a power law correlation is presented in Figure 6.

Discussion

UHMWPE is one of the most common materials found in a hip replacement paired with a metal. However, wear of UHMWPE may contribute to mechanical failure of the hip replacement. Many material combinations have been studied as a means to mitigate harmful sub-micron wear debris in a hip replacement. It is seen that MoM wear is very dependent on the type of metal, surface finish, and tribological design used [33]. These features create a large variation in wear for MoM implants and also a slight variation in CoM wear [33]. UHMWPE on metal also shows a large variation in wear due to the dependence on factors such as radiation and absorption of lubricant [10]. CoC demonstrates a very low variance along with its very low volumetric wear [12,13].

Reviewing the literature, it is seen that there are many different experimental setups as well as presentations of results, which create challenges in directly comparing wear experiments. Using the normalized plots provided in the current work allows for comparisons of different experiments. Interpolated averaged data within confidence intervals for the volumetric wear of UHMWPE against sapphire in the current work shows promise as a bearing combination in joint replacements. The average volumetric wear of CoM and CoC remains the lowest and most comparable to each other. MoM bearings show slightly higher volumetric wear compared to CoM and CoC bearing combinations, and also with greater variations than with CoM and CoC bearings [12,13,34].

The overall average coefficient of friction (COF) was determined using the average COF at each time step at which the experiments were halted to take mass measurements. When these average COFs are averaged, an overall average COF is found to be 0.28. This is an order of magnitude higher than expected for material combinations using UHMWPE, which have a COF range from 0.06 to 0.08, and is on the same order of magnitude when compared to metal-onmetal material combinations which have a COF range from 0.22 to 0.27 [35]. It may be explained by the very small contact area of 0.45mm2, producing a contact pressure of 36.1MPa. This contact pressure is also an order of magnitude greater than the typical contact pressures seen in total hip replacements, and thus explains, at least in part, the high overall average COF. Future experiments will need to be performed using the more realistic 6.5MPa contact pressure and contact area, where average COF values based on these typical values can be calculated and compared.

The power law function presented in Figure 6 demonstrates that the coefficient of friction continues to decrease over time as smaller increments of UHMWPE volume is removed through sliding contact. The fitted power law line displays the relationship between the logarithmic base ten (log₁₀) of friction coefficient between sapphire and UHMWPE with log₁₀ of time, friction force and volume loss of the UHMWPE, from the experimental data. The friction coefficient decreases the same with both time and friction force, both to the power 1.32, or T^1.32 and Ff^1.32., respectively. The friction coefficient has an inverse relation with the UHMWPE volume loss V, such that decreases with increasing UHMWPE volume loss as V^0.88. For the power law equation of Figure 6, the correlation of these parameters follows a coefficient of determination R²=0.977, showing good correlation of the experimental data.

The surface roughness along the wear track of the UHMWPE against sapphire is of interest. The roughness initially decreases during the first 3.33E06mm of the first velocity, an indication that the sapphire disk abraded the UHMWPE surface. The roughness then increases for the next 6.66E06mm of the first velocity, indicating strain hardening of the polymer. After a total distance traveled of 9.99E06mm at the first velocity, the velocity was increased, and the surface roughness along the wear track of the UHMWPE drops significantly. The surface roughness begins to slowly, linearly increase for the remainder of the experiment.

Overall, sapphire against UHMWPE has been found to be a viable bearing surface for implant materials, potentially as a coating for the femoral head component of a total hip replacement. The results show a promising volumetric wear when compared with current material combinations of polyethylene-on-metal and even metal-on-metal. The wear rate of the UHMWPE in the sapphire experimentation was found to be 22.58mm3 per year, which is less than the 40-80mm3 per year that is typically found in a traditional metal-on-polyethylene hip replacement [13]. Further, these wear rate results do not account for serum absorption as discussed in [10,36]. Since the wear rate calculations are derived from gravimetric measurements, serum absorption by the UHMWPE can have a direct effect on the results. An in-vitro study of sapphire and other gem surfaces against currently-used implant materials, as well as accounting for serum absorption, would further explore this potential articulating surface combination. Further possibilities in bearing surfaces may also be determined as useful where longevity is a top priority.

Conclusion

In this study sapphire-on-UHMWPE showed a decrease in UHMWPE wear rate compared to UHMWPE-on-CoCr and the metal of MoM. However, in order to compare debris generation, debris morphology should be analyzed for size and shape differences to current wear debris found in hip replacements.

While this research focuses on sapphire as a coating material in current total joint replacements, another consideration is the use of sapphire as the femoral head material or as a coating in non-metallic joints, combinations of which can be used in CT scans and MRIs. While most metal implants are not magnetic, the metal can still cause distortions in imaging. Additionally, metal combination implants also require users to notify security officers prior to passing through any metal detectors. Utilizing gemstone as a bearing surface against non-metals can eliminate this burden from having metal implants, assuming the gemstone is not solely a coating on a metal surface.

Sapphire may be considered for further testing in tribometers and hip simulators against UHMWPE to more accurately measure the UHMWPE wear rate in-vitro, for 2 to 10million cycles. This will yield results including wear-in and steady-state periods, which can further be compared to those found in the literature. The overall average friction coefficient between sapphire and UHMWPE was found to be 0.28, an order of magnitude higher than expected. Future experiments will need to be performed using the more typical 6.5MPa contact pressures, where average COF values based on these contact pressures can be calculated. The power law function shows that decreases as the volume loss V of UHMWPE increases to the power 0.88, or V^0.88.

The wear rate of the UHMWPE in the sapphire experimentation was found to be 22.58mm³ per year, which is less than the 40- 80mm³ per year that is typically found in a traditional metal-onpolyethylene hip replacement, or approximately 44-72% less, which provides justification to further pursue sapphire as an alternative bearing surface in polymer and metal-based total hip and knee replacements.

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