Mathematical models in equine research involve the application of mathematical techniques and theories to understand and predict various aspects of horse physiology, behavior, and health. These models can simulate complex biological processes, offering insights into areas such as biomechanics, disease spread, and metabolic functions. By integrating data and equations, mathematical models help researchers explore scenarios that may be challenging to study experimentally. Common applications include modeling the dynamics of equine gait, predicting the outcomes of infections, and optimizing nutrition plans. This page compiles peer-reviewed research studies and scholarly articles that explore the development, validation, and application of mathematical models in the study of equine biology and management.
Pollock S, Hull ML, Stover SM, Galuppo LD.Knowledge of the forces that act upon the equine humerus while the horse is standing and the resulting strains experienced by the bone is useful for the prevention and treatment of fractures and for assessing the proximolateral aspect of the bone as a site for obtaining autogenous bone graft material. The first objective was to develop a mathematical model to predict the loads on the proximal half of the humerus created by the surrounding musculature and ground reaction forces while the horse is standing. The second objective was to calculate surface bone stresses and strains at three cross se...
Rüegg SR, Heinzmann D, Barbour AD, Torgerson PR.For the evaluation of the epidemiology of Theileria equi and Babesia caballi in a herd of 510 horses in SW Mongolia, several mathematical models of the transmission dynamics were constructed. Because the field data contain information on the presence of the parasite (determined by PCR) and the presence of antibodies (determined by IFAT), the models cater for maternal protection with antibodies, susceptible animals, infected animals and animals which have eliminated the parasite and also allow for age-dependent infection in susceptible animals. Maximum likelihood estimation procedures were used...
Schmitt D, Cartmill M, Griffin TM, Hanna JB, Lemelin P.At speeds between the walk and the gallop, most mammals trot. Primates almost never trot, and it has been claimed that they transition directly from a walk to a gallop without any distinctive mid-speed running gait. If true, this would be another characteristic difference between the locomotion of primates and that of most other quadrupedal mammals. Presently, however, few data exist concerning the actual presence or absence of intermediate-speed gaits (i.e. gaits that are used between a walk and a gallop) in primates. Video records of running in twelve primate species reveal that, unlike most...
Yildiz H, Yildiz B, Arslan K, Ozgür C.In this study we present a geometric model of the ascending colon of the horse, especially the left ventral colon and the right ventral colon, the left dorsal colon and the right dorsal colon and the pelvic flexure. We also present a mathematical model of the cross sections of these ascending colon parts with the exceptions of the pelvic flexure. We show that these cross-sections correspond to the closed algebraic curves known as epitrochoid.
Jones JH.Taylor and Weibel's principle of symmorphosis hypothesized optimal design of the mammalian respiratory system, with no excess structure relative to its maximal O2 flux, VO2max. Although they found symmorphosis not to be a general principle of design, it might apply to a highly adapted aerobic athlete, e.g. the Thoroughbred racehorse. Using a mathematical model based on empirical data of the equine O2 transport system at normoxic VO2max, the fraction of the total limitation to O2 flux contributed by each of the respiratory transport steps is calculated as either the fractional change (F) in VO2...
Lord CC, Woolhouse ME, Mellor PS.Factors affecting epidemics of African horse sickness in Spain were studied using a mathematical model. The model examined the likelihood of an epidemic after the introduction of the virus, and the effectiveness of vaccination strategies. Two host species (horses and donkeys) and one vector species (the biting midge Culicoides imicola) were included. A stratified random sampling method (Latin hypercube sampling) was used for sensitivity analysis of the likelihood of an epidemic. Systematic variation of vaccination parameters was used to consider alternative control strategies. In general, when...
Ferrante PL, Freeman DE, Ramberg CF, Kronfeld DS.Multicompartmental analysis was applied to study the kinetics of D-xylose distribution after its intragastric administration to healthy mares deprived of food for 12, 36, 72, and 96 hours. Disposition of D-xylose was described by a 5-compartment model. Maximal plasma D-xylose concentration was similar for 12 and 36 hours of food deprivation and was greater (P = 0.0001) than the values for 72 and 96 hours. Peak concentration of D-xylose appeared progressively later as food deprivation proceeded (P = 0.0001). Fractional rate of transfer (k1,6) was less after 96 hours of food deprivation, compare...
Johnson AT, Soma LR, Ferouz C.Exercise-induced pulmonary hemorrhage (EIPH) affects a large portion of racing thoroughbred horses. Sites of hemorrhage and causal mechanisms remain unestablished. Our mathematical model was constructed to test the hypothesis that EIPH could be caused by a combination of respiratory and circulatory mechanical factors occurring during exercise. Various physiological data for respiration, blood circulation and exercise were incorporated into the model. Results show that inhalation pressure drops across airway resistances become great enough during exercise to cause rupture of capillaries for bot...
van den Bogert AJ, Schamhardt HC, Crowe A.Locomotion of the horse is simulated using a mathematical model based on rigid body dynamics. A general method to generate the equations of motion for a two-dimensional rigid body model with an arbitrary number of hinge joints is presented and a numerical solution method, restricted to tree-structured models, is described. Joint movements originating from muscular forces or moments are simulated, but the method also allows that parts of the model follow strictly the pattern of kinematic data. Moment-generators with first-order linear feedback were used as a rotational muscle-equivalent. Ground...
Stamer M, Sumpf D.The live weight development of young warm-blooded stallions at the age of 0 to 30 months of life was investigated in order to derive their energy and protein requirement. The aim of the studies was the derivation of a standard curve for the course of growth. Choice of the best suited model and the corresponding calculations were one of the main investigation objects. The mathematical function developed by Janoschek provided a relatively good description of the material.
Andersson L, Arnason T, Sandberg K.Investigations on relationships between biochemical polymorphism and variation in quantitative traits are of interest from the perspectives of both theoretical quantitative genetics and practical animal breeding. This subject was studied by using racing performance records of more than 25,000 horses of the Swedish Trotter breed born in the period 1970-1979. For all horses data on six blood group and nine electrophoretic loci were available. Two different performance traits were investigated. A racing performance index value was calculated for all individuals which had started in at least five ...
van Gurp M, Schamhardt HC, Hartman W, Crowe A.A dynamic model is developed to describe the swing phase of the hindlimb of a normally walking horse. The limb was represented by four rigid segments constrained to move in a sagittal plane only. The mathematical equations of motion of this four-element pendulum were formulated using Lagrange's theorem. The morphometric parameters from the hindlimb segments of 3 horses were determined using high-speed film analysis. Five muscle groups were incorporated in the model. Muscle activity was derived from earlier EMG measurements. Optimization of muscle moments resulted in a simulated swing movement ...
Staddon GE, Weaver BM, Lunn CE.Standard data for the horse which can be used in physiologically based mathematical computer modelling are presented. The data includes figures for tissue mass, density and perfusion, obtained by measurement mainly from horses weighing 200 to 300 kg. Other related parameters such as mean transit times and tissue blood volume have been calculated and included in the actual values listed for a 250 kg horse.
Kovár J.The possibility of using the test for pulse-rate response to gradated load in the evaluation of the endurance component of horse performance (in other words, response to the degree of horse adaptation to load) is discussed in detail. A mathematic-statistical analysis of regression coefficients is performed in the equations of the dependence of pulse rate on speed obtained in 278 three years old horses in the period following the termination of the basic training (145 Bohemian Warm-Blooded horses, 115 Kladrub Black horses and 18 English Half-Breds). A ten-score scale is calculated on the basis ...
Losch K, Heinze W, Mieth K, Lender S.Pharmacokinetic data of sulphamerazine were recorded from eight heads each of calf, adult cattle, horse, and sheep, following intravenous application of Mebacid 200, and mathematical implications were discussed. Exponential excretion was recorded from all species, according to the following equation: c = B x e-k2 x t The most favourable pharmacokinetic parameters were recorded from calf.
Guan F, You Y, Fay S, Adreance MA, McGoldrick LK, Robinson MA.Doping control is essential for sports, and untargeted detection of doping agents (UDDA) is the holy grail for anti-doping strategies. The present study examined major factors impacting UDDA with metabolomic data processing, including the use of blank samples, signal-to-noise ratio thresholds, and the minimum chromatographic peak intensity. Contrary to data processing in metabolomics studies, both blank sample use (either blank solvent or plasma) and marking of background compounds were found to be unnecessary for UDDA in biological samples, the first such report to the authors' knowledge. The...
Içli S, Soleimani M, Oldenhof H, Sieme H, Wriggers P, Wolkers WF.Cryopreservation can be used to store equine oocytes for extended periods so that they can be used in artificial reproduction technologies at a desired time point. It requires use of cryoprotective agents (CPAs) to protect the oocytes against freezing injury. The intracellular introduction of CPAs, however, may cause irreversible osmotic damage. The response of cells exposed to CPA solutions is governed by the permeability of the cellular membrane towards water and the CPAs. In this study, a mathematical mass transport model describing the permeation of water and CPAs across an oocyte membrane...
van Gurp M, Schamhardt HC, Hartman W, Crowe A.A dynamic model is developed to describe the swing phase of the hindlimb of a normally walking horse. The limb was represented by four rigid segments constrained to move in a sagittal plane only. The mathematical equations of motion of this four-element pendulum were formulated using Lagrange's theorem. The morphometric parameters from the hindlimb segments of 3 horses were determined using high-speed film analysis. Five muscle groups were incorporated in the model. Muscle activity was derived from earlier EMG measurements. Optimization of muscle moments resulted in a simulated swing movement ...
Yildiz H, Yildiz B, Arslan K, Ozgür C.In this study we present a geometric model of the ascending colon of the horse, especially the left ventral colon and the right ventral colon, the left dorsal colon and the right dorsal colon and the pelvic flexure. We also present a mathematical model of the cross sections of these ascending colon parts with the exceptions of the pelvic flexure. We show that these cross-sections correspond to the closed algebraic curves known as epitrochoid.
Andersson L, Arnason T, Sandberg K.Investigations on relationships between biochemical polymorphism and variation in quantitative traits are of interest from the perspectives of both theoretical quantitative genetics and practical animal breeding. This subject was studied by using racing performance records of more than 25,000 horses of the Swedish Trotter breed born in the period 1970-1979. For all horses data on six blood group and nine electrophoretic loci were available. Two different performance traits were investigated. A racing performance index value was calculated for all individuals which had started in at least five ...
Losch K, Heinze W, Mieth K, Lender S.Pharmacokinetic data of sulphamerazine were recorded from eight heads each of calf, adult cattle, horse, and sheep, following intravenous application of Mebacid 200, and mathematical implications were discussed. Exponential excretion was recorded from all species, according to the following equation: c = B x e-k2 x t The most favourable pharmacokinetic parameters were recorded from calf.
Stamer M, Sumpf D.The live weight development of young warm-blooded stallions at the age of 0 to 30 months of life was investigated in order to derive their energy and protein requirement. The aim of the studies was the derivation of a standard curve for the course of growth. Choice of the best suited model and the corresponding calculations were one of the main investigation objects. The mathematical function developed by Janoschek provided a relatively good description of the material.
Pruß D, Yang H, Luo X, Liu D, Hegermann J, Wolkers WF, Sieme H, Oldenhof H.Stallion sperm is typically cryopreserved using low cooling rates and low concentrations of cryoprotective agents (CPAs). The inevitable water-to-ice phase transition during cryopreservation is damaging and can be prevented using vitrification. Vitrification requires high cooling rates and high CPA concentrations. In this study, the feasibility of stallion sperm vitrification was investigated. A dual-syringe pump system was used to mix sperm equilibrated in a solution with a low concentration of CPAs, with a solution containing a high CPA concentration, and to generate droplets of a defined si...
Johnson AT, Soma LR, Ferouz C.Exercise-induced pulmonary hemorrhage (EIPH) affects a large portion of racing thoroughbred horses. Sites of hemorrhage and causal mechanisms remain unestablished. Our mathematical model was constructed to test the hypothesis that EIPH could be caused by a combination of respiratory and circulatory mechanical factors occurring during exercise. Various physiological data for respiration, blood circulation and exercise were incorporated into the model. Results show that inhalation pressure drops across airway resistances become great enough during exercise to cause rupture of capillaries for bot...
Kovár J.The possibility of using the test for pulse-rate response to gradated load in the evaluation of the endurance component of horse performance (in other words, response to the degree of horse adaptation to load) is discussed in detail. A mathematic-statistical analysis of regression coefficients is performed in the equations of the dependence of pulse rate on speed obtained in 278 three years old horses in the period following the termination of the basic training (145 Bohemian Warm-Blooded horses, 115 Kladrub Black horses and 18 English Half-Breds). A ten-score scale is calculated on the basis ...
Schmitt D, Cartmill M, Griffin TM, Hanna JB, Lemelin P.At speeds between the walk and the gallop, most mammals trot. Primates almost never trot, and it has been claimed that they transition directly from a walk to a gallop without any distinctive mid-speed running gait. If true, this would be another characteristic difference between the locomotion of primates and that of most other quadrupedal mammals. Presently, however, few data exist concerning the actual presence or absence of intermediate-speed gaits (i.e. gaits that are used between a walk and a gallop) in primates. Video records of running in twelve primate species reveal that, unlike most...
Lord CC, Woolhouse ME, Mellor PS.Factors affecting epidemics of African horse sickness in Spain were studied using a mathematical model. The model examined the likelihood of an epidemic after the introduction of the virus, and the effectiveness of vaccination strategies. Two host species (horses and donkeys) and one vector species (the biting midge Culicoides imicola) were included. A stratified random sampling method (Latin hypercube sampling) was used for sensitivity analysis of the likelihood of an epidemic. Systematic variation of vaccination parameters was used to consider alternative control strategies. In general, when...
Ferrante PL, Freeman DE, Ramberg CF, Kronfeld DS.Multicompartmental analysis was applied to study the kinetics of D-xylose distribution after its intragastric administration to healthy mares deprived of food for 12, 36, 72, and 96 hours. Disposition of D-xylose was described by a 5-compartment model. Maximal plasma D-xylose concentration was similar for 12 and 36 hours of food deprivation and was greater (P = 0.0001) than the values for 72 and 96 hours. Peak concentration of D-xylose appeared progressively later as food deprivation proceeded (P = 0.0001). Fractional rate of transfer (k1,6) was less after 96 hours of food deprivation, compare...
Cordero VV, Cavinder CA, Tedeschi LO, Sigler DH, Vogelsang MM, Arnold CE.Mathematical nutrition models have been developed for beef and dairy cattle to estimate dietary energy intake needed to change BCS. Similar technology has not been used to improve nutrition and feeding strategies for horses. An accurate equine nutrition model may enhance feeding management and reduce the costs of unnecessary overfeeding and promote an optimal level of fatness to achieve reproductive efficiency. The objectives of this study were to develop and evaluate a mathematical nutrition model capable of accurately predicting dietary energy changes to alter BW, rump fat (RF) thickness, an...
Minetti AE, Cisotti C, Mian OS.Although the 3D trajectory of the body centre of mass during ambulation constitutes the 'locomotor signature' at different gaits and speeds for humans and other legged species, no quantitative method for its description has been proposed in the literature so far. By combining the mathematical discoveries of Jean Baptiste Joseph Fourier (1768-1830, analysis of periodic events) and of Jules Antoine Lissajous (1822-1880, parametric equation for closed loops) we designed a method simultaneously capturing the spatial and dynamical features of that 3D trajectory. The motion analysis of walking and r...
Marti E, Wang X, Jambari NN, Rhyner C, Olzhausen J, Pérez-Barea JJ, Figueredo GP, Alcocer MJ.Insect bite hypersensitivity (IBH) is a seasonal recurrent skin allergy of horses caused by IgE-mediated reactions to allergens present in the saliva of biting insects of the genus Culicoides, and possibly also Simulium and Stomoxys species. In this work we show that protein microarrays containing complex extracts and pure proteins, including recombinant Culicoides allergens, can be used as a powerful technique for the diagnosis of IBH. Besides the obvious advantages such as general profiling and use of few microliters of samples, this microarray technique permits automation and allows the gen...
